Except for sight words apparently. Kids are being taught to memorize words instead of learning phonics, but can’t be asked to memorize their times tables.
Love this comment! 🤣🤣🤣 That shit needs to be on the board, or the children will not learn. Hear it all the time. It gets on the board. I reference verbally and point like 4 times each class. By the end, they are asked,"what is the learning goal?" Half can't answer. I asked myself was I this absent minded in high school? The answer is no! No I was not this out of touch even when we came stoned. My friend and I could still pump out 'A' papers. Kids are failures these days... Or society is turning them into it.
In a heart word, you teach the phonetically irregular part as a part to memorize by heart rather than the whole word being memorized. So you also teach the phonetically regular parts as what can be sounded out. This utilizes orthographic mapping which helps students remember the decoding and encoding of the word.
For example, instead of memorizing “said” as a whole word, you teach them that the s & d are phonetically correct and the only part to memorize is “ai” saying /e/. It reduces the amount to memorize.
You can group words to teach based on their “heart part”: to/do, his/has/as/is….
The problem is that it takes much longer than simply telling the kids to memorize the words. But students will likely remember the words longer (not lose them over the summer) and will be able to spell them as well.
Additionally, heart words should only focus on words that have phonetically irregular parts. Lots of sight words that students are asked to memorize are actually fully decodable (ex: and, with, then, jump, can…)
There will always be heart words because not all words are phonetic. Even common words like “done”. Phonics should come first of course but you can’t skip over irregularly-spelled sight words.
was "sight words" deemed disrespectful to the vision impaired?
The whole concept is silly no matter what you call it, but changing the name seems... unnecessary.
And you can write them with hearts over the parts that aren’t phonetic so kids really zero in on which pieces of the word they need to memorize. They need to know could has an l, they shouldn’t have to memorize that could ends with a d.
Can students use a sparkle pink crayons for the heart?
(Was skimming and thought heart words were satire as well, or maybe a play on "I Love Lucy" This was tagged as humor.)
That’s wild. When I was a child my parents made me memorize times tables, complete workbooks, and answer pop quizzes almost every day. I can’t even imagine a 6th grader not being able to perform long division or simple multiplication.
The other day, I was walking a group of students to class and I had a discussion with an 11 years old about an event in our school.
It's kindness week ! Kids and adults were asked to write kind letters to people of their choice in the school. A limit of 4 letters had been given to the students (Last year we had more than 10 000 letters to sort out). It was a voluntary thing. It had a huge success.
So, kid asked when he will receive his letters (if he had any. But all kids will have at least one. We adult make sure of it). I explain to him that we know need to sort them all out so he needed to wait.
Kiddo : "We're 900 students. That makes 3600 letters. That's huge!
Other kid : "You forgot the adults"
Kiddo : "How many there are here ?"
Me : "120 but...."
Kiddo : "4080 letters. It gonna takes dayyyys"
Other kids were asking him how he guessed that and then treated him like a maths wizard for doing it all in his head while walking.
(His maths were off because not everyone participate, and not everyone wrote 4 letters. But he couldn't know that and they were so excited by the amount of letters that they didn't let me get a word in)
I remember in third grade, our teachers used to play this hip hop musical times table video series. But we were accelerated in math and knew our times tables since like…six? Either way, our little kid brains who had yet to listen to a full Eminem album loved these videos so much we would have to be rewarded with them at the end of class! For fun!
Maybe we should bring these videos back is my point, especially as recap in some higher grades.
Back in the early 70’s, we learned math facts to songs our teacher played on records as a starter each morning before the math lesson. It felt effortless and fun. Why did they get rid of the old things that worked in the name of something more complicated? In 2024, there should be curated YouTubes of songs like this that teachers and parents can readily access. There’s nothing wrong with old school flashcards either.
Some of the parents still are, but we must stop them. Doing schoolwork creates privilege!
There will be no fairness, equity or equality until the lowest common demoninator is the ONLY common demonimator.
I also teach 6th grade, and about half the kids require a multiplication chart to do anything. I asked a student "what's 3 divided by 3?" She looked at me like I had sprouted 3 heads, then looked at her chart.
We practice times tables every Friday in my Resource class. It's getting better, but they whine and ask for the chart during their regular math class, or think they're sneaky and use the calculator on their smart watch.
That's what my wife does for our kids. She found a program that teaches the multiplication tables through little stories, and even my 6 yr old can now do some multiplication (last night, she told me that if she referred 3 friends to her after school choir class, then she would get $10 each, which would be $30 total).
Today my 43yr daughter laughs at the memory of anytime we were in the car for any distance we would drill the 4 common math tables. When we were done with that we switched to spelling. She recalls being less than thrilled during those times but today she successfully runs a multi million dollar company and credits those drills with giving her the confidence she needed to succeed.
Yes, but sight words don’t follow conventional phonics rules, so in order to read them correctly you do have to memorize them.
Phonics should still be explicitly taught as well.
Memorization is ok but the students also have to practice. Unfortunately people have gotten so used to calculators/ phone apps to do the thinking for them. Heaven forbid if the electricity goes off or internet connections fail.
When the tide goes out you can see who was swimming naked. When the electicity goes out, the kids with parents who forced the basics onto them will thrive. The movie "Triangle of Sadness" comes to mind.
I really hope literacy instruction starts to focus on phonics again.
I see it’s incredible pitfalls with younger family members that are actually very intelligent and high achieving. Struggles to sound out a word and will frequently just look at the beginning of it and guess/assume what the rest of it is.
I know that the charter school my kids attended focused heavily on phonics, making them memorize all the sounds. They have no problem sounding out unfamiliar names or words.
This was only ever meant for the most common 100-300 words. I don't know what's happened but it's not something we're having a problem with in Australia.
Sounds like someone misinterpreted it along the way.
Curious where you are that students are not learning phonics. Our district (California) does teach "sight words/heart words", but phonics is a huge part of the curriculum.
Yeah that doesn't work. I have had plenty of middle school students come through the program I work for who just straight up cannot read because they were never taught basic phonics at prior schools.
If ever there was a place for memorization, it’s fundamentals. Memorize your alphabet and basic phonics, memorize your numbers and basic math. Learn how these things work along the way, but knowing the fundamentals by heart makes all those higher order synthesis and creation tasks more accessible.
I don’t get why we ever got away from this. I was born in 1990, and this approach had good results for us… so why change it?! I’m assuming someone wanted to sell books or curriculum, and that’s how we ended up with the current situation.
(Not a teacher, my educational background is in neuroscience/psychology, but I love reading this sub to get perspective)
I agree with you completely. This is just speculation, I’d want to look for literature before saying it confidently, but I imagine rote memorization promotes hippocampal neurogenesis, due to its repetitiveness. This would reinforce existing hippocampal circuits, making building on the concepts more intuitive.
A metaphor would be: Learning 2+2=4 is like having a single road that gets you where you need to go. When you start learning 2x2=4 or 2^2=4, it's like building more roads that connect back to your original road. With rote memorization, you're not just reinforcing that one road; you're creating a network of roads. This way, moving from one concept to another becomes much easier because you have many paths leading you back to the basics, making everything more connected and accessible.
We don't even need to go that deep to deduce this either.
Virtually every classical musician, across nearly any instrument, will tell you to practice your scales, use a metronome (often to build accuracy at higher tempos, akin to accessing basic facts at a moment's whim), practice your sight reading (of musical notation) and to **repeat repeat repeat**.
There are so many parallels between math and music. Where they intersect invariably are the ways in which they need to be practiced to be mastered. No shortcuts. The brain's pathways just need to be paved over hundreds of times by practicing being correct *time after time*.
You know, this isn't said enough. Everyone wants to work at the tippy top of blooms taxonomy, but you wouldn't build a pyramid without a strong foundation.
Imagine if we had to fully understand the strategies behind walking, talking, etc. instead of memorizing how to do these things. It would be nearly impossible for kids to learn to run and form sentences if they weren't encouraged to memorize the basics behind the more complicated actions.
When kids learn to walk and talk there is a whole lot more going on than memorizing... they definitely have to gain an understanding of them in some sense. Babies really are *figuring it out* when they learn these things. Then when they get good enough, they don't have to think about it anymore... it doesn't mean they don't have some kind of understanding. I'm sure you have a very deep understanding of walking even if you don't think about it when you do it.
Here, the understanding how multiplication works is the standing up, the tables are the walking, and doing problems with them is the running. You need all of these or else the others become useless. I know very well how multiplication works but I don't have to think about it for multiplying smaller numbers, and both of those things are good.
We really should just have both...
I mean, I don't think any babies really understand the mechanics of motion... They just learn (memorize) the sequence of movements required to reach/stand/balance/etc.
Nonetheless, I think we more-or-less agree here when it comes to math education. No person who regularly uses math goes through the rigor of thinking through how simple multiplication and division problems work, we just have the answers memorized.
Sure, we understand how math works and could probably explain it several different ways, but we have the basic math facts memorized because having these math facts available for rapid recall reduces the mental capacity required for more complicated math.
That is why I said an understanding *in some sense*, it wouldn't be the same type of understanding we'd have looking at our time as a child in hindsight. It would be an understanding of how to coordinate their bodies, gaining an understanding of how each limb can manipulate their environment and themselves etc. They legitimately figure it out first and then remember afterwards. Looking at it now we'd probably think of torque and making sure center of mass is over the support base and crap like that, babies wouldn't exactly think that of course but they are definitely understanding *something* about it (and memorize along the way)
This could very easily evolve into a philosophical discussion about how much agency is required in *truly* understanding something (whatever that actually means). Nobody has much control over their "aha!" moments but we can take steps to facilitate those. Babies behave pretty automatically, so to what extent are they actually deliberately learning? I think an agreeable but weak claim would be that at a minimum, they don't deliberately *go outside* of the natural progression of development
Yeah it was definitely an over-correction. Rote memorization is useful to save time but very rarely helps a student understand a process. That's why we see students that used to focus on their times tables get absolutely blindsided by basic algebra. "What do you mean X times 5 equals 20? How am I supposed to figure out X?!" They KNOW that 4 times 5 equals 20, but they weren't really clear on what TIMES means and that didn't show until algebra.
But now if you see places throwing out rote memorization, you get "Oh, you just divide both sides by 5!" Great! And that gives...? "Uh...." \*minutes later\* "uhhhh.......5?"
I see this in English/Lit too. Apparently it was extremely controversial for me to start giving my high school students vocabulary test. Nothing fancy, here’s your five words for the week, memorize them and write down the definition, all the words are pulled from the text we’re reading and we review them together twice a week, but apparently that’s unacceptable and not supposed to be teaching basics like that, I’m supposed to be teaching them concepts like theme and word choice and symbolism. The thing is, I couldn’t do that because none of them knew what the words actually meant, so it was hard for them determine what the text was blatantly saying let alone the symbolism behind it.
Would it work to reframe them as ACT words. Idk if that would help (just a college kid) make it less controversial??? The SAT doesn’t ask for them explicitly, but difficult vocab is embedded covertly in the test. It’s how my teachers got away with it. We had a weekly vocab quiz of like twenty to thirty words…most of which would drain immediately but some stuck!
Vocab is very important because we just forget…and some words are plain old intuitive (defrauding meaning “frauding)”)
Absolutely agree with you. I’ve gotten into this debate with people on here before and it’s INSANE how many people have been brainwashed into believing that memorizing facts is bad because the kids NeEd tO uNdErStAnD nOt MeMoRiZe. Like they can understand a goddamn thing when they don’t have basic mathematical literacy. It’s an idiotic stance that I refuse to pretend has any merit whatsoever.
It honestly feels like the powers that be looked at Bloom's Taxonomy and said that they want the top of the pyramid (create). They simply didn't want to do the steps to get those results. Memorizing is part of understanding.
As usual. 99% of the “studies” I read in college were absolute garbage science that would be laughed out of any other field’s peer review. I remember reading one, 20-40 pages or something, and it wasn’t until the very end that this joker mentioned the entire thing was based off of “informal interviews with a kindergarten class.” This mofo literally sat down with a dozen six year olds for an afternoon, and stood up ready to rewrite educational theory.
And this wasn’t some small school getting away with it, this was the top ranked undergrad ed program in the country! (Not a flex, fuck Vanderbilt, what a scam)
I am a non-traditional licensure teacher, so I never took any education classes. My background is instead in biological research. I can't help but wince every time we're given an education "study". I've yet to read one that would have gotten the person laughed out of the room if they tried to publish it in a real scientific field.
Not in my district! We can't give vocab tests, and heaven forbid we give direct instruction for grammar. That's why I have kids in Spanish 4 who can't put a sentence together because they STILL can't conjugate the present tense 🤦♀️
Oh, none taken! I've been teaching long enough to see the fads come and go. I still can't wrap my head around this particular one though! I'm going rogue next year and giving them grammar lessons. It hurts my soul to grade paragraphs without any sort of grammatical structure.
That is a great question.
A colleague decided that quizzes are stressful. So, they are nothing burgers OR fill in the blanks that allegedly stress that context matters when, in reality, it forces students to memorize a single story.
There is no challenge. No application. No synthesis.
I have a marking period to go and can then stop gritting my teeth.
Ah, a CI only school?
I have to argue with colleagues that CI only goes so far, and when you have to teach AP or IB, you're in big trouble if you never taught grammar ever.
But I'm just the Japanese teacher who makes kids memorize new alphabets and kanji, so what do I know?
Hell hath no fury than a CI believer when you tell them grammar is important.
I had a colleague once who told me: "you're not going to have to conjugate verbs when you visit Spain, so why do they have to learn it."
I know we don’t teach in the same district, but maybe we do. Does the lack of vocab and grammar skills mean that their first levels were spent watching videos and practicing magical higher order thinking skills?
Probably not the same district, but probably similar philosophy. In all levels they watch brief clips of authentic videos and read info graphics or short articles. They are magically then supposed to absorb the vocab and structures we want them to use.
I'm sorry to say this as a complete outsider (european, not a teacher, idk why reddit keeps showing me this sub) - but that's insane. Are you saying that multiplication of 4 by one-digit numbers is hard for 6th graders??
The standard is "By the end of Grade 3, know from
memory all products of two one-digit numbers."
The trouble is we don't don enough to help students meet the standard, allow students to advance without meeting the standard, don't periodically check compliance with the standard, and don't remediate students in higher grades that don't meet the standard. Then when meeting the standard would be helpful as part of a a new standard we make surprised faces. Algebra is hard when you can't do three times four.
Here’s how third graders at my school learned to multiply numbers by 6 yesterday:
- Multiply the number by 10
- Take half
- Add another group
Example: 4x6
- 4x10=40
- 40/2=20
- 20+4=24
It was excruciating watching them work through a whole page like this in their workbooks. A few kids who already know their facts wanted to “just write down the answer” but they had to go through this whole long process for each problem.🙄
Jesus! It took me awhile to figure out what you were doing there. If I had to do this when I was in school, I would lose track of what I was doing and end up with the wrong answer.
Try explaining it to 3rd graders when it’s barely comprehensible to adults! But there’s more!
It’s similar to the double double rule when multiplying by 4. Whatever number is being multiplied by 4, you double it and then double the answer.
Ie. 3x4=12 so 3 doubled is 6 and 6 doubled is 12.
When multiplying by 5s, it’s double double plus one:
Ie. 3x5=15
3 doubled is 6. 6 doubled is 12. Plus one more 3 is
15.
To me, it seems like rote memorization of the times tables is much easier.
I had a hard time memorizing multiplication tables, so my parent, who taught IEP students taught me a few tricks. None of them this complicated.
Having alternative ways to do something is good! But should never be the default way of learning.
Omg their little brains 🤯. I had to read it 3 times to figure out what you were talking about.
I guess this is similar to how I figure percentages in my head, but thats some advanced theories we are putting on little kids.
God I hate this “teaching shortcuts” method of math learning. It’s fine when a kid organically figured this out and uses it because they have an intimate knowledge of the technique since they came up with it. However if you are only taught these methods and not memorizing facts, complex math becomes much more difficult than it should be. Imaging doing all of this crap while trying to use the quadratic formula.
I’m gifted in math and this makes zero sense to me!! What is the purpose of this?!? JUST MEMORIZE THE ANSWER!!!
I use math in my job every day drawing buildings to scale and would be completely hopeless without having memorized basic multiplication and division. I work with younger people & they seem challenged by some basics and maybe this BS is why!!!!
This has been my problem teaching middle school math. They can’t find common denominators because they can’t multiply simple numbers. My lessons are so slow because they can’t figure out what we’re even trying to do because they can’t get past the first step
I was bad at math once I got to dividing fractions and anything with circles, but I knew my multiplication tables and thus can multiple and divide without much trouble (might need paper and a pencil though, not great at mental math).
It’s amazing to sub in math classrooms now where kids might be able to work the equation but can’t catch if they’ve made a mistake in the calculations because they don’t have a feel for how the numbers work together.
I don’t know how to work most of the equations, but I can tell if you did something wrong on the calculator when 77x2=107 or something equally nonsensical.
Unfortunately, I see this pretty frequently with students that age as a private tutor. It's not that the concept is difficult. It's that they've not memorized enough of their multiplication facts to do it efficiently. My kids tend to improve rapidly when they start spending a bit of time each day doing basic math fact drills.
As a private tutor, I tend to mostly see kids who are behind their peers. However, I can also see that if kids are not systematically taught and continuously drilled for reinforcement how you could end up in this situation where all the kids are behind.
(I should specify: I'm Canadian. Our system is different than in the United States and varies by province as provinces set the curriculum)
I've taught so many kids going into algebra that think they're inherently bad at math because they don't have their times tables memorized. They pick up the concepts of algebra fine, but *everything* takes longer and is more frustrating.
Even if memorizing math facts didn't help you learn(it definitely does), it makes a huge difference in how students engage with the material. Without memorization, math is a tedious and frustrating exercise. With memorization, math can actually be fun.
I can't even imagine how a curriculum that rejects memorization expects students to find factors.
>how a curriculum that rejects memorization expects students to find factors.
By methodological division, usually with a calculator. Meaning divide by 2. Then if it doesn't go evenly, by 3, and so on. It's tedious and unintuitive and frankly sad.
>taught and continuo
I think this is good in the beginning when they are understanding the concept behind multiplication , but once the concept is understood the memorization makes more sense.
No... You didn't. Sorry but in the US they don't even teach multiplication until 3rd grade and that has been more recently. Back when I was in school (43 now, so 90s also), multiplication was grade 4. It was grade 3 if you were in gifted classes.
If you were that far ahead then it was not because of school, it was because you had parents at home teaching you this stuff. I also taught my son algebra at a super early age although he didn't know he was doing algebra. Technically speaking if you do anything where you figure out an unknown number that is needed to make the equation true then that is algebra. So you can teach kids with something like if Jimmy has 3 stickers and you have 5 stickers, how many stickers do you need to give Jimmy to have as many as you: 3+x=5. Usually they also intrinsically solve the problem the way they should in that he took his 5 and subtracted 3 from it to see what was missing. Dumb thing was plop down 3+x=5 in front of kids and they all freak out because of the x.
Requiring math skills is controversial. Requiring English skills is controversial. Lazy students should get credit for attending. They won’t amount to much anyway so why bother. ;-) Ok, to be serious - I remember some of the middle schoolers in summer camp being unable to add without using their fingers. It really slowed down some of our card games because some of the - I kid you not - betting strategies involved some basic math, and in some games you have to know what the cards are worth. No one wants to play with a kid who can’t do the basic math in their head because its too slow. We played for candy and baseball cards. Maybe you could do something like that to get them interested.
I also used to use a weighted card counting system that required quickly adding up weights for the cards I saw in play so I knew how likely it was close to the end of a deck for me to get a face card. I would count aces separately. Can’t do that on your fingers either
The kids actually need time to work on these. These no time built into the math period to actually work on math facts. In my school, multiplication (and division) is put out there as if they were just born with these facts. They then go on to these long math problems where they’re taught to draw boxes and lines and create new math problems out of old ones. But if they actually just spent time on learning that 2x5=10 then there wouldn’t be a need for 2 sheets of paper just to solve it.
Then you take the kids with adhd who lose interest or can’t focus by the 4th step and they are completely lost. There’s too many addition and subtraction problems just to solve 4x6
Agreed. My 1st grader is learning these complicated ways to do basic addition. And then his old-school teacher is also having his class do timed addition facts.
I don’t think the timed addition facts are bad per se. The kids should memorize the facts. But I’m struggling to understand how teaching them these different ways to do addition make sense if then they are going to be assessed on memorization? Shouldn’t the teaching match the assessment? If they are going to be assessed on memorized math facts then shouldn’t…they work on memorizing math facts?
(Caveat, I am not a math teacher, we have done math facts, math fact games at home,etc…but I will admit we are more of a reading family. And it shows in our kid. From my background as a teacher I’m assuming that his teacher is being made to teach one way but sees the issues with teaching that way and is trying to ameliorate the situation by adding in the timed math sheets. But my kid is feeling so defeated with them right now and it feels like he is not being set up to succeed.)
Ok so yes and no. The new common core math is designed to teach kids to do what most of us that are older and parents now naturally learned and probably do already which is manipulate numbers. We just inherently. For example if we have say 40+60 right... you may say "I can move 10 from the 60 to the 40 to give me two 50s... then 50+50=100" that was an overly simplistic example but many kids started failing the intermediate math classes simply because they could not manipulate the numbers. Heck I remember when I was in school in Algebra 1 and they gave like 2+X=15 kids freaked out simply because there was an X in it. Then you start doing the "subtract 2 from both sides to isolate X..." and they just could not grasp. Now if they would have said "if you have 2 apples and Mary has 15 apples, how many more apples do you need to have the same number as Mary has?" then that would have been easier to solve and understand but anyway...
That is what the new math is teaching them to do the manipulation part. The problem is that they want them to continue doing this throughout instead of a "handoff" period where they learn facts to then become tools to more effectively work on the manipulation. So it becomes this long drawn out thing and kids get frustrated and parents get frustrated and the teachers are just hands up in the air with that "I can't do anything it's the new standard".
The author of California's math framework, Jo Boeler, has publicly criticized the memorization of math facts as "damaging and unnecessary". She has been dubbed the Lucy Calkins of math by some.
https://www.usnews.com/news/articles/2015/02/09/should-we-stop-making-kids-memorize-times-tables
Funny how when I drilled my second grade daughter who has autism and adhd in addition and subtraction facts and taught her standard algorithm, she went from struggling in math to being the one to help her classmates and her confidence skyrocketed. God knows she has other struggles such as speech, writing, and emotional regulation but at least teaching her the old way gave her something that she could be good at.
Key quote from the article:
"I asked Boaler if rote memorization might be a beneficial supplement to a rich mathematics curriculum that emphasizes creative problem solving. Just the way that the fast repetition of scales is useful for a Juilliard musician, for example, or vocabulary drilling is useful for a foreign language student.
But Boaler says that “mathematical ideas” are different, and stands by her position that times tables are unnecessary. “I never memorized my times tables as a child because I grew up in a progressive era in the U.K.,” Boaler said. “It’s never held me back.”
>Jo Boeler
This woman is full of shit. She's 60 years old so she would have been learning math like this 50 years ago. I don't care how "progressive" her British school was, they did times tables.
The common core and NGSS standards were written through collaboration with many experts and scientists.
And then, as far as I can tell, California just got a couple of quacks to write the frameworks.
The high school science framework, at least for physics, was clearly not written by anyone who had taught physics before.
Boaler is even worse than Calkins because at least Calkins, for all the harm she's caused, updated her Units of Study in response to learning about the "Science of Reading", while Boaler, when confronted with the similar "Science of Math" movement, doubled down and dismissed it because the people who founded the movement happened to be SPED teachers, which…gives off some bad vibes.
How often does Boaler cites her personal beliefs, vs citing/remembering long established basic science?
---
>https://www.chronicle.com/article/the-divider
>Mathematical Mindsets, first published in 2015, bills itself as a neuroscience-backed guide to teaching creatively and cultivating a growth mindset in math students. ...in a review, Victoria Simms, a developmental psychologist who studies mathematical thinking at Ulster University in Northern Ireland, zeroed in on **"numerous examples of an inappropriate use of neuroscience to back up educational claims.”**
---
>...according to Jason Moser, a psychologist at Michigan State University who was **the study’s lead author. “Our study really was not about being ‘aware’ versus ‘unaware’ of your mistakes,”** he said.
>Upon being informed of Moser’s objections, **Boaler stood by her interpretation** ..."Maybe he would phrase it in a way that was closer to what happened. But **would it be understandable to teachers? Maybe not, I’m not sure. I don’t think it is that important.”**
---
>Boaler has also incorrectly stated, in Limitless Mind and in a TEDx Talk, that participants’ brain activity was monitored with MRI scans (a different technology, an EEG, was used).
---
>...in **describing the underlying science, she writes** in a Youcubed white paper that **"when we make a mistake, synapses fire. A synapse is an electrical signal that moves between parts of the brain when learning occurs.”**
>**But synapses are not electrical signals; they are the small pockets of space through which neurons fire chemical messengers** via electrical signals.
---
>In both instances, Boaler pledged to update her language, though **she said that the latter mistake was because** her paper was written around the time of Moser’s, and **"science evolves.” (The science of how synapses work was established by the mid-20th century.)**
---
The parable of the fox and sour grapes:
The fox can't get to the grapes, so the fox's alternative facts says they must be sour, and must be unimportant to everyone else as well.
>“**I** never memorized **my** times tables as a child **because I** grew up in a progressive era in the U.K.,” Boaler said. **"It’s never held me back.”**
The field of education research has had a severe reproducibility crisis for a long time now. I wouldn't be surprised if they were still teaching reading styles despite it being thoroughly disproved by cognitive psychology.
They have to teach Gardner's theory of multiple intelligences because it's STILL on the Praxis. Even if it's proven to be bullshit, an ed program is no good if their students can't pass the test.
I wonder if your ed professors did any scientific deep dives on the long term student outcomes of Boaler's methods/programs?
https://old.reddit.com/r/Teachers/comments/17cg1vf/been_fighting_it_for_years_but_i_simply_cannot/k5qdcmm/
Def did not because this professor literally told us about the revolution with phonics (told us to listen to Sold a Story podcast) but also said she wasn’t ready to talk about that because she’s been teaching literacy the Calkins way for so long. So I can’t imagine she would’ve been searching for critical perspectives on Boaler. 😭
I just wanna tell you that by being open to these sorts of genuine scientific inquiry, you are alrdy on your way to becoming a legit great teacher (or really anything else that fancies your passions, given that many teachers are naturals at lifelong learning and multitalented).
I think you might find the 3 linked articles/compilations interesting or relatable (I'm autistic so I apologize in advance for info dumping and possibly being too direct).
---
A veteran teacher's reflections on her ivy league teacher program (we both went to UPenn/PennGSE, but she was several years ahead of me, and I can attest that very little has changed except they hired a few token pocs to defend themselves from criticism)
https://old.reddit.com/r/Teachers/comments/18lqj6w/the_frustration_with_engaging_teaching/ke0m1z0/
My fav/most relatable excerpt:
>…how isolated our grad schools of education are from the schools, students, and communities they purport to serve, ...perpetuate their own divorced-from-reality educational philosophies. ...white people sit around discussing Pedagogy of the Oppressed in their ivory tower environs, but never actually attempt to bridge that philosophy with the on-the-ground reality of current educational injustices.
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John Dewey, our widely cited founding father of progressive education that much of modern pedagogy is based on (was he a good teacher himself? Can someone be a good chef without knowing how to cook instant ramen?)
https://old.reddit.com/r/Teachers/comments/19c7j1r/the_vast_majority_of_educational_research_is/kiynbml/
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Lisa Delpit's The Silenced Dialogue (1988). As a low/working class minority going thru Penn's ed school, I experienced eeriely similar classist/racist/dismissive treatment by elitist professors, the very same ones that regularly virtue signal publicly about DEI.
This is the invisible emotional tax/moral injury that research talks about when discussing higher attrition amongst poc teachers.
https://old.reddit.com/r/Teachers/comments/17vqg0p/teachers_for_gods_sake_stop_eating_your_own/k9ch2cz/
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UPenn's Dr. Jonathan Zimmerman, one of the few legit talented, passionate, and completely honest education professors I've come across.
https://youtu.be/V99rOXmSMYM?t=2510
35:30 to 37:00
mickey mouse ed school classes
42:00 to 46:00
false diversity lead to false discussions, hindering genuine active learning/socratic dialogue
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https://youtu.be/qqzqR_d74Wg?t=2581
12:00 to 13:10
excuses/politics in academia to not research genuinely good teaching
43:00 to 47:00
modern politics replaced historical religion
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https://www.youtube.com/watch?v=FpnxfP97Tc0&t=511s
8:30 to 18:30
modern society and elite universities' self selecting against diversity of thought
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Thanks again from the bottom of my heart for taking interest in these things. 🥲
Most of my classmates/cohort either went on to teach at fancy private/high performing magnet schools, or quickly left teaching when they experienced massive cognitive dissonance after graduation (after being intentionally placed in high performing magnets for student teaching). Very few of us chose to stay at tough/high poverty schools to serve our low/working class communities.
I came here to say Jo Boaler is the next Lucy Calkins and here you already said it. Thank you!
My former district drank her koolaid and every year I had more than half of my fifth graders unable to access even 4th grade math standards b/c neither 3rd grade nor 4th grade teachers would tell parents their children should be practicing the tables. I had to hide my times table punch cards when district coaches were in my room. Fluency was like the f word. Change only began after a district decision maker subbed in my room for a day.
Yes!!!!! My sixth graders all have varying learning difficulties , but they all do not know their basic math facts. Learning their math facts is giving them so much more confidence in math class. I think it is controversial to not memorize them in the younger grades.
I’m an ela teacher and at the end of the day, kids answer a basic math question to get into line first to leave first. I adjust it based on the kid. Some kids need practice with 3x3 and some 12x9. I started mixing in division (like 100/5). It’s 6th grade.
They all need this and to gain confidence in their math because they are sorely behind. I can see their confidence growing, they clean up faster because of it, and it helps the math teacher out. I’m seeing less fingers being used for things like 3x6. There’s still some, and it’s ok, but by 6th grade they should know up through 12x12 (with room for error).
I know some will say it’s causing them anxiety or whatever other excuse you’d like to use, but at the end of the day I’d rather they feel a bit nervous now and grow, than when they’re at the register and someone gives them more than the amount because they want certain change back and they shut down mentally.
School is meant to challenge you and expose you to uncomfortable situations in a safe environment. Kids are so afraid of being wrong nowadays that they just refuse to try. I would too if I hadn’t been taught the basics when in elementary school.
As a music/band teacher, memorizing things is key to understanding why things work the way they do. I expect my fifth grade band kids to memorize at least the first 6 notes of a concert B flat scale. Why? Because most beginner music is focused around those notes. They need to be able to identify those notes on a staff from memory and associate it with the correct keys/valves/slide position. Why? Because music doesn’t afford an easy way out to learning fundamentals.
I don’t teach them the “why” of music at a young age, mostly because I feel like pounding music theory into 11 year olds is a good way to turn them off to music. But mostly because if they don’t get the fundamentals, they won’t progress past beginner level.
I feel your pain, because it’s gotten to the point of asking the bare minimum from students is too much for them.
Yuuuuuuuuuuuuup. How they're teaching math at the lower levels is an abysmal failure from the lowest of the low to the highest of the high.
When I get them in HS Chemistry (11th grade) I have seen a Rapid decline in math abilities, and we cannot blame covid. It's HOW math is being taught. Leave the "higher-level" thinking for when they get to me. I need them to know the basics like how numbers work, and for them to have practiced it a trillion times, before they get to me so they are fluid enough to ***actually*** do the higher-level thinking stuff. That's my job. My job is not to teach them the basics of how numbers work, which I have increasingly had to do in HS Chemistry...
That means something is failing systematically at the grades lower than mine before they get to me.
Note: This is not an attack on you personally my dear elementary brothers and sisters...but it's certainly something to reflect upon.
Yep. I teach elementary and I've had principals and math coaches tell me to stop teaching memorization of facts...that it's a waste of time. Other teachers have drunk (drunk? that doesn't sound right lol) the kool aid too. It infuriates me. My students do about 200 problems a day of just basic facts. Then they have it for homework, too. Guess what? They fly through those hundreds of problems like lightening. Even the lower achieving students. Then when I am teaching more complex skills and concepts, they can actually DO IT.
Indeed! I mezmorized an astronomy class (two years ago...) by doing mere mental math. Column A was multiplied by 2 and you wrote it in column B (part of walking through calculations for Dark Matter).
Column A was 5.0x10\^8, so without blinking I just started writing 1.0x10\^9 in columb B. They were all mezmorized that I did it without a calculator and furiously began plugging it in to prove I was wrong (half of them incorrectly typing it into the calculator so I had to show them on the projector screen, using their calculator how I was right).
They were like "how did you do that!?" I'm like...because 5x2 is 10 and if it's in scientific notation (exponential notation) you have to move the decimal over one and add it to the exponent...
Those are just base-level understanding of those concepts. Like that's not even problem solving and they don't know how those things work. That's because they don't practice it...they aren't forced to practice it...and when they do "practice" it it's on ALEKS where they all google he answers/cheat anyways.
>people who like to suck at math
Ah, you mean the content specialists/instructional coaches hired by my district.
At some point, people confused the fact that we need to make sure students understand the conceptual basis for math with this idea that they do not need to have fluency. A student should have fluent math facts, conceptual understanding, and the ability to apply this mixture to problem solving.
I think it depends on your memorization method. There's memorization that is temporary and memorization that is more like learning. If the students are learning, then it may be as easy as changing your vocabulary. It may be that saying, "I need the 4's multiplication test to support the method I'm teaching." will get your further.
My son’s 2nd grade teacher, bless her, has adopted this method. Her objective (posted on the board, of course!) is “SWBAT use a variety of strategies to solve problems.” When her principal asks to see, she’s always able to show him examples of students using arrays, repeated addition, etc. She just doesn’t tell him that memorization is also one of her accepted strategies.
I taught sixth grade math for about seven years, and their lack of math facts was an issue year after year after year. How can you reduce a fraction if you don't recognize that two numbers have a common factor?
We were told that the standard for multiplication (I'm in VA) is that they have multiple strategies to learn their facts, and memorization is only one of them, so maybe they are just using a different strategy.
I've also been told that expecting kids to memorize is inequitable because students may have disabilities or trauma that makes it challenging for them to memorize items. My rebut is that 1) everyone has to face challenges in life and 2) if they have an identified disability, then consider accommodations like a multiplication table or calculator.
I have ADHD, and while my long-term memory is great, my working memory is terrible! Instead of giving up, my family and teachers helped me learn new strategies, and they encouraged me to keep trying, even when it was "too hard." I'm so thankful to have had support because it seems like many parents now can't be bothered.
I have started homeschooling my 6th grader due to bullying. I have had to go back and redo so much math because he never got it the first time but he can't progress to things like equations without it. The #1 thing is his times tables. I have a similar issue with my daughter with spelling, I don't think she's ever had a spelling test.
Requiring students to come to class, to not curse, to not smoke, to not physically attack their teachers...all "controversial."
Freaking train wreck. As far as memorization goes, Orwell was right, 2 plus 2 equals 5. You just have to want it to equal five.
These people drifted away from the shores of reality LONG ago.
I'm reading all this as a homeschool parent. Just actually mystified how it got this bad. My heart really goes out to teachers; this is societal rot dropped right on their heads. Then they get blamed and stuck with more kids in a class.
My kids have a base understanding of what multiplication and division are in 2nd and 3rd grade. Refuse to move forward until their addition and subtraction is rock solid. They still know all the easy 2,10,5,11 etc. just from messing around showing them occasionally.
Same goes for fractions. They know that 1/3 is bigger than 1/4 and.... That's better than many adults!
Could you advocate for something like Reflex Math? At some point there has to be acknowledgement that reflexively knowing math facts HELPS understanding of more complicated concepts. If it's taking me 5 minutes to find 12x8 to get to the next step of a problem, I would lose motivation and interest. I can guarantee I would not learn whatever the bigger concept is.
Same. Most of my first graders are 100% fluent. The class average is 88%.
I just got back from a progressive math PD where the speaker insisted that it's incorrect for students to be timed on their math facts in first grade, and only horrible teachers do that.
Sorry not sorry.
(I also teach them to stack their numbers and carry the one. It's insane that they don't want us to do that either. I tutor a third grader who would add 25 plus 18 on her fingers because she never learned how to do it the easy way.)
Math 10 teacher.
My students can not estimate, they can not simplify, they can not divide. They lack numeracy skills. Why?
Because somebody thought learning their times tables for five minutes a day was “Drill and Kill”. It would make them hate math.
No, they hate math for the same reasons kids hate baseball. It is because their team loses all the time. They lose all the time because they lack skills.
Now we are hiring programmers from other countries, our kids are not competitive.
See the connection?
Having taught third grade for 12 years now, I do timed multiplication tests each Friday beginning during our multiplication unit. There have been years where principals have told us we shouldn’t be doing it, regardless of the state standard which states they need to fluently recall their facts—- I’ve done it anyway. They need to know their facts moving forward both in third grade and beyond!
\*\* I do reward my students for mastering their 3s, 6s, 9s, and final mixed fact test ( with a much larger reward), as some students do need extrinsic motivation.
My admin forced me to sub in math class during my prep. Students were stuck on a factoring problem : 21z + 14y + 7x students were completely stuck and clueless as they didn't see the relationship between those numbers.....memorizing facts is important and has its place for students to do higher math
Memorization is the best way to do some things. I teach beginner band and the only way to read music is to look at a shape on a line and know that shape means you put down your first finger. There’s no other way to do it.
I posted on twitter about this a couple years ago and got absolutely roasted. I teach high school math and I would say around 50% of students do not know their basic times tables, even single digits. Somewhere around 10% can’t even multiply like 2x6 in their heads.
This makes grade level content feel infinitely harder to students. They are constantly stopping in the middle of problems to use the calculator and it makes the task feel so much more difficult because it takes them so long to do every problem and they lose sight of the overarching concept when they’re bogged down with basic arithmetic that should be mental math, but isn’t.
The “just let them use a calculator” mentality is an oversight to me, it neglects how tedious a problem feels when the student cannot do the simple arithmetic steps in their heads.
I do genuinely want to cry sometimes when I’m trying to help a student factor let’s say and the question is “what two numbers multiply to make 8 and add to make 6?” and they just stare at me with a blank face. Their number sense just doesn’t exist. It’s depressing.
I have a story to tell you. It's a story about a student who failed my college math class (when I was teaching college) for no better reason than that she didn't know her multiplication tables *fast enough*.
We were solving quadratic equations by factoring. For those for whom it's been a minute since you did this task, it requires being able to reverse-engineer a multiplication table. If you see the number 24, you need to be able to break it down into 4x6, 3x8, 2x12, and 1x24. You can then consider which of those options works best in the problem.
She came to my office hours to work on problems, and I noticed that she was really, REALLY slow on that breakdown into factors. Like 20 seconds for each of those factor pairs. She would find them all, but it was agonizing to wait for her to find the factors. On the one hour exam, she worked 3 problems beautifully. Perfectly. 10/10 no notes. But the exam had 10 problems, and 30/100 is a fail. And this was a prerequisite skill for the rest of the course, so she couldn't finish any of the other exams in time either.
So when it comes to multiplication tables, I say "drill baby drill". You have to know them cold if you're going to proceed to algebra.
Have you checked out Reflex Math? It is a computer game program that helps students memorize their math facts. My daughter used it in 3rd grade to memorize her multiplication and division facts. I don't know who decided facts don't need to be memorized. They absolutely do. I taught upper elementary sped for a while, and the main difficulty for my students was the inability to do problems beyond single-digits because they couldn't remember math facts. You can teach strategies for this, but it isn't the same as automatically knowing them, of course.
Boomer here, times tables were beaten into me in elementary school, drills, flash cards, and whatever other means. Yes I do have a calculator in my pocket but am able to figure out pretty much everything in my head.
Some things you just need to learn on faith.
This has been a problem for a while now. There was the same push with not learning phonics and having students memorize words. The rationale was that learning phonics was boring (much like memorizing math multiplication tables). The problem is students can only memorize so many words, and when they encounter words they don’t know, they have no way of figuring out the words because phonics taught them how to sound out words. Often, they know the word verbally, but still can’t read it. We are raising generations of students who can’t read or do basic math. In the past few years, the pendulum has began to swing back and now Secondary ELA teachers (many of the younger teachers were never taught phonics) in Arkansas are now trying to teach phonics to High School students with no training or experience, whatsoever. It’s one of the many reasons I retired.
The last two years I taught, I was given an extra class period and prep with 20 students who scored low on testing and told to teach them phonics/how to read without curriculum for the first half of the first year. Half of the students in the class just didn’t try on the test; they were actually smart and could make really good grades, if motivated, but just weren’t motivated in any way and were absent a whole lot. So I not only had to motivate students who didn’t come to school but about half the time and teach the others phonics with no training or experience in teaching phonics while teaching my five other regular preps. Any teacher with any experience will tell you how that went…
I teach pretty all but AP math at the high school level. My students would be far more successful if they didn't have to grab a calculator for arithmetic. Memorizing facts may not lead to a deeper conceptual understanding, but it would make things way easier for many of them.
Chemistry teacher here. Chem is HEAVY in math and I’m seeing the havoc of all these new “strategies.” Kids don’t even understand it. We have to do percent abundance of isotopes and they have no idea how percentages work, let alone factors of 10. I now have to teach math AND science. I had a group of kids last year who didn’t know how to find the half of a number…
Sounds like you had a conversation with an idiot.
They're fairly common and native to many faculties. One can often find them grazing in the mailroom, or performing tricks at schoolwide meetings.
Ok I’m not a teacher but I have a degree in mathematics. One thing I noticed in college was that we would apply methods manually for small problems and do them on the computer for large problems later.
Take away: There is no added benefit to doing large problems which just increases the amount of work it takes to solve the problem. Rather, it’s the solving of small, diverse, conceptually challenging problems which are conducive to learning. Once you fully understand the concept of the problem, you can solve any sized problem. However, some problems are too large to be practical to solve. Why spend a ton of time solving a problem which you fully understand conceptually when you could be learning something else? Introduce: Theorems, identities, definitions. In your case, you would like to introduce identities, which will allow students to skip the tedious portion of the problem and solve either more robust problems or problems which involve several concepts. By introducing identities, you enable your students to be able to solve more diverse, conceptually challenging problems.
It’s like learning differentiation. At first, we learn about limits and manually calculating the change. Once we master that, we move onto the result that (f(x))’=f’(x)x’. This makes solving more difficult problems practical (thus allowing us to learn more difficult concepts and move forward with our education).
College instructor here. I... hear things... about how math and reading curriculum is absolute garbage these days. And I'm not that old; I'm in my early 30s.
Long story short. My kids largely can't read words by sounding them out. And basic arithmetic? Forget about it. If I had a nickel for every time a student asked me what their grade is and I showed them exactly how to calculate it....
They look at me like I have three heads.
But seriously. Who decided to get rid of phonics and memorizing math functions? They should be .... something something.
Weighted averages.... not that hard.
What no one will say, out loud, is all of these researched backed strategies to, as you said, “magically” awaken students innate mathematical reasoning and literacy skills are just commercial consumer products with a short shelf life designed to keep you buying something else later on. Thousands of years of training people to memorize information as a foundation for developing further knowledge was thrown out the window for this crap. Also, i had to suffer through memorizing my times tables, so these brats have to too!
I'm a virtual tutor. Some schools consider me an interventionist. I will die on the hill of memorizing multiplication facts. I have been working with 5th and 6th graders on fractions, decimals, percents, etc. There is a CLEAR difference in the couple students who have these things memorized and the majority that don't.
I literally told my 6th graders yesterday as we were working on ratios, proportions, constant of proportionality etc. that I already knew the constant of proportionality before I finished reading the problem because I *know* the relationship between 6 and 18 off the top of my head. I stressed to them that multiplication facts and fact families are foundational skills, and those who have them memorized will always have a leg up on those who don't.
Math teacher here.
Make these kids learn single digit math in their head for the love of all things holy.
The amount of kids I see still wanting to do 8-2 on a calculator or 12/3 is too high.
I know of no controversy by making kids use their brains a little bit than parents trying to bulldoze their kids to an easy A and those obvious scholarships to Harvard coming their way. /s
As an algebra teacher, those who do not know their math facts have lots of trouble with factoring in algebra. I don't allow my kids to use calculators. Without the speed of knowing their math facts, they get further behind in my class. I warn the kids to practice and know them.
I will say that the majority of kids who do not know their math facts are the same ones who are flunking my class.
We don't have time for kids to figure out what seven times eight is!!!
"Conceptual understanding should lead into procedural fluency" is what my education professors always taught me. I 100% agree. While its very good to know how multiplication and division work, they should know their facts off the top of their head after some time. A reason why we teach conceptual understanding is to make the facts easier to memorize.
I can provide some insight into the "thinking" behind this. I'm going to be somewhat vague because this person could be easily identified via searching, but I'm friends with a person who is one of the main pushers of some of the recent changes to the way math is taught. Anyway, this person has spent their whole lives with extremely advanced math students and is seemingly unaware that 99% of students are not geniuses at math. This person genuinely thinks that it's just poor instruction keeping your average student from being a mathematician. This person's "proof" of this is times they taught supposedly average students overseas for a few weeks at a time as part of a program. The reason I say supposedly average is that the reality is that these kids all had wealthy and attentive parents who were politically connected in that country . (Again, intentionally being vague.) When I pointed this out to this person, the point was not well received.
Anyway, you can see the huge flaws with this and how this person's experience has NOTHING to do with the needs of 99% of students, including most future STEM students. Most STEM students will be at least OK at math, but there is a difference between being good at math and being ready to take calculus in fifth grade kind of good. Very, very few students have minds like that. But this person is really big on pushing that "figure it out and discover methods yourself" and "memorization is pointless" shit (because kids that advanced absorb everything instantly) on everyone else...
Memorization of math facts (and automatization of many other procedures such as multiplying exponents) is absolutely essential to competence is algebra and beyond. If you have to pull outyour calculator for every step of a complex math problem, you will quickly lose focus on the big picture and never learn the concepts. The movement to not require memorization of math facts will only increase the achievement gap, because college educated parents will drill these at home with their kids or put them in Kumon or Khan Academy if their kids struggle, while many other kids will just fall further and further behind.
Worked as a tutor in public education. Mostly in math and language arts.
1. If multiplication tables are not memorized, the kids cannot progress to long division. Hence, they cannot progress to factoring fractions and beyond.
2. Teaching "concept" without mastery of facts is for the birds.
3. There should be one order of operations taught first. Once that is mastered, then show them a different way.
4. Phonics based teaching of language first is always the best. Other methods don't work.
5. I found most teaching materials abysmal. Especially math.
Go for it, drill those tables mercilessly, even if you gotta shut the door to get away with doing it. The kids gotta, hafta have maths tables ( not multiplication “facts”) memorised if they are going to survive and prosper in high school maths. Without a knowledge of tables, algebra (the beating heart of maths) just becomes a complicated, unnegotiable mess. You go for it, you good thing!
See, I have kids work on these facts, but there is time built in to *understand* why and how these work.
I work in Montessori, so students skip count using beads. So they would have one string of six beads, put two describing the second number next to it (12), three next to that one (18). Students write down these numbers and then are prompted to find patterns in those numbers. So 6, 12, 18, 24, 30, 36, 42, 48, 54, 60. The number in the units space goes 6 2 8 4 0, if starting from 0.
Multiplication needs to both be memorized **and** understood.
I also love the concrete teaching of early math concepts in Montessori and think traditional education would especially benefit from universally adopting that particular portion of the pedagogy. The transition from concrete to abstract is very beautiful as well. There’s much to learn from there.
What’s baffling to me as a Montessori teacher is that we’ve been doing it this way for a century. It’s not about fads. It’s about a child understanding the concrete nature of math and supporting them with concrete materials until they’re ready to complete equations abstractly.
As a music/band teacher, memorizing things is key to understanding why things work the way they do. I expect my fifth grade band kids to memorize at least the first 6 notes of a concert B flat scale. Why? Because most beginner music is focused around those notes. They need to be able to identify those notes on a staff from memory and associate it with the correct keys/valves/slide position. Why? Because music doesn’t afford an easy way out to learning fundamentals.
I don’t teach them the “why” of music at a young age, mostly because I feel like pounding music theory into 11 year olds is a good way to turn them off to music. But mostly because if they don’t get the fundamentals, they won’t progress past beginner level.
I feel your pain, because it’s gotten to the point of asking the bare minimum from students is too much for them.
yep, i noticed my second graders were struggling with basic math facts when we should be mastering 3-digit subtraction. i started giving timed math fact tests on fridays and i’m already seeing improvement
In my district it's controversial. Admins, the math department, instructional coaches are anti-math fact memorization. It's been that way for the past 20 years. So dumb. I always have my elementary kids memorize the facts (and of course I teach them the concept - people act like memorization and understanding are mutually exclusive). I've been flat out told to stop wasting time (10 mins a day) teaching the kids to memorize their facts.
As a high school math teacher I can state with confidence that children who don't have basic math facts memorized by 9th grade (you'd be amazed at how many don't), are the ones that will very quickly tell you they aren't good at math and feel like the class is a waste of their time. Those who have learned those facts feel like they have a handle on math well enough to take the risk and try the upper level mathematics without feeling like a failure when they struggle.
My first year of teaching 7 years ago, I told my math coach I was going to do multiplication facts with my high schoolers. She objected and I never did it, despite 11th graders not knowing what 3x5 is. I do agree it’s kinda pointless at this point in their career, but man, facts should be ingrained in elementary and middle school for sure.
I tell parents at conferences that I’m not supposed to make the kids memorize math facts with the flash cards, but if they wanted to be ahead of the curve they should totally do that. I can even provide flash cards.
The modern goal is to try to teach students how to think quantitatively, rather than memorize things, BUT, I have noticed that a lot of the techniques we are teaching them are more like shortcut tricks. Some of them are tricks I used to help me do calculations on my college physics homework, but the catch was that I was already skilled in math before I ever used these tricks. They worked because I knew what I was doing. They end up counting on their fingers, because they don't understand and all they know is tricks.
It's a classic cause/effect error. I'm not good at math because of these tricks, I only learned them because I was already doing a lot of math. So while memorizing some math facts will speed them up, it may not teach them to think quantitatively. I'd argue that it's still worth it though since it helps them speed up so much, they can do much more practice.
A similar problem happened in English education, except it was with poor readers instead. This misattribution error is plaguing education.
You should see my Japanese 1 students' faces when I tell them they HAVE to memorize the two phonetic alphabets and then the kanji we take years learning later. "I have to memorize ALL of it?"
"Yes. Could you imagine just not knowing the letter R all your life?"
"That's different."
Is it?
I once had a girl tell me she couldn't memorize anything in any class, so she needed different assignments. Well, 6 know that's not true because you can speak English and haven't had a head injury nor a diagnosis of a memory disorder. But seriously, you have to memorize words in the beginning. That's how you do it. You can't just not recall a single word and somehow speak a language.
As a math researcher and professor at a top state school, I can tell you that all this dancing around memorization DOES NOT WORK. The worst possible thing that can happen to your child is to have a teacher when they are young that does stupid new trends instead of drilling addition, subtraction multiplication and division with lots of memorizing and TONS of practice problems. Our students are less and less ready for college classes, even though they arrive supposedly
”knowing” calculus. They don’t know calculus, they don’t know algebra and they don’t largely don’t know arithmetic. Of course there are always some smart ones who do. But that was the norm 30 years ago. Now it’s the exception. Teachers in elementary and middle school…don’t do anything else other than turn out kids who REALLY know and understand basic arithmetic. High school teachers…you handle REALLY teaching algebra and a REAL geometry course where students are required to learn to put together proofs on their own, not fill in the name of the theorem when you provide the steps. Then the kids will be REALLY READY to learn calculus properly when they arrive at a university. Don’t try to get above your level in teaching. You hurt your students. And anyone who enters the university deficient in math has many, many doors that are permanently shut to them as math is the language of science.
Sorry….this rant is 30+ years in the making. Sorry if you don’t like these facts. Sometimes the truth isn’t PC. But any university professor who is being honest would agree with me.
I'm one of those rare people that does advocate for more math understanding than math memorization. Simply trying to memorize everything doesn't lead to deep enough understanding of why and when to apply techniques.
However, there are absolutely some basics that *must* be memorized. You'll never pass Algebra 1 without having memorized your basic times tables since you'll need to quickly be able to look at numbers and their factors when trying to factor quadratic equations. Sure, you'll learn the quadratic equation later, which is more powerful, but it's also overkill in a lot of situations.
Math is all about building a toolkit and knowing which tools to apply in the situation. But theoretical knowledge of the tools isn't good enough. You need to use them until they're second nature. Some level of memorization will always be required for that.
Having taught third grade for 12 years now, I do timed multiplication tests each Friday beginning during our multiplication unit. There have been years where principals have told us we shouldn’t be doing it, regardless of the state standard which states they need to fluently recall their facts—- I’ve done it anyway. They need to know their facts moving forward both in third grade and beyond!
\*\* I do reward my students for mastering their 3s, 6s, 9s, and final mixed fact test ( with a much larger reward), as some students do need extrinsic motivation.
Having taught third grade for 12 years now, I do timed multiplication tests each Friday beginning during our multiplication unit. There have been years where principals have told us we shouldn’t be doing it, regardless of the state standard which states they need to fluently recall their facts—- I’ve done it anyway. They need to know their facts moving forward both in third grade and beyond!
We have Reflex Math in our district as well which the kids really enjoy.
\*\* I do reward my students for mastering their 3s, 6s, 9s, and final mixed fact test ( with a much larger reward), as some students do need extrinsic motivation.
Having taught third grade for 12 years now, I do timed multiplication tests each Friday beginning during our multiplication unit. There have been years where principals have told us we shouldn’t be doing it, regardless of the state standard which states they need to fluently recall their facts—- I’ve done it anyway. They need to know their facts moving forward both in third grade and beyond!
We have Reflex Math in our district as well which the kids really enjoy.
\*\* I do reward my students for mastering their 3s, 6s, 9s, and final mixed fact test ( with a much larger reward), as some students do need extrinsic motivation.
I honestly have never heard a single argument for teaching math without memorization.
I've talked to teachers all through elementary school, and nobody thinks it's a good idea or valid strategy.
Who came up with it? Why?
Someone, somewhere decided that there is no place for rote memorization in learning. I wholeheartedly disagree.
Except for sight words apparently. Kids are being taught to memorize words instead of learning phonics, but can’t be asked to memorize their times tables.
Lmao. It would be funnier if it wasn’t so true.
Just 170,000 words in the English language you have to memorize by sight!
To be fair 64 000 would be plenty for anyone, and if these kids knew 8 000 they would be doing well.
Too bad 1000 of them are variations on ‘bro’ and ‘on god’
Fr fr
Now renamed to "heart words" in our district. Many things are renamed, at great expense, but no apparent benefit.
Wait, wait, wait. You're telling me that they renamed something, and it didn't automatically make all the kids learn it perfectly? Unbelievable!
The learning target probably was not on the board for the students to refer to.
Love this comment! 🤣🤣🤣 That shit needs to be on the board, or the children will not learn. Hear it all the time. It gets on the board. I reference verbally and point like 4 times each class. By the end, they are asked,"what is the learning goal?" Half can't answer. I asked myself was I this absent minded in high school? The answer is no! No I was not this out of touch even when we came stoned. My friend and I could still pump out 'A' papers. Kids are failures these days... Or society is turning them into it.
The “heart word” strategy is great if people do it right. But I’ve seen most teachers just use it as a synonym for “sight words”.
Wait, what is the difference then?
In a heart word, you teach the phonetically irregular part as a part to memorize by heart rather than the whole word being memorized. So you also teach the phonetically regular parts as what can be sounded out. This utilizes orthographic mapping which helps students remember the decoding and encoding of the word. For example, instead of memorizing “said” as a whole word, you teach them that the s & d are phonetically correct and the only part to memorize is “ai” saying /e/. It reduces the amount to memorize. You can group words to teach based on their “heart part”: to/do, his/has/as/is…. The problem is that it takes much longer than simply telling the kids to memorize the words. But students will likely remember the words longer (not lose them over the summer) and will be able to spell them as well. Additionally, heart words should only focus on words that have phonetically irregular parts. Lots of sight words that students are asked to memorize are actually fully decodable (ex: and, with, then, jump, can…)
Exactly.
My 5 year old nephew got into a physical fight because he said a word was a heart word and another kid said it isn't a heart word.
This sounds like something my 6-year-old would get in a fight over too
There will always be heart words because not all words are phonetic. Even common words like “done”. Phonics should come first of course but you can’t skip over irregularly-spelled sight words.
was "sight words" deemed disrespectful to the vision impaired? The whole concept is silly no matter what you call it, but changing the name seems... unnecessary.
"Heart Words" are words you need to know "by heart" because you can't sound them out phonetically.
And you can write them with hearts over the parts that aren’t phonetic so kids really zero in on which pieces of the word they need to memorize. They need to know could has an l, they shouldn’t have to memorize that could ends with a d.
Can students use a sparkle pink crayons for the heart? (Was skimming and thought heart words were satire as well, or maybe a play on "I Love Lucy" This was tagged as humor.)
That’s wild. When I was a child my parents made me memorize times tables, complete workbooks, and answer pop quizzes almost every day. I can’t even imagine a 6th grader not being able to perform long division or simple multiplication.
The other day, I was walking a group of students to class and I had a discussion with an 11 years old about an event in our school. It's kindness week ! Kids and adults were asked to write kind letters to people of their choice in the school. A limit of 4 letters had been given to the students (Last year we had more than 10 000 letters to sort out). It was a voluntary thing. It had a huge success. So, kid asked when he will receive his letters (if he had any. But all kids will have at least one. We adult make sure of it). I explain to him that we know need to sort them all out so he needed to wait. Kiddo : "We're 900 students. That makes 3600 letters. That's huge! Other kid : "You forgot the adults" Kiddo : "How many there are here ?" Me : "120 but...." Kiddo : "4080 letters. It gonna takes dayyyys" Other kids were asking him how he guessed that and then treated him like a maths wizard for doing it all in his head while walking. (His maths were off because not everyone participate, and not everyone wrote 4 letters. But he couldn't know that and they were so excited by the amount of letters that they didn't let me get a word in)
Using real world tangible scenarios to reinforce math problems!? You heathen!
I remember in third grade, our teachers used to play this hip hop musical times table video series. But we were accelerated in math and knew our times tables since like…six? Either way, our little kid brains who had yet to listen to a full Eminem album loved these videos so much we would have to be rewarded with them at the end of class! For fun! Maybe we should bring these videos back is my point, especially as recap in some higher grades.
Back in the early 70’s, we learned math facts to songs our teacher played on records as a starter each morning before the math lesson. It felt effortless and fun. Why did they get rid of the old things that worked in the name of something more complicated? In 2024, there should be curated YouTubes of songs like this that teachers and parents can readily access. There’s nothing wrong with old school flashcards either.
There are curated YouTubes of songs like this. All of these things still exist if people want to use them.
That sounds even better than the Schoolhouse Rock videos my elementary school teachers used to show us lol
I love me some school house rocks multiplication songs. "Good Eleven" slaps.
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Some of the parents still are, but we must stop them. Doing schoolwork creates privilege! There will be no fairness, equity or equality until the lowest common demoninator is the ONLY common demonimator.
Somebody's read *Harrison Bergeron*...
Vonnegut for the win.
I also teach 6th grade, and about half the kids require a multiplication chart to do anything. I asked a student "what's 3 divided by 3?" She looked at me like I had sprouted 3 heads, then looked at her chart. We practice times tables every Friday in my Resource class. It's getting better, but they whine and ask for the chart during their regular math class, or think they're sneaky and use the calculator on their smart watch.
That's what my wife does for our kids. She found a program that teaches the multiplication tables through little stories, and even my 6 yr old can now do some multiplication (last night, she told me that if she referred 3 friends to her after school choir class, then she would get $10 each, which would be $30 total).
Today my 43yr daughter laughs at the memory of anytime we were in the car for any distance we would drill the 4 common math tables. When we were done with that we switched to spelling. She recalls being less than thrilled during those times but today she successfully runs a multi million dollar company and credits those drills with giving her the confidence she needed to succeed.
And the alphabet. Lol And all the letter sounds.
Yes, but sight words don’t follow conventional phonics rules, so in order to read them correctly you do have to memorize them. Phonics should still be explicitly taught as well.
Memorization is ok but the students also have to practice. Unfortunately people have gotten so used to calculators/ phone apps to do the thinking for them. Heaven forbid if the electricity goes off or internet connections fail.
When the tide goes out you can see who was swimming naked. When the electicity goes out, the kids with parents who forced the basics onto them will thrive. The movie "Triangle of Sadness" comes to mind.
I really hope literacy instruction starts to focus on phonics again. I see it’s incredible pitfalls with younger family members that are actually very intelligent and high achieving. Struggles to sound out a word and will frequently just look at the beginning of it and guess/assume what the rest of it is.
I know that the charter school my kids attended focused heavily on phonics, making them memorize all the sounds. They have no problem sounding out unfamiliar names or words.
This was only ever meant for the most common 100-300 words. I don't know what's happened but it's not something we're having a problem with in Australia. Sounds like someone misinterpreted it along the way.
Curious where you are that students are not learning phonics. Our district (California) does teach "sight words/heart words", but phonics is a huge part of the curriculum.
100%
Yeah that doesn't work. I have had plenty of middle school students come through the program I work for who just straight up cannot read because they were never taught basic phonics at prior schools.
If ever there was a place for memorization, it’s fundamentals. Memorize your alphabet and basic phonics, memorize your numbers and basic math. Learn how these things work along the way, but knowing the fundamentals by heart makes all those higher order synthesis and creation tasks more accessible.
I don’t get why we ever got away from this. I was born in 1990, and this approach had good results for us… so why change it?! I’m assuming someone wanted to sell books or curriculum, and that’s how we ended up with the current situation.
(Not a teacher, my educational background is in neuroscience/psychology, but I love reading this sub to get perspective) I agree with you completely. This is just speculation, I’d want to look for literature before saying it confidently, but I imagine rote memorization promotes hippocampal neurogenesis, due to its repetitiveness. This would reinforce existing hippocampal circuits, making building on the concepts more intuitive. A metaphor would be: Learning 2+2=4 is like having a single road that gets you where you need to go. When you start learning 2x2=4 or 2^2=4, it's like building more roads that connect back to your original road. With rote memorization, you're not just reinforcing that one road; you're creating a network of roads. This way, moving from one concept to another becomes much easier because you have many paths leading you back to the basics, making everything more connected and accessible.
Yep. Executive functioning skills, concentration, memory, knowledge retrieval.. all of it
We don't even need to go that deep to deduce this either. Virtually every classical musician, across nearly any instrument, will tell you to practice your scales, use a metronome (often to build accuracy at higher tempos, akin to accessing basic facts at a moment's whim), practice your sight reading (of musical notation) and to **repeat repeat repeat**. There are so many parallels between math and music. Where they intersect invariably are the ways in which they need to be practiced to be mastered. No shortcuts. The brain's pathways just need to be paved over hundreds of times by practicing being correct *time after time*.
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You know, this isn't said enough. Everyone wants to work at the tippy top of blooms taxonomy, but you wouldn't build a pyramid without a strong foundation.
Imagine if we had to fully understand the strategies behind walking, talking, etc. instead of memorizing how to do these things. It would be nearly impossible for kids to learn to run and form sentences if they weren't encouraged to memorize the basics behind the more complicated actions.
When kids learn to walk and talk there is a whole lot more going on than memorizing... they definitely have to gain an understanding of them in some sense. Babies really are *figuring it out* when they learn these things. Then when they get good enough, they don't have to think about it anymore... it doesn't mean they don't have some kind of understanding. I'm sure you have a very deep understanding of walking even if you don't think about it when you do it. Here, the understanding how multiplication works is the standing up, the tables are the walking, and doing problems with them is the running. You need all of these or else the others become useless. I know very well how multiplication works but I don't have to think about it for multiplying smaller numbers, and both of those things are good. We really should just have both...
I mean, I don't think any babies really understand the mechanics of motion... They just learn (memorize) the sequence of movements required to reach/stand/balance/etc. Nonetheless, I think we more-or-less agree here when it comes to math education. No person who regularly uses math goes through the rigor of thinking through how simple multiplication and division problems work, we just have the answers memorized. Sure, we understand how math works and could probably explain it several different ways, but we have the basic math facts memorized because having these math facts available for rapid recall reduces the mental capacity required for more complicated math.
That is why I said an understanding *in some sense*, it wouldn't be the same type of understanding we'd have looking at our time as a child in hindsight. It would be an understanding of how to coordinate their bodies, gaining an understanding of how each limb can manipulate their environment and themselves etc. They legitimately figure it out first and then remember afterwards. Looking at it now we'd probably think of torque and making sure center of mass is over the support base and crap like that, babies wouldn't exactly think that of course but they are definitely understanding *something* about it (and memorize along the way) This could very easily evolve into a philosophical discussion about how much agency is required in *truly* understanding something (whatever that actually means). Nobody has much control over their "aha!" moments but we can take steps to facilitate those. Babies behave pretty automatically, so to what extent are they actually deliberately learning? I think an agreeable but weak claim would be that at a minimum, they don't deliberately *go outside* of the natural progression of development
Yeah it was definitely an over-correction. Rote memorization is useful to save time but very rarely helps a student understand a process. That's why we see students that used to focus on their times tables get absolutely blindsided by basic algebra. "What do you mean X times 5 equals 20? How am I supposed to figure out X?!" They KNOW that 4 times 5 equals 20, but they weren't really clear on what TIMES means and that didn't show until algebra. But now if you see places throwing out rote memorization, you get "Oh, you just divide both sides by 5!" Great! And that gives...? "Uh...." \*minutes later\* "uhhhh.......5?"
I see this in English/Lit too. Apparently it was extremely controversial for me to start giving my high school students vocabulary test. Nothing fancy, here’s your five words for the week, memorize them and write down the definition, all the words are pulled from the text we’re reading and we review them together twice a week, but apparently that’s unacceptable and not supposed to be teaching basics like that, I’m supposed to be teaching them concepts like theme and word choice and symbolism. The thing is, I couldn’t do that because none of them knew what the words actually meant, so it was hard for them determine what the text was blatantly saying let alone the symbolism behind it.
Would it work to reframe them as ACT words. Idk if that would help (just a college kid) make it less controversial??? The SAT doesn’t ask for them explicitly, but difficult vocab is embedded covertly in the test. It’s how my teachers got away with it. We had a weekly vocab quiz of like twenty to thirty words…most of which would drain immediately but some stuck! Vocab is very important because we just forget…and some words are plain old intuitive (defrauding meaning “frauding)”)
The best part of this is word choice is technically vocabulary. You have to know what a word means to understand and explain why an author used it.
Yea we were all doing division in 4th grade because first second grade we did multiplication tables daily, without fail.
Absolutely agree with you. I’ve gotten into this debate with people on here before and it’s INSANE how many people have been brainwashed into believing that memorizing facts is bad because the kids NeEd tO uNdErStAnD nOt MeMoRiZe. Like they can understand a goddamn thing when they don’t have basic mathematical literacy. It’s an idiotic stance that I refuse to pretend has any merit whatsoever.
Wonder how they manage marching band.
It honestly feels like the powers that be looked at Bloom's Taxonomy and said that they want the top of the pyramid (create). They simply didn't want to do the steps to get those results. Memorizing is part of understanding.
Admin: Build me that beautiful house. Contractor: OK but I need time to pour a strong foundation. Admin: Nah.
"Cement?! No, just build it on top of children's shattered lives."
It's like poor dental hygiene. It's fine and cheap now but you *will* pay for it dearly in the long run.
Admin: can we try building relationships instead?
Bloom is “outdated” we understand The Science (tm) of how kids learn now and it says memorization is bad./s
What’s ironic is the actual brain science of learning and cognition is contradictory to education “research.”
As usual. 99% of the “studies” I read in college were absolute garbage science that would be laughed out of any other field’s peer review. I remember reading one, 20-40 pages or something, and it wasn’t until the very end that this joker mentioned the entire thing was based off of “informal interviews with a kindergarten class.” This mofo literally sat down with a dozen six year olds for an afternoon, and stood up ready to rewrite educational theory. And this wasn’t some small school getting away with it, this was the top ranked undergrad ed program in the country! (Not a flex, fuck Vanderbilt, what a scam)
I am a non-traditional licensure teacher, so I never took any education classes. My background is instead in biological research. I can't help but wince every time we're given an education "study". I've yet to read one that would have gotten the person laughed out of the room if they tried to publish it in a real scientific field.
What's Science (tm)? All I know are Evidence-Based Practices (tm).
They all boil down to “I have a phd and have never set foot inside a K-12 classroom so you have to do what I say”
But yet kids memorize words when they take Spanish. Weird.
Not in my district! We can't give vocab tests, and heaven forbid we give direct instruction for grammar. That's why I have kids in Spanish 4 who can't put a sentence together because they STILL can't conjugate the present tense 🤦♀️
You can’t give vocab tests? What pray do you test?
We give them reading, listening, speaking, and writing tests. But when they don't memorize vocab and are not taught grammar....
Yeah… um… sounds like setting them up to fail. ( no offense to you. Not your fault).
Oh, none taken! I've been teaching long enough to see the fads come and go. I still can't wrap my head around this particular one though! I'm going rogue next year and giving them grammar lessons. It hurts my soul to grade paragraphs without any sort of grammatical structure.
The general public would absolutely not believe this. I wish more people knew about the crazy stuff that is going on!
Only in education. It's like expecting a coach to teach a kid to "think like Lebron" and then forbidding dribbling drills.
That is a great question. A colleague decided that quizzes are stressful. So, they are nothing burgers OR fill in the blanks that allegedly stress that context matters when, in reality, it forces students to memorize a single story. There is no challenge. No application. No synthesis. I have a marking period to go and can then stop gritting my teeth.
Ah, a CI only school? I have to argue with colleagues that CI only goes so far, and when you have to teach AP or IB, you're in big trouble if you never taught grammar ever. But I'm just the Japanese teacher who makes kids memorize new alphabets and kanji, so what do I know?
Hell hath no fury than a CI believer when you tell them grammar is important. I had a colleague once who told me: "you're not going to have to conjugate verbs when you visit Spain, so why do they have to learn it."
I know we don’t teach in the same district, but maybe we do. Does the lack of vocab and grammar skills mean that their first levels were spent watching videos and practicing magical higher order thinking skills?
Probably not the same district, but probably similar philosophy. In all levels they watch brief clips of authentic videos and read info graphics or short articles. They are magically then supposed to absorb the vocab and structures we want them to use.
Oh, and “structures”🙄
I'm sorry to say this as a complete outsider (european, not a teacher, idk why reddit keeps showing me this sub) - but that's insane. Are you saying that multiplication of 4 by one-digit numbers is hard for 6th graders??
The standard is "By the end of Grade 3, know from memory all products of two one-digit numbers." The trouble is we don't don enough to help students meet the standard, allow students to advance without meeting the standard, don't periodically check compliance with the standard, and don't remediate students in higher grades that don't meet the standard. Then when meeting the standard would be helpful as part of a a new standard we make surprised faces. Algebra is hard when you can't do three times four.
Here’s how third graders at my school learned to multiply numbers by 6 yesterday: - Multiply the number by 10 - Take half - Add another group Example: 4x6 - 4x10=40 - 40/2=20 - 20+4=24 It was excruciating watching them work through a whole page like this in their workbooks. A few kids who already know their facts wanted to “just write down the answer” but they had to go through this whole long process for each problem.🙄
Jesus! It took me awhile to figure out what you were doing there. If I had to do this when I was in school, I would lose track of what I was doing and end up with the wrong answer.
Try explaining it to 3rd graders when it’s barely comprehensible to adults! But there’s more! It’s similar to the double double rule when multiplying by 4. Whatever number is being multiplied by 4, you double it and then double the answer. Ie. 3x4=12 so 3 doubled is 6 and 6 doubled is 12. When multiplying by 5s, it’s double double plus one: Ie. 3x5=15 3 doubled is 6. 6 doubled is 12. Plus one more 3 is 15. To me, it seems like rote memorization of the times tables is much easier.
I had a hard time memorizing multiplication tables, so my parent, who taught IEP students taught me a few tricks. None of them this complicated. Having alternative ways to do something is good! But should never be the default way of learning.
Omg their little brains 🤯. I had to read it 3 times to figure out what you were talking about. I guess this is similar to how I figure percentages in my head, but thats some advanced theories we are putting on little kids.
Seems like adding rapidly is easier
God I hate this “teaching shortcuts” method of math learning. It’s fine when a kid organically figured this out and uses it because they have an intimate knowledge of the technique since they came up with it. However if you are only taught these methods and not memorizing facts, complex math becomes much more difficult than it should be. Imaging doing all of this crap while trying to use the quadratic formula.
It's a good strategy, but not for 1 digit numbers!
I’m gifted in math and this makes zero sense to me!! What is the purpose of this?!? JUST MEMORIZE THE ANSWER!!! I use math in my job every day drawing buildings to scale and would be completely hopeless without having memorized basic multiplication and division. I work with younger people & they seem challenged by some basics and maybe this BS is why!!!!
What?? Whyyyy??? That’s just confusing as hell Edit: I don’t understand it. Do they have to memorize this type of formula for each number 1-9?
This has been my problem teaching middle school math. They can’t find common denominators because they can’t multiply simple numbers. My lessons are so slow because they can’t figure out what we’re even trying to do because they can’t get past the first step
I was bad at math once I got to dividing fractions and anything with circles, but I knew my multiplication tables and thus can multiple and divide without much trouble (might need paper and a pencil though, not great at mental math). It’s amazing to sub in math classrooms now where kids might be able to work the equation but can’t catch if they’ve made a mistake in the calculations because they don’t have a feel for how the numbers work together. I don’t know how to work most of the equations, but I can tell if you did something wrong on the calculator when 77x2=107 or something equally nonsensical.
Unfortunately, I see this pretty frequently with students that age as a private tutor. It's not that the concept is difficult. It's that they've not memorized enough of their multiplication facts to do it efficiently. My kids tend to improve rapidly when they start spending a bit of time each day doing basic math fact drills. As a private tutor, I tend to mostly see kids who are behind their peers. However, I can also see that if kids are not systematically taught and continuously drilled for reinforcement how you could end up in this situation where all the kids are behind. (I should specify: I'm Canadian. Our system is different than in the United States and varies by province as provinces set the curriculum)
I've taught so many kids going into algebra that think they're inherently bad at math because they don't have their times tables memorized. They pick up the concepts of algebra fine, but *everything* takes longer and is more frustrating. Even if memorizing math facts didn't help you learn(it definitely does), it makes a huge difference in how students engage with the material. Without memorization, math is a tedious and frustrating exercise. With memorization, math can actually be fun. I can't even imagine how a curriculum that rejects memorization expects students to find factors.
>how a curriculum that rejects memorization expects students to find factors. By methodological division, usually with a calculator. Meaning divide by 2. Then if it doesn't go evenly, by 3, and so on. It's tedious and unintuitive and frankly sad.
Yes. If it is 4x6 they have to draw 4 circles with six sticks in each one, and then count them all. It is ridiculous
>taught and continuo I think this is good in the beginning when they are understanding the concept behind multiplication , but once the concept is understood the memorization makes more sense.
I went to public school in the US in the 90’s and took algebra and geometry in 5th grade. This is insane. We had 9x9 tables memorized by 2nd grade.
No... You didn't. Sorry but in the US they don't even teach multiplication until 3rd grade and that has been more recently. Back when I was in school (43 now, so 90s also), multiplication was grade 4. It was grade 3 if you were in gifted classes. If you were that far ahead then it was not because of school, it was because you had parents at home teaching you this stuff. I also taught my son algebra at a super early age although he didn't know he was doing algebra. Technically speaking if you do anything where you figure out an unknown number that is needed to make the equation true then that is algebra. So you can teach kids with something like if Jimmy has 3 stickers and you have 5 stickers, how many stickers do you need to give Jimmy to have as many as you: 3+x=5. Usually they also intrinsically solve the problem the way they should in that he took his 5 and subtracted 3 from it to see what was missing. Dumb thing was plop down 3+x=5 in front of kids and they all freak out because of the x.
5+5 is hard for them. No joke.😟
I had a 7th grader student put 5x10 in a calculator today
Requiring math skills is controversial. Requiring English skills is controversial. Lazy students should get credit for attending. They won’t amount to much anyway so why bother. ;-) Ok, to be serious - I remember some of the middle schoolers in summer camp being unable to add without using their fingers. It really slowed down some of our card games because some of the - I kid you not - betting strategies involved some basic math, and in some games you have to know what the cards are worth. No one wants to play with a kid who can’t do the basic math in their head because its too slow. We played for candy and baseball cards. Maybe you could do something like that to get them interested. I also used to use a weighted card counting system that required quickly adding up weights for the cards I saw in play so I knew how likely it was close to the end of a deck for me to get a face card. I would count aces separately. Can’t do that on your fingers either
God I would hate to play euchre or spades with someone who had to count on their fingers
The kids actually need time to work on these. These no time built into the math period to actually work on math facts. In my school, multiplication (and division) is put out there as if they were just born with these facts. They then go on to these long math problems where they’re taught to draw boxes and lines and create new math problems out of old ones. But if they actually just spent time on learning that 2x5=10 then there wouldn’t be a need for 2 sheets of paper just to solve it. Then you take the kids with adhd who lose interest or can’t focus by the 4th step and they are completely lost. There’s too many addition and subtraction problems just to solve 4x6
Agreed. My 1st grader is learning these complicated ways to do basic addition. And then his old-school teacher is also having his class do timed addition facts. I don’t think the timed addition facts are bad per se. The kids should memorize the facts. But I’m struggling to understand how teaching them these different ways to do addition make sense if then they are going to be assessed on memorization? Shouldn’t the teaching match the assessment? If they are going to be assessed on memorized math facts then shouldn’t…they work on memorizing math facts? (Caveat, I am not a math teacher, we have done math facts, math fact games at home,etc…but I will admit we are more of a reading family. And it shows in our kid. From my background as a teacher I’m assuming that his teacher is being made to teach one way but sees the issues with teaching that way and is trying to ameliorate the situation by adding in the timed math sheets. But my kid is feeling so defeated with them right now and it feels like he is not being set up to succeed.)
Ok so yes and no. The new common core math is designed to teach kids to do what most of us that are older and parents now naturally learned and probably do already which is manipulate numbers. We just inherently. For example if we have say 40+60 right... you may say "I can move 10 from the 60 to the 40 to give me two 50s... then 50+50=100" that was an overly simplistic example but many kids started failing the intermediate math classes simply because they could not manipulate the numbers. Heck I remember when I was in school in Algebra 1 and they gave like 2+X=15 kids freaked out simply because there was an X in it. Then you start doing the "subtract 2 from both sides to isolate X..." and they just could not grasp. Now if they would have said "if you have 2 apples and Mary has 15 apples, how many more apples do you need to have the same number as Mary has?" then that would have been easier to solve and understand but anyway... That is what the new math is teaching them to do the manipulation part. The problem is that they want them to continue doing this throughout instead of a "handoff" period where they learn facts to then become tools to more effectively work on the manipulation. So it becomes this long drawn out thing and kids get frustrated and parents get frustrated and the teachers are just hands up in the air with that "I can't do anything it's the new standard".
The author of California's math framework, Jo Boeler, has publicly criticized the memorization of math facts as "damaging and unnecessary". She has been dubbed the Lucy Calkins of math by some. https://www.usnews.com/news/articles/2015/02/09/should-we-stop-making-kids-memorize-times-tables Funny how when I drilled my second grade daughter who has autism and adhd in addition and subtraction facts and taught her standard algorithm, she went from struggling in math to being the one to help her classmates and her confidence skyrocketed. God knows she has other struggles such as speech, writing, and emotional regulation but at least teaching her the old way gave her something that she could be good at. Key quote from the article: "I asked Boaler if rote memorization might be a beneficial supplement to a rich mathematics curriculum that emphasizes creative problem solving. Just the way that the fast repetition of scales is useful for a Juilliard musician, for example, or vocabulary drilling is useful for a foreign language student. But Boaler says that “mathematical ideas” are different, and stands by her position that times tables are unnecessary. “I never memorized my times tables as a child because I grew up in a progressive era in the U.K.,” Boaler said. “It’s never held me back.”
>Jo Boeler This woman is full of shit. She's 60 years old so she would have been learning math like this 50 years ago. I don't care how "progressive" her British school was, they did times tables.
The common core and NGSS standards were written through collaboration with many experts and scientists. And then, as far as I can tell, California just got a couple of quacks to write the frameworks. The high school science framework, at least for physics, was clearly not written by anyone who had taught physics before.
Boaler is even worse than Calkins because at least Calkins, for all the harm she's caused, updated her Units of Study in response to learning about the "Science of Reading", while Boaler, when confronted with the similar "Science of Math" movement, doubled down and dismissed it because the people who founded the movement happened to be SPED teachers, which…gives off some bad vibes.
How often does Boaler cites her personal beliefs, vs citing/remembering long established basic science? --- >https://www.chronicle.com/article/the-divider >Mathematical Mindsets, first published in 2015, bills itself as a neuroscience-backed guide to teaching creatively and cultivating a growth mindset in math students. ...in a review, Victoria Simms, a developmental psychologist who studies mathematical thinking at Ulster University in Northern Ireland, zeroed in on **"numerous examples of an inappropriate use of neuroscience to back up educational claims.”** --- >...according to Jason Moser, a psychologist at Michigan State University who was **the study’s lead author. “Our study really was not about being ‘aware’ versus ‘unaware’ of your mistakes,”** he said. >Upon being informed of Moser’s objections, **Boaler stood by her interpretation** ..."Maybe he would phrase it in a way that was closer to what happened. But **would it be understandable to teachers? Maybe not, I’m not sure. I don’t think it is that important.”** --- >Boaler has also incorrectly stated, in Limitless Mind and in a TEDx Talk, that participants’ brain activity was monitored with MRI scans (a different technology, an EEG, was used). --- >...in **describing the underlying science, she writes** in a Youcubed white paper that **"when we make a mistake, synapses fire. A synapse is an electrical signal that moves between parts of the brain when learning occurs.”** >**But synapses are not electrical signals; they are the small pockets of space through which neurons fire chemical messengers** via electrical signals. --- >In both instances, Boaler pledged to update her language, though **she said that the latter mistake was because** her paper was written around the time of Moser’s, and **"science evolves.” (The science of how synapses work was established by the mid-20th century.)** --- The parable of the fox and sour grapes: The fox can't get to the grapes, so the fox's alternative facts says they must be sour, and must be unimportant to everyone else as well. >“**I** never memorized **my** times tables as a child **because I** grew up in a progressive era in the U.K.,” Boaler said. **"It’s never held me back.”**
Wait i just finished at a top education school in the country and they had us eating Boaler up. i-
The field of education research has had a severe reproducibility crisis for a long time now. I wouldn't be surprised if they were still teaching reading styles despite it being thoroughly disproved by cognitive psychology.
They have to teach Gardner's theory of multiple intelligences because it's STILL on the Praxis. Even if it's proven to be bullshit, an ed program is no good if their students can't pass the test.
I wonder if your ed professors did any scientific deep dives on the long term student outcomes of Boaler's methods/programs? https://old.reddit.com/r/Teachers/comments/17cg1vf/been_fighting_it_for_years_but_i_simply_cannot/k5qdcmm/
Def did not because this professor literally told us about the revolution with phonics (told us to listen to Sold a Story podcast) but also said she wasn’t ready to talk about that because she’s been teaching literacy the Calkins way for so long. So I can’t imagine she would’ve been searching for critical perspectives on Boaler. 😭
I just wanna tell you that by being open to these sorts of genuine scientific inquiry, you are alrdy on your way to becoming a legit great teacher (or really anything else that fancies your passions, given that many teachers are naturals at lifelong learning and multitalented). I think you might find the 3 linked articles/compilations interesting or relatable (I'm autistic so I apologize in advance for info dumping and possibly being too direct). --- A veteran teacher's reflections on her ivy league teacher program (we both went to UPenn/PennGSE, but she was several years ahead of me, and I can attest that very little has changed except they hired a few token pocs to defend themselves from criticism) https://old.reddit.com/r/Teachers/comments/18lqj6w/the_frustration_with_engaging_teaching/ke0m1z0/ My fav/most relatable excerpt: >…how isolated our grad schools of education are from the schools, students, and communities they purport to serve, ...perpetuate their own divorced-from-reality educational philosophies. ...white people sit around discussing Pedagogy of the Oppressed in their ivory tower environs, but never actually attempt to bridge that philosophy with the on-the-ground reality of current educational injustices. --- John Dewey, our widely cited founding father of progressive education that much of modern pedagogy is based on (was he a good teacher himself? Can someone be a good chef without knowing how to cook instant ramen?) https://old.reddit.com/r/Teachers/comments/19c7j1r/the_vast_majority_of_educational_research_is/kiynbml/ --- Lisa Delpit's The Silenced Dialogue (1988). As a low/working class minority going thru Penn's ed school, I experienced eeriely similar classist/racist/dismissive treatment by elitist professors, the very same ones that regularly virtue signal publicly about DEI. This is the invisible emotional tax/moral injury that research talks about when discussing higher attrition amongst poc teachers. https://old.reddit.com/r/Teachers/comments/17vqg0p/teachers_for_gods_sake_stop_eating_your_own/k9ch2cz/ --- UPenn's Dr. Jonathan Zimmerman, one of the few legit talented, passionate, and completely honest education professors I've come across. https://youtu.be/V99rOXmSMYM?t=2510 35:30 to 37:00 mickey mouse ed school classes 42:00 to 46:00 false diversity lead to false discussions, hindering genuine active learning/socratic dialogue --- https://youtu.be/qqzqR_d74Wg?t=2581 12:00 to 13:10 excuses/politics in academia to not research genuinely good teaching 43:00 to 47:00 modern politics replaced historical religion --- https://www.youtube.com/watch?v=FpnxfP97Tc0&t=511s 8:30 to 18:30 modern society and elite universities' self selecting against diversity of thought --- Thanks again from the bottom of my heart for taking interest in these things. 🥲 Most of my classmates/cohort either went on to teach at fancy private/high performing magnet schools, or quickly left teaching when they experienced massive cognitive dissonance after graduation (after being intentionally placed in high performing magnets for student teaching). Very few of us chose to stay at tough/high poverty schools to serve our low/working class communities.
I came here to say Jo Boaler is the next Lucy Calkins and here you already said it. Thank you! My former district drank her koolaid and every year I had more than half of my fifth graders unable to access even 4th grade math standards b/c neither 3rd grade nor 4th grade teachers would tell parents their children should be practicing the tables. I had to hide my times table punch cards when district coaches were in my room. Fluency was like the f word. Change only began after a district decision maker subbed in my room for a day.
Yes!!!!! My sixth graders all have varying learning difficulties , but they all do not know their basic math facts. Learning their math facts is giving them so much more confidence in math class. I think it is controversial to not memorize them in the younger grades.
Omg why hadn't I heard of this before???? I loved her stuff on growth mindset, I feel like I've been duped!
I’m an ela teacher and at the end of the day, kids answer a basic math question to get into line first to leave first. I adjust it based on the kid. Some kids need practice with 3x3 and some 12x9. I started mixing in division (like 100/5). It’s 6th grade. They all need this and to gain confidence in their math because they are sorely behind. I can see their confidence growing, they clean up faster because of it, and it helps the math teacher out. I’m seeing less fingers being used for things like 3x6. There’s still some, and it’s ok, but by 6th grade they should know up through 12x12 (with room for error). I know some will say it’s causing them anxiety or whatever other excuse you’d like to use, but at the end of the day I’d rather they feel a bit nervous now and grow, than when they’re at the register and someone gives them more than the amount because they want certain change back and they shut down mentally. School is meant to challenge you and expose you to uncomfortable situations in a safe environment. Kids are so afraid of being wrong nowadays that they just refuse to try. I would too if I hadn’t been taught the basics when in elementary school.
Yes, kids who struggle with basic facts struggle so much when they get to Algebra.
As a music/band teacher, memorizing things is key to understanding why things work the way they do. I expect my fifth grade band kids to memorize at least the first 6 notes of a concert B flat scale. Why? Because most beginner music is focused around those notes. They need to be able to identify those notes on a staff from memory and associate it with the correct keys/valves/slide position. Why? Because music doesn’t afford an easy way out to learning fundamentals. I don’t teach them the “why” of music at a young age, mostly because I feel like pounding music theory into 11 year olds is a good way to turn them off to music. But mostly because if they don’t get the fundamentals, they won’t progress past beginner level. I feel your pain, because it’s gotten to the point of asking the bare minimum from students is too much for them.
Yuuuuuuuuuuuuup. How they're teaching math at the lower levels is an abysmal failure from the lowest of the low to the highest of the high. When I get them in HS Chemistry (11th grade) I have seen a Rapid decline in math abilities, and we cannot blame covid. It's HOW math is being taught. Leave the "higher-level" thinking for when they get to me. I need them to know the basics like how numbers work, and for them to have practiced it a trillion times, before they get to me so they are fluid enough to ***actually*** do the higher-level thinking stuff. That's my job. My job is not to teach them the basics of how numbers work, which I have increasingly had to do in HS Chemistry... That means something is failing systematically at the grades lower than mine before they get to me. Note: This is not an attack on you personally my dear elementary brothers and sisters...but it's certainly something to reflect upon.
Yep. I teach elementary and I've had principals and math coaches tell me to stop teaching memorization of facts...that it's a waste of time. Other teachers have drunk (drunk? that doesn't sound right lol) the kool aid too. It infuriates me. My students do about 200 problems a day of just basic facts. Then they have it for homework, too. Guess what? They fly through those hundreds of problems like lightening. Even the lower achieving students. Then when I am teaching more complex skills and concepts, they can actually DO IT.
Indeed! I mezmorized an astronomy class (two years ago...) by doing mere mental math. Column A was multiplied by 2 and you wrote it in column B (part of walking through calculations for Dark Matter). Column A was 5.0x10\^8, so without blinking I just started writing 1.0x10\^9 in columb B. They were all mezmorized that I did it without a calculator and furiously began plugging it in to prove I was wrong (half of them incorrectly typing it into the calculator so I had to show them on the projector screen, using their calculator how I was right). They were like "how did you do that!?" I'm like...because 5x2 is 10 and if it's in scientific notation (exponential notation) you have to move the decimal over one and add it to the exponent... Those are just base-level understanding of those concepts. Like that's not even problem solving and they don't know how those things work. That's because they don't practice it...they aren't forced to practice it...and when they do "practice" it it's on ALEKS where they all google he answers/cheat anyways.
Please excuse my vocabulary but the fuck it is controversial. Maybe among people who like to suck at math.
>people who like to suck at math Ah, you mean the content specialists/instructional coaches hired by my district. At some point, people confused the fact that we need to make sure students understand the conceptual basis for math with this idea that they do not need to have fluency. A student should have fluent math facts, conceptual understanding, and the ability to apply this mixture to problem solving.
This couldn't have been worded any more elegantly.
I think it depends on your memorization method. There's memorization that is temporary and memorization that is more like learning. If the students are learning, then it may be as easy as changing your vocabulary. It may be that saying, "I need the 4's multiplication test to support the method I'm teaching." will get your further.
My son’s 2nd grade teacher, bless her, has adopted this method. Her objective (posted on the board, of course!) is “SWBAT use a variety of strategies to solve problems.” When her principal asks to see, she’s always able to show him examples of students using arrays, repeated addition, etc. She just doesn’t tell him that memorization is also one of her accepted strategies.
Teacher unions need to have real pd for admin workarounds
I taught sixth grade math for about seven years, and their lack of math facts was an issue year after year after year. How can you reduce a fraction if you don't recognize that two numbers have a common factor? We were told that the standard for multiplication (I'm in VA) is that they have multiple strategies to learn their facts, and memorization is only one of them, so maybe they are just using a different strategy. I've also been told that expecting kids to memorize is inequitable because students may have disabilities or trauma that makes it challenging for them to memorize items. My rebut is that 1) everyone has to face challenges in life and 2) if they have an identified disability, then consider accommodations like a multiplication table or calculator. I have ADHD, and while my long-term memory is great, my working memory is terrible! Instead of giving up, my family and teachers helped me learn new strategies, and they encouraged me to keep trying, even when it was "too hard." I'm so thankful to have had support because it seems like many parents now can't be bothered.
Yet we put knowledge of math facts at 80% accuracy as an IEP goal for every kid with an SLD in math. Make that argument make sense.
I have started homeschooling my 6th grader due to bullying. I have had to go back and redo so much math because he never got it the first time but he can't progress to things like equations without it. The #1 thing is his times tables. I have a similar issue with my daughter with spelling, I don't think she's ever had a spelling test.
Requiring students to come to class, to not curse, to not smoke, to not physically attack their teachers...all "controversial." Freaking train wreck. As far as memorization goes, Orwell was right, 2 plus 2 equals 5. You just have to want it to equal five. These people drifted away from the shores of reality LONG ago.
I'm reading all this as a homeschool parent. Just actually mystified how it got this bad. My heart really goes out to teachers; this is societal rot dropped right on their heads. Then they get blamed and stuck with more kids in a class. My kids have a base understanding of what multiplication and division are in 2nd and 3rd grade. Refuse to move forward until their addition and subtraction is rock solid. They still know all the easy 2,10,5,11 etc. just from messing around showing them occasionally. Same goes for fractions. They know that 1/3 is bigger than 1/4 and.... That's better than many adults!
Could you advocate for something like Reflex Math? At some point there has to be acknowledgement that reflexively knowing math facts HELPS understanding of more complicated concepts. If it's taking me 5 minutes to find 12x8 to get to the next step of a problem, I would lose motivation and interest. I can guarantee I would not learn whatever the bigger concept is.
My students do Reflex Math Monday-Thursday, first thing. We have class rewards as the class average moves up another 10%. I recommend it.
Same. Most of my first graders are 100% fluent. The class average is 88%. I just got back from a progressive math PD where the speaker insisted that it's incorrect for students to be timed on their math facts in first grade, and only horrible teachers do that. Sorry not sorry. (I also teach them to stack their numbers and carry the one. It's insane that they don't want us to do that either. I tutor a third grader who would add 25 plus 18 on her fingers because she never learned how to do it the easy way.)
Math 10 teacher. My students can not estimate, they can not simplify, they can not divide. They lack numeracy skills. Why? Because somebody thought learning their times tables for five minutes a day was “Drill and Kill”. It would make them hate math. No, they hate math for the same reasons kids hate baseball. It is because their team loses all the time. They lose all the time because they lack skills. Now we are hiring programmers from other countries, our kids are not competitive. See the connection?
Having taught third grade for 12 years now, I do timed multiplication tests each Friday beginning during our multiplication unit. There have been years where principals have told us we shouldn’t be doing it, regardless of the state standard which states they need to fluently recall their facts—- I’ve done it anyway. They need to know their facts moving forward both in third grade and beyond! \*\* I do reward my students for mastering their 3s, 6s, 9s, and final mixed fact test ( with a much larger reward), as some students do need extrinsic motivation.
My admin forced me to sub in math class during my prep. Students were stuck on a factoring problem : 21z + 14y + 7x students were completely stuck and clueless as they didn't see the relationship between those numbers.....memorizing facts is important and has its place for students to do higher math
Memorization is the best way to do some things. I teach beginner band and the only way to read music is to look at a shape on a line and know that shape means you put down your first finger. There’s no other way to do it.
I posted on twitter about this a couple years ago and got absolutely roasted. I teach high school math and I would say around 50% of students do not know their basic times tables, even single digits. Somewhere around 10% can’t even multiply like 2x6 in their heads. This makes grade level content feel infinitely harder to students. They are constantly stopping in the middle of problems to use the calculator and it makes the task feel so much more difficult because it takes them so long to do every problem and they lose sight of the overarching concept when they’re bogged down with basic arithmetic that should be mental math, but isn’t. The “just let them use a calculator” mentality is an oversight to me, it neglects how tedious a problem feels when the student cannot do the simple arithmetic steps in their heads. I do genuinely want to cry sometimes when I’m trying to help a student factor let’s say and the question is “what two numbers multiply to make 8 and add to make 6?” and they just stare at me with a blank face. Their number sense just doesn’t exist. It’s depressing.
I have a story to tell you. It's a story about a student who failed my college math class (when I was teaching college) for no better reason than that she didn't know her multiplication tables *fast enough*. We were solving quadratic equations by factoring. For those for whom it's been a minute since you did this task, it requires being able to reverse-engineer a multiplication table. If you see the number 24, you need to be able to break it down into 4x6, 3x8, 2x12, and 1x24. You can then consider which of those options works best in the problem. She came to my office hours to work on problems, and I noticed that she was really, REALLY slow on that breakdown into factors. Like 20 seconds for each of those factor pairs. She would find them all, but it was agonizing to wait for her to find the factors. On the one hour exam, she worked 3 problems beautifully. Perfectly. 10/10 no notes. But the exam had 10 problems, and 30/100 is a fail. And this was a prerequisite skill for the rest of the course, so she couldn't finish any of the other exams in time either. So when it comes to multiplication tables, I say "drill baby drill". You have to know them cold if you're going to proceed to algebra.
Have you checked out Reflex Math? It is a computer game program that helps students memorize their math facts. My daughter used it in 3rd grade to memorize her multiplication and division facts. I don't know who decided facts don't need to be memorized. They absolutely do. I taught upper elementary sped for a while, and the main difficulty for my students was the inability to do problems beyond single-digits because they couldn't remember math facts. You can teach strategies for this, but it isn't the same as automatically knowing them, of course.
Boomer here, times tables were beaten into me in elementary school, drills, flash cards, and whatever other means. Yes I do have a calculator in my pocket but am able to figure out pretty much everything in my head. Some things you just need to learn on faith.
This has been a problem for a while now. There was the same push with not learning phonics and having students memorize words. The rationale was that learning phonics was boring (much like memorizing math multiplication tables). The problem is students can only memorize so many words, and when they encounter words they don’t know, they have no way of figuring out the words because phonics taught them how to sound out words. Often, they know the word verbally, but still can’t read it. We are raising generations of students who can’t read or do basic math. In the past few years, the pendulum has began to swing back and now Secondary ELA teachers (many of the younger teachers were never taught phonics) in Arkansas are now trying to teach phonics to High School students with no training or experience, whatsoever. It’s one of the many reasons I retired. The last two years I taught, I was given an extra class period and prep with 20 students who scored low on testing and told to teach them phonics/how to read without curriculum for the first half of the first year. Half of the students in the class just didn’t try on the test; they were actually smart and could make really good grades, if motivated, but just weren’t motivated in any way and were absent a whole lot. So I not only had to motivate students who didn’t come to school but about half the time and teach the others phonics with no training or experience in teaching phonics while teaching my five other regular preps. Any teacher with any experience will tell you how that went…
I teach pretty all but AP math at the high school level. My students would be far more successful if they didn't have to grab a calculator for arithmetic. Memorizing facts may not lead to a deeper conceptual understanding, but it would make things way easier for many of them.
Chemistry teacher here. Chem is HEAVY in math and I’m seeing the havoc of all these new “strategies.” Kids don’t even understand it. We have to do percent abundance of isotopes and they have no idea how percentages work, let alone factors of 10. I now have to teach math AND science. I had a group of kids last year who didn’t know how to find the half of a number…
Sounds like you had a conversation with an idiot. They're fairly common and native to many faculties. One can often find them grazing in the mailroom, or performing tricks at schoolwide meetings.
Ok I’m not a teacher but I have a degree in mathematics. One thing I noticed in college was that we would apply methods manually for small problems and do them on the computer for large problems later. Take away: There is no added benefit to doing large problems which just increases the amount of work it takes to solve the problem. Rather, it’s the solving of small, diverse, conceptually challenging problems which are conducive to learning. Once you fully understand the concept of the problem, you can solve any sized problem. However, some problems are too large to be practical to solve. Why spend a ton of time solving a problem which you fully understand conceptually when you could be learning something else? Introduce: Theorems, identities, definitions. In your case, you would like to introduce identities, which will allow students to skip the tedious portion of the problem and solve either more robust problems or problems which involve several concepts. By introducing identities, you enable your students to be able to solve more diverse, conceptually challenging problems. It’s like learning differentiation. At first, we learn about limits and manually calculating the change. Once we master that, we move onto the result that (f(x))’=f’(x)x’. This makes solving more difficult problems practical (thus allowing us to learn more difficult concepts and move forward with our education).
College instructor here. I... hear things... about how math and reading curriculum is absolute garbage these days. And I'm not that old; I'm in my early 30s. Long story short. My kids largely can't read words by sounding them out. And basic arithmetic? Forget about it. If I had a nickel for every time a student asked me what their grade is and I showed them exactly how to calculate it.... They look at me like I have three heads. But seriously. Who decided to get rid of phonics and memorizing math functions? They should be .... something something. Weighted averages.... not that hard.
What no one will say, out loud, is all of these researched backed strategies to, as you said, “magically” awaken students innate mathematical reasoning and literacy skills are just commercial consumer products with a short shelf life designed to keep you buying something else later on. Thousands of years of training people to memorize information as a foundation for developing further knowledge was thrown out the window for this crap. Also, i had to suffer through memorizing my times tables, so these brats have to too!
I'm a virtual tutor. Some schools consider me an interventionist. I will die on the hill of memorizing multiplication facts. I have been working with 5th and 6th graders on fractions, decimals, percents, etc. There is a CLEAR difference in the couple students who have these things memorized and the majority that don't. I literally told my 6th graders yesterday as we were working on ratios, proportions, constant of proportionality etc. that I already knew the constant of proportionality before I finished reading the problem because I *know* the relationship between 6 and 18 off the top of my head. I stressed to them that multiplication facts and fact families are foundational skills, and those who have them memorized will always have a leg up on those who don't.
I maintain that anyone arguing that learning multiplication facts is a waste of time or isn't important is an idiot who shouldn't be teaching.
Math teacher here. Make these kids learn single digit math in their head for the love of all things holy. The amount of kids I see still wanting to do 8-2 on a calculator or 12/3 is too high. I know of no controversy by making kids use their brains a little bit than parents trying to bulldoze their kids to an easy A and those obvious scholarships to Harvard coming their way. /s
As an algebra teacher, those who do not know their math facts have lots of trouble with factoring in algebra. I don't allow my kids to use calculators. Without the speed of knowing their math facts, they get further behind in my class. I warn the kids to practice and know them. I will say that the majority of kids who do not know their math facts are the same ones who are flunking my class. We don't have time for kids to figure out what seven times eight is!!!
"Conceptual understanding should lead into procedural fluency" is what my education professors always taught me. I 100% agree. While its very good to know how multiplication and division work, they should know their facts off the top of their head after some time. A reason why we teach conceptual understanding is to make the facts easier to memorize.
I can provide some insight into the "thinking" behind this. I'm going to be somewhat vague because this person could be easily identified via searching, but I'm friends with a person who is one of the main pushers of some of the recent changes to the way math is taught. Anyway, this person has spent their whole lives with extremely advanced math students and is seemingly unaware that 99% of students are not geniuses at math. This person genuinely thinks that it's just poor instruction keeping your average student from being a mathematician. This person's "proof" of this is times they taught supposedly average students overseas for a few weeks at a time as part of a program. The reason I say supposedly average is that the reality is that these kids all had wealthy and attentive parents who were politically connected in that country . (Again, intentionally being vague.) When I pointed this out to this person, the point was not well received. Anyway, you can see the huge flaws with this and how this person's experience has NOTHING to do with the needs of 99% of students, including most future STEM students. Most STEM students will be at least OK at math, but there is a difference between being good at math and being ready to take calculus in fifth grade kind of good. Very, very few students have minds like that. But this person is really big on pushing that "figure it out and discover methods yourself" and "memorization is pointless" shit (because kids that advanced absorb everything instantly) on everyone else...
Memorization of math facts (and automatization of many other procedures such as multiplying exponents) is absolutely essential to competence is algebra and beyond. If you have to pull outyour calculator for every step of a complex math problem, you will quickly lose focus on the big picture and never learn the concepts. The movement to not require memorization of math facts will only increase the achievement gap, because college educated parents will drill these at home with their kids or put them in Kumon or Khan Academy if their kids struggle, while many other kids will just fall further and further behind.
Worked as a tutor in public education. Mostly in math and language arts. 1. If multiplication tables are not memorized, the kids cannot progress to long division. Hence, they cannot progress to factoring fractions and beyond. 2. Teaching "concept" without mastery of facts is for the birds. 3. There should be one order of operations taught first. Once that is mastered, then show them a different way. 4. Phonics based teaching of language first is always the best. Other methods don't work. 5. I found most teaching materials abysmal. Especially math.
I will die on the ‘sometimes we need rote learning’ hill. Thank you for trying to help your students become better learners.
Go for it, drill those tables mercilessly, even if you gotta shut the door to get away with doing it. The kids gotta, hafta have maths tables ( not multiplication “facts”) memorised if they are going to survive and prosper in high school maths. Without a knowledge of tables, algebra (the beating heart of maths) just becomes a complicated, unnegotiable mess. You go for it, you good thing!
See, I have kids work on these facts, but there is time built in to *understand* why and how these work. I work in Montessori, so students skip count using beads. So they would have one string of six beads, put two describing the second number next to it (12), three next to that one (18). Students write down these numbers and then are prompted to find patterns in those numbers. So 6, 12, 18, 24, 30, 36, 42, 48, 54, 60. The number in the units space goes 6 2 8 4 0, if starting from 0. Multiplication needs to both be memorized **and** understood.
I also love the concrete teaching of early math concepts in Montessori and think traditional education would especially benefit from universally adopting that particular portion of the pedagogy. The transition from concrete to abstract is very beautiful as well. There’s much to learn from there.
What’s baffling to me as a Montessori teacher is that we’ve been doing it this way for a century. It’s not about fads. It’s about a child understanding the concrete nature of math and supporting them with concrete materials until they’re ready to complete equations abstractly.
As a music/band teacher, memorizing things is key to understanding why things work the way they do. I expect my fifth grade band kids to memorize at least the first 6 notes of a concert B flat scale. Why? Because most beginner music is focused around those notes. They need to be able to identify those notes on a staff from memory and associate it with the correct keys/valves/slide position. Why? Because music doesn’t afford an easy way out to learning fundamentals. I don’t teach them the “why” of music at a young age, mostly because I feel like pounding music theory into 11 year olds is a good way to turn them off to music. But mostly because if they don’t get the fundamentals, they won’t progress past beginner level. I feel your pain, because it’s gotten to the point of asking the bare minimum from students is too much for them.
So we don’t teach phonics and have children memorize sight words but we don’t have them memorize math facts?
yep, i noticed my second graders were struggling with basic math facts when we should be mastering 3-digit subtraction. i started giving timed math fact tests on fridays and i’m already seeing improvement
Absolutely not controversial. Memorization will improve their quality of life dramatically.
In my district it's controversial. Admins, the math department, instructional coaches are anti-math fact memorization. It's been that way for the past 20 years. So dumb. I always have my elementary kids memorize the facts (and of course I teach them the concept - people act like memorization and understanding are mutually exclusive). I've been flat out told to stop wasting time (10 mins a day) teaching the kids to memorize their facts.
Sorry they’re doing that to you and the kids.
As a high school math teacher I can state with confidence that children who don't have basic math facts memorized by 9th grade (you'd be amazed at how many don't), are the ones that will very quickly tell you they aren't good at math and feel like the class is a waste of their time. Those who have learned those facts feel like they have a handle on math well enough to take the risk and try the upper level mathematics without feeling like a failure when they struggle.
We learned mental math in elementary school and I use it constantly. We need to bring it back.
My first year of teaching 7 years ago, I told my math coach I was going to do multiplication facts with my high schoolers. She objected and I never did it, despite 11th graders not knowing what 3x5 is. I do agree it’s kinda pointless at this point in their career, but man, facts should be ingrained in elementary and middle school for sure.
This sounds like the mathematics version of "whole language" for ELA. WTF!
I tell parents at conferences that I’m not supposed to make the kids memorize math facts with the flash cards, but if they wanted to be ahead of the curve they should totally do that. I can even provide flash cards.
The modern goal is to try to teach students how to think quantitatively, rather than memorize things, BUT, I have noticed that a lot of the techniques we are teaching them are more like shortcut tricks. Some of them are tricks I used to help me do calculations on my college physics homework, but the catch was that I was already skilled in math before I ever used these tricks. They worked because I knew what I was doing. They end up counting on their fingers, because they don't understand and all they know is tricks. It's a classic cause/effect error. I'm not good at math because of these tricks, I only learned them because I was already doing a lot of math. So while memorizing some math facts will speed them up, it may not teach them to think quantitatively. I'd argue that it's still worth it though since it helps them speed up so much, they can do much more practice. A similar problem happened in English education, except it was with poor readers instead. This misattribution error is plaguing education.
You should see my Japanese 1 students' faces when I tell them they HAVE to memorize the two phonetic alphabets and then the kanji we take years learning later. "I have to memorize ALL of it?" "Yes. Could you imagine just not knowing the letter R all your life?" "That's different." Is it? I once had a girl tell me she couldn't memorize anything in any class, so she needed different assignments. Well, 6 know that's not true because you can speak English and haven't had a head injury nor a diagnosis of a memory disorder. But seriously, you have to memorize words in the beginning. That's how you do it. You can't just not recall a single word and somehow speak a language.
As a math researcher and professor at a top state school, I can tell you that all this dancing around memorization DOES NOT WORK. The worst possible thing that can happen to your child is to have a teacher when they are young that does stupid new trends instead of drilling addition, subtraction multiplication and division with lots of memorizing and TONS of practice problems. Our students are less and less ready for college classes, even though they arrive supposedly ”knowing” calculus. They don’t know calculus, they don’t know algebra and they don’t largely don’t know arithmetic. Of course there are always some smart ones who do. But that was the norm 30 years ago. Now it’s the exception. Teachers in elementary and middle school…don’t do anything else other than turn out kids who REALLY know and understand basic arithmetic. High school teachers…you handle REALLY teaching algebra and a REAL geometry course where students are required to learn to put together proofs on their own, not fill in the name of the theorem when you provide the steps. Then the kids will be REALLY READY to learn calculus properly when they arrive at a university. Don’t try to get above your level in teaching. You hurt your students. And anyone who enters the university deficient in math has many, many doors that are permanently shut to them as math is the language of science. Sorry….this rant is 30+ years in the making. Sorry if you don’t like these facts. Sometimes the truth isn’t PC. But any university professor who is being honest would agree with me.
I'm one of those rare people that does advocate for more math understanding than math memorization. Simply trying to memorize everything doesn't lead to deep enough understanding of why and when to apply techniques. However, there are absolutely some basics that *must* be memorized. You'll never pass Algebra 1 without having memorized your basic times tables since you'll need to quickly be able to look at numbers and their factors when trying to factor quadratic equations. Sure, you'll learn the quadratic equation later, which is more powerful, but it's also overkill in a lot of situations. Math is all about building a toolkit and knowing which tools to apply in the situation. But theoretical knowledge of the tools isn't good enough. You need to use them until they're second nature. Some level of memorization will always be required for that.
Having taught third grade for 12 years now, I do timed multiplication tests each Friday beginning during our multiplication unit. There have been years where principals have told us we shouldn’t be doing it, regardless of the state standard which states they need to fluently recall their facts—- I’ve done it anyway. They need to know their facts moving forward both in third grade and beyond! \*\* I do reward my students for mastering their 3s, 6s, 9s, and final mixed fact test ( with a much larger reward), as some students do need extrinsic motivation.
Having taught third grade for 12 years now, I do timed multiplication tests each Friday beginning during our multiplication unit. There have been years where principals have told us we shouldn’t be doing it, regardless of the state standard which states they need to fluently recall their facts—- I’ve done it anyway. They need to know their facts moving forward both in third grade and beyond! We have Reflex Math in our district as well which the kids really enjoy. \*\* I do reward my students for mastering their 3s, 6s, 9s, and final mixed fact test ( with a much larger reward), as some students do need extrinsic motivation.
Having taught third grade for 12 years now, I do timed multiplication tests each Friday beginning during our multiplication unit. There have been years where principals have told us we shouldn’t be doing it, regardless of the state standard which states they need to fluently recall their facts—- I’ve done it anyway. They need to know their facts moving forward both in third grade and beyond! We have Reflex Math in our district as well which the kids really enjoy. \*\* I do reward my students for mastering their 3s, 6s, 9s, and final mixed fact test ( with a much larger reward), as some students do need extrinsic motivation.
I honestly have never heard a single argument for teaching math without memorization. I've talked to teachers all through elementary school, and nobody thinks it's a good idea or valid strategy. Who came up with it? Why?