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in which I rant about Common Core a bit
So Firefox/Pocket recommended me this article on the "New New Math" [Common Core] vs. the Old Math, and this reminded me I have been meaning to rant about this since the summer. Apparently ranting about pedagogy is a thing I do now? :P
Anyone in the US who has a child of school age is well aware that the US has recently revamped its elementary math pedagogy system and (more slowly) the curriculum to something called "Common Core." In principle I think is a great idea! Common Core emphasizes having a deeper understanding of the mathematical concepts instead of rote memorizing of equations and algorithms for doing specific calculations.
Until I had a child go through this, my chief issue with it was that teacher training and curriculum were not keeping up with the reforms, so that it was and is often implemented poorly. To be fair this is still often a major issue with Common Core. But I thought it was a great idea when implemented correctly! What's not to love about having a deeper understanding of mathematical concepts??
Now that I have had a child go through this system... In practice, it turns out that actually a lot of the time in arithmetic it does actually make your life easier if you just memorize the algorithm for doing a specific calculation, because that is what these algorithms are for. Here is what happened last summer that completely made me do a 180 on it: E took a programming class (Art of Problem Solving's intro Python class, which I was impressed by and which she enjoyed and which changed my attitude towards homework, but that's another story) and because it's a more mathematically intensive class than most beginning programming classes (the gestalt is that they teach programming at least partially as a tool to do mathematical computations, on an elementary level of course), there was a little test you could take beforehand to see whether you were ready to take the class. So I had E take the test. I didn't anticipate her having any difficulty.
Tears and meltdown and "I don't want to dooooo this!" Now, with another kid I might have understood this, but math is E's favorite subject! What?? I dug into it deeper and it turned out she didn't want to do the long division problems "because they take forever." (There were only three of them!)
I asked her to do a long division problem for me. She did one. (Easier when it's just one, and for an audience.)
And at the end of it I totally understood why she was melting down and refusing to do three of these. I would have too if someone had made me do long division the Common Core way! Because they wanted to make sure the kids understood what exactly was going on at each step in the process, they had to write down all the zeros at each step of the process and add everything up and... It's a lot. It's basically writing down the. entire. multidigit division process by hand. Whereas the whole point of doing long division the way you and I learned it in school is as a SHORTCUT so you don't HAVE to write all of these things down!
I taught her the "traditional" way of doing long division and told her that from now on she was to use solely that method (in order for her to practice it and get it solid in her brain) unless a teacher specifically told her she needed to use the Common Core method (which is unlikely with her current teacher, at least).
This fall I also had to repeat this process with multi-digit multiplication, which I also didn't realize was an issue until a very similar thing happened.
I'd also like to show you this graphic from the article that set off this whole rant today:
So...the graphic says it like it's a bad thing that kids learn the algorithm if a/b = c/d, ad = bc... I mean, I do agree with a lot of what the graphic is saying! I agree that (a) using that algorithm to solve that particular problem is way overkill, and (2) okay, tangentially, just teaching them the algorithm without teaching them why it's true is a terrible idea! Though it's tangential, I feel particularly strongly about (2) because my mom did exactly that and I was sooooo confused and didn't understand at all! (My mom, bless her, is amazing at math but completely and utterly terrible at pedagogy.) But... like... it takes two seconds for a math student to understand why this is true algebraically speaking. Multiply both sides by d, multiply both sides by b. Done.
And of course the Common Core way of doing it is great, it's awesome that kids are learning what proportions really mean, and the connection to linear graphs, that's awesome! And for the specific problem shown in the graphic the Common Core way is definitely better! I'm just saying that... at some point... by the time they get to higher mathematics... they also will find their lives easier if they've learned that if a/b = c/d, then ad = bc as a useful shortcut for algebraic manipulation :P
I fear that what will actually happen after Common Core is that we will turn out a generation of students who don't remember the deeper understanding of the mathematical concepts (because they don't need to know that in their everyday lives) AND don't know how to multiply two-digit numbers or do long division or find proportions that aren't 2/3, which... worries me.
Anyone in the US who has a child of school age is well aware that the US has recently revamped its elementary math pedagogy system and (more slowly) the curriculum to something called "Common Core." In principle I think is a great idea! Common Core emphasizes having a deeper understanding of the mathematical concepts instead of rote memorizing of equations and algorithms for doing specific calculations.
Until I had a child go through this, my chief issue with it was that teacher training and curriculum were not keeping up with the reforms, so that it was and is often implemented poorly. To be fair this is still often a major issue with Common Core. But I thought it was a great idea when implemented correctly! What's not to love about having a deeper understanding of mathematical concepts??
Now that I have had a child go through this system... In practice, it turns out that actually a lot of the time in arithmetic it does actually make your life easier if you just memorize the algorithm for doing a specific calculation, because that is what these algorithms are for. Here is what happened last summer that completely made me do a 180 on it: E took a programming class (Art of Problem Solving's intro Python class, which I was impressed by and which she enjoyed and which changed my attitude towards homework, but that's another story) and because it's a more mathematically intensive class than most beginning programming classes (the gestalt is that they teach programming at least partially as a tool to do mathematical computations, on an elementary level of course), there was a little test you could take beforehand to see whether you were ready to take the class. So I had E take the test. I didn't anticipate her having any difficulty.
Tears and meltdown and "I don't want to dooooo this!" Now, with another kid I might have understood this, but math is E's favorite subject! What?? I dug into it deeper and it turned out she didn't want to do the long division problems "because they take forever." (There were only three of them!)
I asked her to do a long division problem for me. She did one. (Easier when it's just one, and for an audience.)
And at the end of it I totally understood why she was melting down and refusing to do three of these. I would have too if someone had made me do long division the Common Core way! Because they wanted to make sure the kids understood what exactly was going on at each step in the process, they had to write down all the zeros at each step of the process and add everything up and... It's a lot. It's basically writing down the. entire. multidigit division process by hand. Whereas the whole point of doing long division the way you and I learned it in school is as a SHORTCUT so you don't HAVE to write all of these things down!
I taught her the "traditional" way of doing long division and told her that from now on she was to use solely that method (in order for her to practice it and get it solid in her brain) unless a teacher specifically told her she needed to use the Common Core method (which is unlikely with her current teacher, at least).
This fall I also had to repeat this process with multi-digit multiplication, which I also didn't realize was an issue until a very similar thing happened.
I'd also like to show you this graphic from the article that set off this whole rant today:
So...the graphic says it like it's a bad thing that kids learn the algorithm if a/b = c/d, ad = bc... I mean, I do agree with a lot of what the graphic is saying! I agree that (a) using that algorithm to solve that particular problem is way overkill, and (2) okay, tangentially, just teaching them the algorithm without teaching them why it's true is a terrible idea! Though it's tangential, I feel particularly strongly about (2) because my mom did exactly that and I was sooooo confused and didn't understand at all! (My mom, bless her, is amazing at math but completely and utterly terrible at pedagogy.) But... like... it takes two seconds for a math student to understand why this is true algebraically speaking. Multiply both sides by d, multiply both sides by b. Done.
And of course the Common Core way of doing it is great, it's awesome that kids are learning what proportions really mean, and the connection to linear graphs, that's awesome! And for the specific problem shown in the graphic the Common Core way is definitely better! I'm just saying that... at some point... by the time they get to higher mathematics... they also will find their lives easier if they've learned that if a/b = c/d, then ad = bc as a useful shortcut for algebraic manipulation :P
I fear that what will actually happen after Common Core is that we will turn out a generation of students who don't remember the deeper understanding of the mathematical concepts (because they don't need to know that in their everyday lives) AND don't know how to multiply two-digit numbers or do long division or find proportions that aren't 2/3, which... worries me.
no subject
but the insistence that students need to justify themselves at every single step and show their work at every single step to PROVE that they have learned the concepts.
YES. Why does E still need to do this every time she multiplies out multi-digit numbers, even though she's long since progressed to other topics??
In reality the students learn a lot of different methods, so they get confused between them, and they are very very very slow because they don't get enough practice with any one method.
Yes, this is part of what worries me although I see i didn't articulate this well. I could still as an adult do long division without using any of my brain, just because it's so drilled into me. I'm not sure that's true of my child, even though I think she's better at math than I was at her age -- she still has to think about it, and then the way that CC asks her to do it is sooooo slooooow! (She's actually very fast at calculation in general.)
bc there's some pedagogical theory that holds that even kindergarteners can solve equations and do other abstract operations if you call them "number sentences" or something like that. The higher level, more abstract concepts are pushed down to a younger age, but simplified to be age-appropriate, supposedly.
Huhhhh, that's very interesting. I don't know how I feel about this at ALL -- again in principle maybe? But in practice I feel like you might encourage kids not to adopt an algebraic language because they're so used to abstract concepts only using words and visualization and such? (And then my child, who always does things by opposites, was actually so relieved when they finally got to variables and algebraic notation, and suddenly I went from her math teachers telling me how terrible her communication was to her math teacher telling me that she was a great communicator, which was a bit of whiplash I still think is hilarious.) But maybe you have more perspective on how this works in practice?
no subject
And there's so much emphasis on showing work, I have students who think showing your work is a PART of the problem, instead of just a step to find the actual solution. They lose track of what's "process" and what's "answer" but I think this comes from bad prior level instruction, from teachers who weren't really sure themselves.
And like you said, at a certain point you just have to consider that they know how to multiply because there are bigger fish to fry...
***
I think we can waste some time re-teaching the vocabulary, sure. They had to learn what a number sentence is, then at high school you have to re-teach what an equation is! They end up learning the vocabulary twice. But hey, at least your kid can appreciate the notation :) Kids are always stumbling over notation like it's the most difficult part of doing math, when actually we invented notation to make things easier...
no subject
You know what the notation thing reminds me of though, it reminds me of reading music, which of course is notation to make things easier. But bringing up kids playing violin or what-have-you in the Suzuki method, which does a lot (a LOT) of ear training in the early years, often results in kids who freak out a bit when reading music is introduced and never really get at all good at it, which really starts holding them back after a while. (I managed to escape this, along with my kids, by all three of us also learning non-Suzuki(-ish, in my case) piano, which is much stricter about teaching reading music from the very beginning, but e.g. my sister, who never really got into piano as much, has a much harder time, and I've met others who have an even harder time than she does.)
no subject