I looked at my kid’s third-grade math assignment and couldn’t complete it. Not because I’m particularly bad at math but – and this is the funny part – I’m apparently not good at language. The task asks children to “use the Commutative Property of Multiplication.” That’s the actual spelling, and I don’t have the foggiest what it’s supposed to mean and why the words are capped.
On the one hand, I’m glad third-graders are assumed to be able to read this kind of words. On the other, this seems like a way to scare very young children away from math because what is a fun activity at this age is made to sound prohibitively complicated and boring. “Hey, kids, let’s do this fun game about a guy who had two buckets of pears and had to share them equally among his friends” might attract 8-year-olds more than “let’s use the Commutative Property”, is what I’m saying.
Clarissa's Blog 
“use the Commutative Property of Multiplication.”
5x -20 = 0 The “use the Commutative Property of Multiplication.”, what you do on one side of the equation you must equally do on the other side of the equation. 5X -20 + 20 = 20. 1/5 X 5 = 20/5. X = 4
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I ultimately found it on Google but why do 8-year-olds need this terminology is my question.
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Started studying Calculus in 7th Grade.
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That definition is wrong! Commutativity means you can swap two numbers (in this case, numbers that have been multiplied). a times b equals b times a, e.g. 2 x 3 = 3 x 2
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That’s correct. I described the Equivalence Principle. Thanks my bad.
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It should definitely not be capitalized. I am not entirely sure why “commutative” should be in a vocabulary of an 8-year old, and I am saying that as someone with a math degree. The way mathematics is taught to children in the US is an abomination. People here have this aversion to memorization of basic things (such as multiplication tables), but do not think twice about thrusting words like “commutative” on children.
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Exactly. It’s like it’s done on purpose to make kids associate math with unpleasantness.
And I also wonder at why memorization is so vilified both in mathematics and in languages. Teachers of pedagogy say “rote memorization” with such disgust like somebody could really learn a language without it.
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It is OK not to understand everything you are learning for the first time. Every subject has some basics (a set of building blocks) that need to be memorized. Understanding will come later. It is like trying to teach someone to read without having them memorize the letters of alphabet first.
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“like trying to teach someone to read without having them memorize the letters of alphabet first”
Which is basically the methodology of ‘whole language’ approach to teaching reading.
I just barely missed that and was taught with a phonics type method that concentrated on connections between letters and sounds, learning rules and the exceptions (which of course are…. a lot, really… a lot). From a scientific point of view it’s basically voodoo but for children learning to read it got the job done.
I really don’t think I would’ve done well with a ‘whole language’ approach….
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It was much better 20 or so years ago when I was in school, though far from perfect
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FWIW, my children definitely had to memorize multiplication tables (public school in California). They did some memorization in third grade but the bulk in fourth grade – timed tests each week (100 multiplication facts in five minutes). I agree that you need a thorough understanding of what multiplication/division means first, but then you need to just memorize them all as facts to free up cognitive space for solving the actual difficult parts of harder math problems later on.
My bugbear with the way math is taught is the frequent “explain how you know xyz” – my kids fully understand what they are doing and why it works but have a hard time translating that math knowledge into sentences sometimes. I told them it’s okay to write the explanation in more numbers (intermediate equations, etc.).
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Intermediate steps are great. That’s how you show your thinking.
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I remember learning math terms like that as a young child and they didn’t turn me off at all. I don’t understand the animosity.
It’s a word, a term. You need one to reference this rule of multiplication. What word do you think would not be unpleasant yet easy to associate with this property?
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Surprisingly, long, unfamiliar words are not a problem for young kids. I’ve taught names of plants to 2nd graders (and younger) on nature hikes and they will remember a 4-syllable latin name after hearing it once, while my undergrads bitch and complain about having to learn scientific names of organisms and other longish scientific terms- we always have to promise those terms will be limited on exams and give them study sheets with the list of those terms/names they have to know.
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I’ve taught my kids both math, and plant identification, and… I begin to suspect there’s some deep-seated evolutionary survival thing going on there. Show them the plant once, tell them the name– common, scientific, doesn’t matter– and family (mint, spurge, primrose), point out the identifying features (square stem, fuzzy leaves, toothed edges), and note whether it’s edible, poisonous, medicinal, or useful in some other way, and they will remember it forever. Bee food. Fiber plant. Goat forage. Edible tubers. They pay attention like their lives depend on it (and perhaps they did, for our ancestors).
Math terms though? Not so much! They remember the operation, but not always the word for it.
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I once read that indigenous children typically could identify up to 200 local plant and animal species. Orangutan mothers have been observed teaching their young which plants were edible or useful medicinally. Obviously there must be a window where young are hungry for and able to easily absorb this information as my undergrads find it painful.
Sybil
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>indigenous children typically could identify up to 200 local plant and animal species
meant to add “by age six”
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That would be children in general, if they live in an environment with 200 visible local species, no?
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Of course all children are capable of learning their local flora and fauna, which was the point (I learned that factoid while training to lead hikes for schoolchildren at a nature preserve). The point was that usually they aren’t taught about their local species. It’s a lost opportunity.
Sybil
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This reminds me of the “new math”. It hadn’t yet been phased out when I was in elementary school so I got the tail end of it. Apparently, they thought it was a good idea to teach about the commutative, associative, and distributive properties before teaching basic arithmetic.
(commenter formerly known as AcademicLurker)
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This is not new or unique. It is Common Core in action.
Make math harder, side benefit: confuse parents and make their kids think they are stupid
Amanda
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We intuitively grasped those concepts through practice of math facts and then in prealgebra or algebra were told the names so we could communicate about how we’d manipulate equations/inequalities/etc
Amanda
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In 3rd grade, the only goal of education should be to teach kids to love learning, to enjoy it, to see that it’s something that they can master with effort and practice. Just don’t kill my child’s love of learning is all I ask.
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Get a sane old-fashioned curricula, and teach math at home.
Ignore whatever the heck they are doing at school, it’ll only confuse things. Give permission to neglect school math assignments because “we’re doing it this other way”.
–easier said than done, but it is what I would do with my kids, if they were stuck with going to school.
Elementary school grades don’t count for anything, and once you get to a point where it matters, you can just say “we got a tutor over the summer: just let her take a placement test”.
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— and at 8, there are dozens of better choices for math. Spectrum, Life of Fred, Math Mammoth, Ray’s Arithmetic, whatever tickles your fancy and appeals to your kid. Don’t feel like you have to do it the school’s dumb way.
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That’s excellent advice. Placing out is a great idea, as well.
My Dad used to say that the absolute least possible amount of time and energy should be expended on a Soviet school and whatever it taught. Little did I know that his advice would be relevant to me in America in the 21 century.
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As a math crackpot myself:
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…mother tongue…
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we can also say “independent of order”.
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…mother tongue…
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