- Twitter users can't figure out a first grader's math homework.
- Cutting-edge pedagogy seeks to draw out children's different ideas (literally!) to explore how they're thinking.
- Expanding critical thinking and daily math literacy helps students learn math more resiliently.
Last week, The New Yorker's Helen Rosner shared an obtusely written children’s math problem, and the internet responded accordingly:
My friend just sent me this pic of his 1st grader’s math workbook and neither he nor I have even the tiniest clue what the kid is supposed to do here pic.twitter.com/Xz2wP6P9j1— Helen R. (@hels) October 6, 2020
Guesses varied a great deal.
subtract the fruit to show how you get from a full basket to an empty basket, the point is to reinforce the relationship between abstract math and the physical world— ben (@BenMahtin) October 6, 2020
(Ben is right, but it's hard to explain in just a tweet.)
College math instructor here. My thought: make sure that both baskets have the same number of fruit. You could do this by adding 3 oranges and 2 bananas to the right, but you could also add FOUR oranges and 2 bananas, and then an extra orange to the left!— Bill Shillito (@solidangles) October 6, 2020
Is Oglethorpe University's Bill Shillito right? What does this math problem mean?
➗ You love numbers. So do we. Let's nerd out over numbers together.
The shared problem follows a now-common formula with updated math pedagogies of different kinds. A parent, who hasn’t read or just isn’t given the right materials to understand the pedagogy, takes a clip out of context and laughs at how it seems to be nonsense. In this case, the homework is using language students likely learned in class.
A math drawing is a child’s rendered version of how they’d count objects like blocks or even their fingers in real life. They draw circles, for example, that correspond to the number of objects in the question. Then they also draw relationships by circling some objects, crossing some out, placing them in different groups, and so forth.
If this sounds like pretty sophisticated stuff, it is and it isn’t—children gravitate toward this kind of thinking, but to adults outside of fields like combinatorics or set theory, it’s found almost exclusively in infographics.
📚 The Best Math Books
Let’s reason through what math drawings are, and why this kind of pedagogy is taking off for mathematics. Math, in particular, is vulnerable to a lot of pain points in education. Math-anxious elementary school teachers communicate that anxiety to students and affect their outcomes, and that’s before anything is even taught.
In the 2005 book How Students Learn: Mathematics in the Classroom, itself a followup to some other well known psychology books about learning, the experts focus on ways to engage with students about math in order to show how they’re thinking about problems. Children acquire numbers in a more tangible way, like seeing quantities of things set on the counter or counting along their fingers.
Because the relationship between a real, countable, holdable thing and the numerals you begin to write on your math homework isn’t always clear, experts say, some students are bottlenecked simply by trying to communicate their thoughts about how to solve problems.
Older children are encouraged to show their work, though honestly, that seems more like a way to pick out cheating rather than to explore how they’re thinking. Now, mathematical pedagogy says talking younger children through their thoughts is also a big help. “Such communication about mathematical thinking can help everyone in the classroom understand a given concept or method because it elucidates contrasting approaches, some of which are wrong—but often for interesting reasons,” the authors write in How Students Learn.
This is a key point. If you’ve ever taken a Princeton Review or other test prep course, you know one of the major ways writers trap test takers into wrong answers is by offering something almost right. If you made one common and key mistake, your work directs you to the red herring answers. And understanding different common errors in thinking is a great way to help children reason through their options in an environment that doesn’t punish them for thinking it through. Here at Popular Mechanics, we’re on Team Math Drawing.
So, now that you're up to speed on math drawings and countable things, take a look at the problem again. How would you solve it?
Tell us in the comments. 💬 ⬇
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