On June 4, 2023, @PicturesFoIder tweeted the following grade one question:
If you were a dad or mum who’s not familiar with teaching and learning math that focuses on relational understanding, not just on instructional understanding, most teachers and homeschoolers would sympathize with you. You’re not alone!
Make a ten is a simple but not simplistic strategy, commonly used by Singapore math and Common Core math elementary school teachers to teach the operations of addition and subtraction meaningfully rather than procedurally through rote learning.
Angry parents would say, “Why make math more complicated? Wouldn’t that (noble?) way of teaching frighten kids rather than motivate them to do math?” They do have a point, don’t they?
Summary page from CPDD’s “Primary Mathematics Textbook 1A” (2021)
Of course, it’s easier said than done, because given a choice, most of us, teachers, tutors, and parents, would find it more convenient or faster to getting children learn math by rote, by rationalizing that they’d naturally know why the procedure works in later years. For now, just teach them the hows—don’t bother about the whys.
Summary page from CPDD’s “Primary Mathematics Textbook 1A” (2021)
In most parts of the world, teaching math the algorithmic way is the default mode of teaching. A common reply or complaint is “Who’s the time and patience to ensure that 30-odd students in a class have really understood why the procedures for adding and subtracting whole numbers make sense to them?”
The Hows and the Whys
What percentage of grades 1–2 teachers worldwide teach both the hows and whys of addition and subtraction? Do they consciously tell children why they need to learn the algorithms rather than using their fingers to count? Or why is it to their benefit that they learn multiplication and division as a shortcut of addition and division, respectively, not to say, the algorithms to perform these operations?
Just because the majority of us didn’t learn school math relationally or meaningfully in our formative years doesn’t mean we’d also subject schoolchildren to the same boring or uncreative pedagogical ritual due to limited time, or to mimimize conceptual overload or potential confusion.
Teach Not the Way You Learned!
School teachers and parents of yesteryear most likely didn’t know or learn about concepts like “make a ten” and “draw a model,” but our present generation of math educators do know. So there’s no excuse not to introduce them to schoolchildren.
We often underestimate young children thinking that they’d not understand or appreciate the whys, because most are already trying or struggling to make sense of the hows. Valid as this argument may be, patiently (and painfully) providing a good mathematical foundation in the early years would bear much fruit in later years, because understanding trumps rote learning any time.
Relationally and meaningfully yours
© Yan Kow Cheong, June 11, 2023.
