Intuition vs process

In September 2013 on September 26, 2013 at 11:19 am


Sarah: I’ve been helping my son learn how to do long division.

Being a bit of a maths lover, it’s something I enjoy to devoting time to. Plus, you know, helping my kids is nothing but pure bliss each and every day (apply highly sarcastic tone whilst reading that last phrase).

And yet I’ve come up against a bit of a dilemma.

I walked the kid through the steps that I follow when doing division, something like:

Problem: Divide 492 by 3

–> 3 goes into 4 one time, then carry the 1 into the next column

–> 3 goes into 19 six times, carry the 1 into the next column

–> 3 goes into 12 four times

Answer: 164

Good. It made sense. He told me that he got it, and did a few examples to prove his point.

In the classroom, he has been working with his teacher (a fantastic and dedicated lady) using blocks to carry out similar types of sums. The blocks consist of groupings of hundreds (a square of 10×10), tens (a column of 10) and units (individual blocks).

To create a visual image of the mathematical problem, the kids are asked to use the blocks to represent the large number to be divided in each case, and then work out how to divide them into groups. So using the example above, we would use the blocks to represent 492, and then divide the blocks into 3 groups of 164.

It makes sense, it’s visual, I like it.

But my kid is a bit inclined to be sloppy. Spending time and using fine motor skills to put teeny blocks into neat little piles is not his thing. He usually makes a mistake. This messes up the maths problem, and leads him to the wrong answer, or an inaccurate visualisation of what he’s supposed to be creating.

So this is my dilemma. I know using the blocks is valuable, and converts an ‘on paper’ maths problem into a 3D representation. But he can find his way through the division without them, and is improving with more practise. Should we insist he use the blocks? Or just let him work out his own favoured way?

I’m torn.

  1. From a long-time maths tutor: totally let him work out his favoured way. Some people easily manipulate maths in their head in a kind of spatial/visual way, some need it to be more sequential and following a set of steps. Both ways make some kinds of maths easier later on. But forcing a not-so-spatial thinker to rely on the method that messes up more often for them just means maths overall becomes something that “other people get right”.

  2. Thank-you Tiki, your advice sounds spot on. 🙂

  3. Eeeee, it sounds exactly like the number lines my daughter is doing in school. Jumping from one number along a line of ticks to the answer. It has confused her, she doesn’t need it, and so she does it to please her teacher only. We talked about her never needing to use it unless she simply cannot add two numbers. In which case they are probably too big to use number lines anyway! I say do it his way too!

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