## Be careful what you ask for: a cautionary tale of homework sheets

Welcome back to the school year. By now you have met your classes and are well underway, no doubt. I thought I’d share this story with you, as it might be all too common…and avoidable with a little forethought.

Picture this:

Miss 14 turns up to her first day at a new school to begin Year 9. She doesn’t know anybody in her classes, and although she can certainly hold her own, she is a little apprehensive and could do with a little reassurance. She told me at dinner that she had homework to do and ‘it’s stupid and I don’t get it. Why do they bother with all those letters and stuff?’

Yes, algebra and Miss 14 were not friends.

So I have a look at her notes from the day, copied down meticulously from the board.

‘Linear and Simultaneous Equations’ was her heading. The notes included definitions on ‘coefficient,’ ‘equation,’ ‘expression’ and ‘term’…very basic for Year 9, and possibly just a gentle reminder to the class before the ‘new Year 9 algebra,’ I thought. There was talk of BODMAS, how to write simple algebraic expressions from words and vice versa, but again, very basic and no higher than Year 7 level. We discussed the notes and she ‘got it…but I don’t get the homework.’

This was the homework sheet:

ALGEBRA MATCH UP

Find the expressions on the left that match those on the right (download PDF homework sheet below).

She had managed to correctly match up some, and I ask her how she did it, since there was no working, and on checking, she was not required to show her ‘thinking.’

Miss 14 is clever. She knows that whilst algebra is not her strong point, street smarts are.

‘Well, I looked for the letters which matched. And a couple of times I copied from the girl next to me, because she seemed pretty smart.’

Matching A with 7 was a no-brainer – she knew how to change a simple worded expression into an algebraic expression, and besides, ‘it’s the only one with an f.’ From here, she went to D, and began looking for, and easily matched it with 13. Now where? Back to B. It had an ‘a’ in it, so it had to be either 2 or 9…but she was looking for 2x + 4, and ‘it wasn’t there.’ I talked to her about equivalent expressions, and although she thought it was stupid, agreed that 9 was the correct match.

‘Why didn’t they just have the answer instead of trying to confuse me?’

Why didn’t “they” indeed.

Close inspection of the homework sheet sent me into a Mathematics Educator fury. Was there any correlation to the notes and examples? Hardly. Had she ever seen binomial expansions? Of course not. Was she at the level to realise the “hidden answers?” Definitely not.

Remember, we are dealing with a teenage girl attending her first maths class in her new school; a girl who had little confidence in her mathematical ability to boot. She was frustrated and disillusioned. She felt that she was not smart enough to complete the homework, and angrily stated to me, ‘I hate maths!’

I didn’t blame her: this could be a lesson in how to get a student offside in one easy step.

We persisted. She genuinely wanted to know how to do it, and it was homework after all, so it should be doable and ‘completed by next lesson.’

Much discussion was had and a variety of examples were explored. She got to ask questions, as did I, and it became evident to me when she “got it” and when she didn’t. Matching C with 10 was easy enough, but where was the 7x2y or 7yx2 or to match with F? ‘Aren’t you supposed to drop the multiplication sign?’ she asks. ‘If the correct match is 1, why did they write it like that?’

Why did “they” indeed. I reassured her that we would like our students to have dropped the sign in such a problem, but the answer was equivalent, just not expressed in its “simplest form.”

She had determined that G matched with 3, as ‘it had to contain a u and a v,’ and we had a discussion about why was equivalent to –20uv, and why we would never have written our answer to G like that? Similarly, matching I with 4 (since it had to contain s and t) was a logical, if not mathematical, conclusion. The ‘WHY?’ continued, from both of us. I’m not sure who was more frustrated. I think it was me.

But then J had s and t as well! And we had run out of just s and t answers to match on the right. So where was the answer to J? Matched with 14…of course. Isn’t it obvious?

K with it’s a and b clearly matched up with the only a and b in 11, and after some discussion there was an acceptance that number 11 was in fact the same as –12ab.

But why? Why didn’t M just match with 24 instead of number 5?

Expansion of brackets was an issue, as was the need for care with regard to the signs in H and N, so finding the ‘hidden’ forms in matching with 2 and 6 respectively was made even more difficult.

We were left with E and L, and when my blood pressure dropped I proceeded to explain to Miss 14 that she was not stupid. She was not expected to know how to do this, and that in my 30 years’ experience, this concept was generally taught in the second half of Year 9. I talked double distributive law, FOIL and binomial expansions to satisfy the completion of the sheet, but we were not happy campers. Why would you write your answer to L as 12?

Why would you even give this sheet? It was so wrong on so many different levels.

If Miss 14 didn’t have someone to help her that weekend, I fear all would have been lost. She was ready to give up…on day one.

So, next time you throw a sheet at the kids for homework, can I just remind you, be careful what you ask for. Maybe, just maybe, you are doing more harm than good.

Footnote: I asked Miss 14 how her next class was, and what the teacher had to say about the homework.