I was discussing homework in mathematics with my friend and colleague Susan Ryan just the other day. Initially the topic of conversation was homework. Soon we realized we were pretty much of the same mind about it—specifically that it’s a good practice when given in the appropriate amount, thus implying that teachers need to be judicious regarding exactly what tasks they assign.
While there are no doubt many homes in which creative effective learning can take lace it’s been my experience that quite a few are not, and, in the interest of fairness to all, it’s vital to ensure that homework tasks are things that all students have a fair opportunity to get done well at home. I am therefore of the mind that it’s generally a good idea to assign some of the more routine tasks such as review drill and practice as homework. For example back when I taught grade ten math, before covering the factoring of trinomials I found it useful to assign a review of math facts (I am not kidding. That was grade ten and I am thinking of the 1980s. The whole problem about remembering math facts is truly nothing new) before getting started as a significant number of the students were rusty, especially regarding the multiplication facts bigger than 7×7. Since it was not worth taking class time with I’d just pass out a boring review worksheet. Similarly, the following year, just before we started the unit on quadratics I’d also assign review on factoring polynomials as homework, again for the same reason. These days if I was still doing it I’d certainly make use of a flipped classroom approach and provide a modern version of essentially the same thing.
The talk then turned to things that do not work well for homework. Both of us, as parents, could easily recount numerous stories of especially frustrating experiences we’d had when our children asked for help with certain tasks that had been sent home. We then put on our cynical retired teachers’ hats and concluded that in many of these instances what had been sent home were items from the textbook that the teacher did not feel comfortable with handling in class.
My particular “favourites” were the ones that start with, “explain why…” such as “Explain why you chose the solution you did,” or “Explain why a polynomial function of degree n can have, at most, n zeros.” I was particularly not fond of questions that started with “Write to explain…” Now, don’t get me wrong—I am very much in favour of students working on their mathematics communication skills. It’s just that sometimes the questions do not lend themselves to independent thought and are much better handled as a group or whole-class discussion when many ideas can be drawn out, thus forming something of a mosaic of shared understanding.
When tough questions like the ones above are posed to individuals, the students tend to find themselves totally stuck and most either totally give up or turn to the parents. In the absence of classroom context it’s not hard to see how those same parents would become equally confused, frustrated and absolutely angry at a mathematics program that would expect from young children to be able to respond to such open ended and difficult questions; questions that in the absence of context (after all they were not in class and can’t be expected to see how it fits in) seem pointless.
Me—I would never knowingly do that. I would have no problem taking up those “explain why…” questions but never for homework.
And that’s where things got interesting. Susan then more-or-less agreed, but took the conversation in a different direction. She encouraged me to think about those questions and how, so very often, they form the stuff of angry, frustrated Facebook posts. You know what I’m talking about, don’t you? Some samples that I have seen at one time or another follow.
Regarding those posts, as is often the case, the extreme frustration is generally due to two errors. First, the teacher likely made an error in judgement and either selected a problem that was too difficult and, second, the parent assumed that the child know much more than they did. For example, in the above letter back to ‘Jack” the parent clearly has no idea of how difficult place value is for young children, and that the idea of ‘borrowing’ to do computation makes absolutely no sense until the child does have that firm grasp. Simply put, children and not small adults. Sure, the suggested parent solution seems obvious to someone with a university education but for a grade school child—no! That response–the letter to Jack–while venting pent-up frustration, just suggests the enormity of the gulf that exists between the child’s grasp of math and the adult’s grasp. As Susan would point out, the parent’s solution amounts to no more than “squiggles on a page” for most young children until a LOT of development work is done on number sense, place value and subtraction itself.
We don’t always acknowledge the simple fact that things that we know very well seem obvious to us. The better we know them the more obvious they are and, in fact, the less perceived need for any external learning strategy.
Just because things are obvious to us, doesn’t mean that are equally discernible for others, though. That’s a fundamental problem we all have as parents—we think that young children are just smaller versions of their adult selves and totally forget the fact that as the body develops physically so, too, does the brain. The mental capacities we have as adults are not necessarily developed to the same extent for kids.
That, then led to Susan showing me one of the activities she has used with parents to help explain why teachers do what they do. She asked, “why is 2 + 3 = 5?”
I was caught unawares with the question and mumbled something. She laughed and said, “hang on. Let’s think what students might say instead of what you might say.” She got out a sheet of paper and wrote this:
“There will be some students in the class who just ‘get it’ intuitively and it will seem obvious to them. They see it as most adults do. It’s not that they can’t explain it—no it’s just that it’s so obvious to them they suspect you’re daft to even ask (just like most adults). They are where they need to be and are ready to move on.”
Then she wrote this:
3 4 5
“Some students know to start from 2 and just count up three more. They’ve also pretty much got it. They need a little help, perhaps, as they’re not thinking abstractly just yet, but it’s safe to say they probably understand what’s going on well enough to take it to the next level.”
Then she wrote:
1 2 3 4 5
“Some students need to write the whole thing out from the start. They are still pretty concrete as they have to have 5 ‘things’ before them in order to understand what’s happening. Perhaps they will even draw 2 dots and 3 dots. They have the essence of addition but are still heavily reliant on the concrete. Perhaps it’s a development thing, and you just have to allow them time for their brains to develop more, or perhaps they just need more help—a decent explanation of what addition is might be all that’s required for some. Either way, you know there’s a hump to be overcome before they have it nailed down.”
Then, finally she said, “and, finally there are the ones who have to look at what everyone else has done. You might call it cheating or copying, or whatever. At any rate they will be unable to complete the activity and are certainly not ready to do anything further unless more development is done. They can complete work and make it look good, but it’s not their own work. For these students it makes little sense to memorize addition facts as they have no idea what it’s all about anyway.”
“So people often wonder why teachers ask what seem to be silly, even stupidly obvious questions. The fact is, though, that they’re not necessarily silly. The answers the students give is tell an important part of the story regarding the degree to which they understand any given topic. In turn this informs our own practice.”
Funny how one thing leads to another, isn’t it? Homework led to a discussion of questions and how what seems to be nonsense on the surface can be something quite useful when you consider it in context. Most things are like that, aren’t they?
Oh, and since this rambling disquisition seemed to start with homework it might as well end there. Any way you look at it homework is something that should be carefully considered. After all, while students’ time in the classroom is precious and needs to be spent wisely, so too, is their time out of it. Many other things besides school subjects need attention—sports, the arts, learning social interactions, volunteer time, and just having fun, to name just a few. If a school subject needs to occupy that time then it seems to be the respectful and wise thing to choose carefully the when, the how much and, most importantly, the what.
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