Homework and Questions in Math: a Lob Scouse

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:

5

“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.

Final Note: perhaps you don’t know what a lob scouse is? Click the link to find out.

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3 thoughts on “Homework and Questions in Math: a Lob Scouse

  1. A really interesting series, Maurice!

    From your experience, what does it take to stir curiosity and perseverance in children (or whatever you may call it) so that they are able to do homework mostly unassisted, even if that entails some intermittent frustration, even if some ‘difficult’ problems are included? So that they are going to enjoy exactly this ‘frustrating’ process perhaps?
    I feel that this is the most useful thing I practised and honed in any educational system. Or was I just one of the lucky few bookish children for whom homework was not so different from other enjoyable things?

    Here in Austria we have ongoing political battles about secondary education. One opinion is that children should spend all the day at school (and that this should be mandatory); in the afternoon they should be supervised while doing their homework instead of being sent home and ‘left alone’. The theory behind is that children don’t have piece and quiet at home or lack the appropriate help – and it would solve the issue of supervising children when parents are working. I understand the good intentions – but I feel sorry on behalf of more introverted nerdy children who like to learn on their own.

    1. I am pretty sure you’ve covered it all and that the only thing I can add is the obvious comment that the real trouble starts whenever someone decides to lump every student into the same category as is clearly the case in your ongoing debate. My own assessment is that, rather than trying to do just one thing for everyone the system would be better off with some smaller scale programs to make things better for the students who need it. Two programs in my own place come to mind: 1–tutoring for tuition. This program pairs gifted students with those that need help and pays them for their efforts in the form of a university tuition voucher. In my previous job we put together an online version of this program and had online tutors available in the evenings(no fee). The system used a live exchange through a software app called Blackboard Collaborate. 2–Tutoring work experience program. This program hired 3rd and 4th year university students to serve as tutors in schools in May and June as students prepared for finals.

      The others thing is determining what motivates students. While there’s no one answer to it I can state two things: 1–students need to know that they are being listened to. This means that those who are falling behind need to be a part of the solution. Schools will fail if they devise and implement solutions that do not involve consulting with the students. 2–we know for absolute certainty that students learn best from teachers who show that they care. Disaffected, cynical and just plain mean teachers are basically useless and need to be counseled out of the profession.

      1. Yes, you are right – the discussion is about one category for all. It is perhaps a over-reaction to the existing completely separated schools. I also don’t understand why you can’t offer one ‘school’ with different programs / options as there are schools that do offer such programs anyway… so why keep up this artificial barrier between diverse schools. But is is about politics – one of the traditional left versus right debates…

        The tutoring program is a great idea. One experiment I’d advocate (I think it is not very popular which is a pity) is combining high school diploma and hands-on vocational experience normally only available to pupils having picked the ‘trade school’ type of secondary education (apprenticeship in a company plus school). Maybe it might solve the problem of motivation for those whose are not that bookish while it makes sure that the nerds have some real-life experience 🙂

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