Previously I analysed homework in terms of cognitive effort and looked at the benefits of homework review. This post proposes an effective method of homework review.

Traditional homework review

The “default” approaches for homework review seem to be:

1. Solution developed on board by the teacher who simultaneously explains it as though it was an example

• Advantages: Explanation of steps for learners who are struggling.
• Disadvantages: Time consuming, little benefit to learners who can do the problem. Because the teacher is doing the work, many learners will not actually engage with the problem, but just copy down the steps while thinking of other things.

2. Writing up the solution in advance (or accessing it from the teacher’s guide), scanning and projecting it

• Advantages: can be prepared in advance; learners who partially solved the problem can identify how to get past their sticking place. Learners are forced to at least look over the correct solution while they are copying it down.
• Disadvantages: learners copy down the solution without engaging with it; slow (or distracted) learners or those who didn’t attempt the problem keep the others waiting; those who were successful are left with nothing to do.

3. Handing out copies of the completed solution

• Advantages: quick, can be prepared in advance; learners who partially solved the problem can identify how to get past their sticking place. Those who were successful will not have their time wasted.
• Disadvantages: many learners will simply file and forget. Expensive!

4. Guiding the class to develop the solution themselves

• Advantages: more likely to elicit engagement; the learners in the Low Effort column will get some benefit from seeing the solution.
• Disadvantages: time consuming. Learners who can do the problem may provide all the input while the others just coat-tail along.

All of these are unsatisfactory in one way or another, but can be useful in particular circumstances. For instance, if the whole class is struggling with some section of the work, options 1 and 4 will benefit most of the learners and give the teacher the opportunity to elicit questions, identify sticking places, or put additional scaffolding in place to assist the learners.

The quadrant view of homework outcomes

Ideally we would like all learners to be making a high cognitive effort, but realistically this is often not going to be the case.  I identified four different categories of learners and this suggests that we need different approaches to homework review, which can run simultaneously without wasting time.

My own classroom is small and physically rearranging the learners into groups depending on their category is not feasible and would definitely be a time waster. We can’t have permanently assigned groups, since learners can migrate between categories from day to day.

Here is the quadrant model of homework responses that I developed in the previous post, for reference.

Requirements for homework review

Based on this model, I came up with some requirements for homework review:

• The best option for Quadrant 1 learners is to give them the chance to put in some of the effort they didn’t produce the previous afternoon. In this way, the learning opportunity is still available to them.
• Quadrant 2 learners should get some scaffolding problems to try and fill in the gaps in their schemas to be able to move from “following steps” or “didn’t succeed” to actually understanding what they are doing.
• Quadrant 3 learners may benefit from more of the same type of problem to develop fluency; if they are confident in what they have done they may need extension work.
• Quadrant 4 learners should be given some extension work. Those who knew how but slipped up need to do some self-diagnosis to identify where they made errors; they may need the teacher’s assistance in this – we all know how it is possible to stare at your own obvious error without noticing the mistake.

What does all this translate to in the classroom?

First of all, learners need to know that when the homework is done they should check the answers in the back of the textbook.  If a problem is wrong they should try again.

Each learner walks into my class, sits down, opens their exercise book to the previous days homework which they have already marked from the answers in the back of the textbook. Something cool is up on the board or happening over the speakers in my classroom (Numberphile is great for this) and while they are engaging with that, I pick up my diary and start walking around the class looking carefully at each learner’s book.  Firstly I check for:

• Is the homework done?
• Is it marked?
• If the answer is incorrect, has the learner re-attempted it?

Learners who don’t meet these criteria get their names in my diary – if this is more than an occasional lapse, consequences happen!

Since the answers are marked I get a quick overview of where there were difficulties; usually quite a few learners will have struggled with the same one or two question in the exercise. By the time I have looked over all the homework, I know which questions these are. It also allows me to give individual assistance with error diagnosis for slip-ups. If I pick up that a learner has had a lot of trouble I will spend an extra minute at his desk, trying to get the hang of what the problem is. Sometimes it is a simple misunderstanding which only takes a few seconds to clear up, or a quick hint (“You forgot to square the whole expression” or “Try the tan-chord theorem”) is enough for learners who are stuck and they can re-attempt the problem immediately. If not I make a note to come back to assist the learner when I get a chance. If there are a few of them who seem to be having similar difficulties I may schedule 10 minutes after the homework check to spend some time on this. On a normal day I can get around the whole class in around 10 minutes.

If notice that there are one or two problems that are more problematic than others I will get the class to help develop the solution on the board.

Once the learners are familiar with this procedure it should only take a few minutes of the lesson.

A review method that works

Let me first talk about the kids who sailed through the homework. On the right hand page of my Smartboard I put some kind of “thinking” problem. This may be an extension exercise, or an application of the skills in an unfamiliar context, or a question from a mathematics competition or a nice juicy problem from a previous exam. Allowing learners to work in pairs and discuss and argue about the problem can work well if the learners are able to stay focused and keep the noise level down. A+ Click is a great source of questions that should only take a few minutes – and a little reward works wonders.

One the left page of the board I copy and paste the questions that I saw a number of kids struggling with. (I have the exercise scanned before the lesson, so it is easy enough just to copy and paste the relevant problems across). I deal with these slowly. The key here is that I don’t “do” the problem the way I would explain the example. Instead I get the kids to develop the solution by prompting or offering scaffolding when they can’t move on. In particular I ensure the involvement of those who I know struggled and also the “didn’t try” kids. Sometimes, I need to backtrack a little and create a quick scaffolding problem first to make sure the kids have got the basic ideas sorted. The golden rule to follow here is: “Do not be too helpful!”

 

If I find there are more than just one or two Quadrant 4 learners – didn’t know, didn’t try – I will issue demerits or detention, ask them to sit outside class and try to do the homework. In this case tell them they have 10 minutes to make up for a lost learning opportunity, and let them get on with it.  You may have other tools available for discipline, but you want this to go as quickly as possible: don’t waste time fussing at them.

Some days don’t go so well

On some days you may find that the whole exercise was too difficult, that many kids weren’t able to do it. Then it is time to take a few steps back and re-teach as necessary. But don’t forget the few who DID succeed, and keep some copies of old exam problems ready as an alternative for them.