Giving the tests back

My school follows the Maths Mastery programme, which involves pre-assessments at the beginning and post-assessments at the end of each half term. The final week of each half-term is then review week where we go over topics highlighted by the assessments as needing more work. The first lesson is, of course, giving the test papers back to the class. I have never particularly looked forward to these lessons. I often feel that pupils have the wrong attitude to this important part of their learning and don’t use the time well in lessons. So I took to Twitter last week to get some ideas and have combined these with my own in this post.

Some approaches will work with some classes, not with others. But hopefully this is a useful menu to chose from next time round. I’m working on the assumption that the assessments have been marked by the teacher (not always strictly necessary) and that the results have been recorded in an APP-style spreadsheet which means marks are recorded for each question. This is the bare minimum. A successful lesson is going to require further preparation, some approaches requiring more than others. Some approaches also present greater classroom management challenges or risk of disengagement and require a good relationship with the class. I have ranked each approach with the classic Indian restaurant scale of 1, 2 or 3 chillies! I’d love to hear your opinion on these!

Teacher exposition of questions

Possibly the least imaginative approach, but sometimes necessary especially when the whole class struggled with a question that you feel they should have had the skills and knowledge to attempt. OK for the odd question or two but avoid going through a whole test like this. Having said that it is a good idea to have the whole test ready to write on in a way you can display it to the whole class either on slides on the IWB or using a visualiser if you have one.

Preparation:            Classroom mgt: 

Pupil experts in groups

The core principle here is that pupils who were successful in a topic deepen their understanding by explaining to others so everyone is benefiting. The process needs to be explained to pupils so that everyone knows what they need to do. i.e. experts are there to give explanations, not answers and those being coached need to ask questions as they go. Requires you to identify the experts beforehand; nice when different pupils are experts in different topics but more difficult when it is always the same pupils as experts. Make sure mini-whiteboards are available.

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Pupil experts by question

A variation on the above is when you chop up the exam paper and put the individual questions around the room. You designate an expert for each question and then ask pupils to go round the room with their red pens getting help on the questions they need. Again, nice when there is an even range of success across questions, more difficult whn this is not the case.

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Self-analysis of marks using a structure / template

To analyse their own test I have used the following codes a lot with A level classes, but I think they could work for any assessment.

• SM: Silly mistake. Something you can immediately see where you went wrong and why.
• R: Revision. Something that was forgotten. If your revision had been more effective you could have got these marks as this is a topic you understand.
• ET: Exam Technique / timing, i.e. you didn’t read the question properly or took too long working on something that wasn’t necessary and therefore ran out of time on other questions.
• U: Understanding. You don’t understand this topic well enough yet to answer this question.

Then get pupils to add up scores they would have got if they add back in SM and R. Can be a good confidence boost. This could form the basis of an “Exam wrapper” – a reflection sheet that is filled in by students after their test and filed with the test. Here is a great example of one of these, thanks to @takepi21 for contributing this. More detail on exam wrappers here.

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Self-assess using mark scheme / worked examples

Mark schemes provided by exam boards are often not very helpful if you didn’t understand the question in the first place, so I’m reluctant to just give these out. I often write out full sets of worked solutions to a paper, or you might find something good that already exists. Even if you have to do it yourself, this is quicker than writing the same explanation on 15-20 individual papers. I believe in writing the bare minimum on the paper when marking tests. Sometimes I’ll even just enter the marks directly onto the spreadsheet and not actually “mark” them at all. Pupils are given their totals / grades only after they have spent the required time engaging with their assessment. This causes groans the first few times you do it, but they will get used to it and hopefully appreciate the progress they make in these lessons.

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Do a re-test with different numbers soon after you have reviewed the test

This can be a powerful motivator if students know it is coming, as they will have a very clear measure of progress. Clearly this could be quite a bit of work but if you are using packages such as Exam Wizard, Exam Pro, Test base, Exam Quest, Create-a-test, Maths Print or MathsNet to create tests in the first place, then it gets a lot easier.

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Exam question carousel

Another way of following up the test review lesson is with an exam question carousel or “Gecko game.” You have individual exam questions on separate bits of paper. Students do them one at a time and come up to you with answers. If they get it right, they move onto the next one. I have found this particularly effective with A level classes but it can become unwieldy once you get above 20 pupils.

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Finding the nth term

I’ve used this simple booklet with a range of classes and it just works! Many thanks to my former colleague Nick McIvor for creating it and sharing it.  A well structured set of examples that enables students to see the patterns. I would still teach the nth term more formally after using this, but it’s a great introduction and it builds confidence.

For quadratic sequences, here’s a similar approach from @mathsjem

Triangle numbers

In common with most Maths teachers, I love Don Steward’s site Median for the fantastic range of quality resources and ideas.  All the ideas in post come from here. I have taken some of them and put them into a PowerPoint with some solutions.  As teachers, we should do the Maths that we are asking our students to do in lessons. Which is, I guess, why most of the resources on Median don’t have solutions with them.  However, in the midst of a busy term, lesson planning has to be time-efficient and so I have added a slide in here with some possible solutions (there may be more elegant options).  The idea being that lesson planning is then a case choosing how to present this and involves deleting pieces of this solution which is much quicker that creating them from scratch.

Indices and Standard form

Good to practice using a calculator for standard from:

This one is non-calc:

As is this:

Deeper Questions for Mean, Mode, Median

Some quick questions, Powerpoint here.  You could also ask pupils to draw pictures (e.g. scaled bar models) to represent their examples.

And then these to from @Craigos87. Need a really good explanation!

Other questions:

• What’s the average number of wheels on a vehicle on a motorway?
• What’s the average number of children a woman (in UK, in India, etc.) has in her life?
• What’s the average number of arms a human being has?

Or, if you’re feeling brave:

Guess Who – Straight Line Graphs

I think this works well as a paired consolidation activity.  Based on the popular board game, but rather than identifying people, you are identifying graphs and rather than asking about hair colour, you are asking about gradient, y-intercept, etc.

Full details and graphs to print on a nice big A3 sheet are in this Powerpoint.

Mastering Subtraction with Dienes Blocks, Diffy and 1089

We are spending the first term with Year 7 on fundamental number skills to ensure solid foundations. This week, we are looking at subtraction.  There won’t be any specific methods or techniques that they haven’t already seen at primary school, but I know the degree to which they have mastered these techniques will vary markedly within the class.

Rather than feeling daunted at the prospect of teaching them something they already know, I’m seeing this an opportunity to show them some (hopefully) cool maths that requires them to use and practise their skills.

My new school has a wealth of manipulatives which I have had little opportunity to use before.  I’m looking forward to using dienes blocks to show why the column subtraction method works and why we cross out digits before embarking on the subtraction.

It’s not really “borrowing” it’s “re-distributing” one of the tens into the ones column.

Next up, Diffy, which I learned about from Don Steward’s blog post here.  The post contains some great ideas on how to do it. I love a good spreadsheet so created this which does all the calculations for you!  The real reason though is so I can give my students a chart to help them structure their Diffy calculations.

I really want to focus on clarity of instruction with this class. They are a typical Year 7 class who need instructions broken right down and economy of language from me. My measure of success will be the number of questions I get asked before they start!

There is more about Diffy in this great blog post from Colleen Young

I also really like these rquestions from Maths Mastery:

I shall insist on 100% silence, pens down and do a Think, Pair, Share on this. The “Think” will be 30 seconds in complete silence with a timer with pupils just looking at the calculations.  I’m hoping for an excited rush of discussion once the 30 seconds is up and they are itching to tell their neighbour what they’ve spotted.  Then they will check their hypothesis by actually completing the calculations in their books.

And finally the old classic 1089. Powerpoint slide here.

What happens when you put a group of Year 10s in a hall with a group of Year 6s

I started at a new school this year.  I could write pages about this experience, but that’s not what this blog is for, I want to share things that are genuinely useful to other Maths teachers!

My new school is much nearer to my home, and one of its feeder primary schools is where my own children go.  I was Treasurer of the PTFA there some years ago so have lots of connections with the primary school.  I got talking to one of the awesome teachers there and we discussed bringing a group of my Year 10s to help with tutoring some their Year 6 pupils.

Today was our first 30 minute session.  I knew I wouldn’t have much preparation time with my Year 10s, so I took the approach of being fairly prescriptive putting together a sheet of tasks for them.

It went well; very quickly, in fact.  I gathered my group together at the end and told them how impressed I was with their coaching.  I had a fairly mixed group of 13 students, some capable mathematicians amongst them but also some students that don’t show the best focus in their own maths lessons whom I was quite concerned about.  But as soon as the Year 6s entered the hall, they suddenly took their job very seriously and made great efforts to engage the pupils.

Many of the Year 10s found that the Year 6s already had a good understanding of place value and they reported that they found the task quite easy.  As teachers, we know how to use questioning to really probe depth of understanding, but maybe this is too much to expect of a 14 year old.  What intrigued me was the variety of ways my students responded to this challenge with some of them going completely off-piste and explaining pi!  But I want to encourage this.  It’s a luxury to have no specific learning objectives to fulfil or curriculum to follow.  We are doing it 3.00-3.30 on a Friday afternoon, which I’m pretty sure means the Year 6 pupils are not missing critical learning time!

Looking forward, I want my Year 10s to take a gradually greater responsibly for planning activities.  We have agreed, that we are going to have some element of “game” in every session and we started looking at some of the huge range of Nrich activities.  I’ve put together a Google doc for next week to allow the Year 10s to collaborate and contribute ideas.  I not expecting them all to contribute, but I think a few will.

I’m also really enjoying discovering some resources and games that I’m sure will be useful in my own teaching practice.  I’m relishing not having to follow a scheme of work.  My only objective is to keep everyone engaged and learning and to “make maths fun”. If we achieve this, it’s going to make me think long and hard about how we teach maths at secondary!

If anyone has the opportunity to do this sort of partnership, or in fact is already doing it, then please get in touch by leaving a comment below.  It would be fascinating to share ideas. Also, if you have any good ideas of resources, then let me know.  I have many weeks ahead to fill!