review/revision – In Pursuit of Great Mathematics Teaching

Test Champions

This idea was recently shared with me by Pietro Tozzi. He is a maths teacher at Gumley House Convent School in London but also works for Pearson (the Edexcel exam board) two days a week. We brought him out to our school in Singapore to do some training for the team about the new A-level in maths. (By the way, if you are looking for an A-level or (I)GCSE trainer, I would highly recommend him.)

During our time together, he shared this idea for returning a test. As it turns out I had a KS3 test to return and tried it out. As I marked I kept track of the best answers for each question. When I compiled this table, I made sure that every student was listed and students with lower scores were listed more frequently, if possible.

The class score represents the fact that among all the students, they have expertise to get full marks; someone scored perfectly on every question.

After passing back the tests, I asked students to get up and meet others who could help them correct their errors. They spent about half an hour up and about, talking over their questions, and making notations (using a coloured pen) on their tests. While they were doing this, I was able to work around the room and talk to those who had difficulties that their peers couldn’t solve.

They enjoyed this way of reviewing and correcting their tests. Having them out of their seats was good for their concentration (for the most part!) and also allowed me to be less conspicuous in my help of a few key students.

I completed this lesson with a fill-in sheet for students to list strengths and targets based on the test. We spent the following lesson with students doing individual work on their targets before we moved on to our next topics of study.

Building Collaboration Using Changing Partners Activities

A few classes needed to revise at the end of teaching units and I wanted them to collaborate while they did so. I printed off a class set of these small checklists with the first names of everyone in the class.

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I also printed some review questions onto colourful card. I separated my tables and spread the questions out over the tables, with two or three on each table. I put some tables facing the wall or the windows so that pairs of students would hopefully focus better on just their partner and the question at hand.

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I gave each student a name checklist to glue into their notes and displayed these instructions.

From time to time there were not two students looking for new partners at the same time. As a result, sometimes they would have to work in a group of three. Other times there was one person who had to wait a minute to start their next problem. However, this didn’t happen too much and overall I would say that the students did a lot of work. Sometimes in a revision lesson such as this one, students get bored and lose momentum. Not so during this lesson. They stayed on task until the end (80 minutes later) and completed loads of questions. In the last few minutes of class we checked their work as I displayed the answers on the board.

I have tried this with a few classes now and it has worked well every time. It goes most smoothly when the class size is 20 or more. Though I did try it one day when lots of students were at a field trip and I only had seven learners. That still worked but it was a little harder for students to begin and end questions at the same time as others. it devolved into mixed group work instead.

One time I tried this in my class that has a wheelchair student. This also worked smoothy. I positioned her in a place where she wouldn’t be bumped by others walking by. From time to time I prompted students to go over to her since she can’t come to them.

Some tips for myself and others to make this work well:

A class size of 20 or more works best.
It works best if you have enough tables to have at least two empty tables at the start for the first students who finish and find new partners to move to.
Having three questions on each table means students can sit down at the same table a second or third time with different partners and solve different questions.
Make sure the questions are numbered (or lettered) and students write these down as they solve. Then sharing the answers becomes easy.
Mixed revision from several units of study can be done this way. Just mix up the questions around the room.

Do you have ideas about helping students collaborate in math(s) class?

Exam Preparation Activity: Collaborative Practice Questions

My students are preparing for winter exams. As a review activity we are making our own revision questions. I set up two shared Google Docs: one for revision questions, and one for the solutions. Each student had to make up at least one revision question for everyone and add it to the first document.

Writing the questions requires an understanding of the concepts behind our topic, so this activity let me see what my students understood and how well.

Students had to say which MYP level their question was. Our upcoming exam focuses on MYP Criterion A: Knowledge and Understanding, which is graded from 0 to 8. We regularly discuss the criteria in class and so students are beginning to become familiar with the descriptions of the levels.

We had a good variety of questions added, and I circulated to encourage some students to fill holes I thought I saw. I urged some students to write harder questions. In the end, the activity is self-differentiating: each student works on problems at the exact right level. And for each student there are harder problems to stretch them, with me providing the stretch for the topmost students.

As for the solutions document, some students chose to type their mathematics using the (minimally acceptable) equation editor on Google Docs’ Insert menu. Others worked on their mini whiteboards and then took photos to upload to the document.

After students had made at least one question, I encouraged them to go on to make another, harder one or to answer the questions of their classmates. I assigned as homework to work through all the questions in preparation for our exam.

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What exam preparation strategies work for you and your students?

Teaching to the Test

While reading today, I discovered an unexpected side effect of the practise of teaching to the test. (At least it was unexpected to me; perhaps you will not find it so surprising?)

First, the “usual” problems with extended coaching[1] for exams:

the exam is no longer a good indicator of what students understand since they have only been narrowly trained to do specific question types
the exam is no longer a useful way of selecting students for further courses since we don’t know if they really understood the mathematics they have “learned”
the possible ranking of schools (for example, league tables in the UK) by student grades is not accurate since some schools have used extensive coaching while others have not
employers can not be sure that students’ ability matches their test score

All these arguments are ones I have heard before about coaching students to pass an exam. But one undesirable side effect of exam coaching stood out to me:

younger children see older ones being coached to success and they learn that at just they right time, they, too, will be spoon-fed what they need to know

As a result students learn that they do not need to take responsibility for their own learning, they do not need to study seriously or make an effort to understand and connect what they are learning.

Wow! I was shocked by this. One of my main goals is to make sure students understand what they are learning and can connect their mathematical ideas. I don’t want younger ones to learn that they don’t really need to work hard until the exam coaching begins.

My school only partly subscribes to the idea of coaching for exams. But I fully subscribe to the idea that students need to take responsibility for their own learning.

What exam preparation strategies do you use?

[1] I am talking about the repetitious, algorithmic coaching that happens in the lead up to standardised tests. Students, especially those who are near a grade level borderline, are taken (forcibly, at times) though many, many revision resources.