3.1 Ideas to enable you to assess your students’ mathematical learning

Ask a question worth thinking about

Figure 4 Students working together

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A group of students sitting around a table, talking and listening to each other.

Figure 4 Students working together

When you have asked a question worth thinking about, then the discussions needs to continue. You might collect answers from the whole class, write them on the board without comment and then ask some people to explain why that answer was given. You might also ask other students to comment on the explanation, either to correct it, or (more likely) to add some other insight. You may have to emphasise that the discussion is a common quest for understanding, not a competition to be the one with the right answer.

Or you might ask the students to work in pairs to devise an explanation and then ask them to give that explanation to a larger group. The discussion would then be about putting together the best explanation using all the ideas expressed. Each group then gives their explanation to the class. If there is a ‘wrong’ explanation, as opposed to an incomplete or not very clear one, then the class might be asked if they could see why the pair had got the idea. Thus ‘wrong’ answers are seen as interesting and challenging for the class, and often open up ideas and misconceptions that others share.

Students writing their own questions

Towards the end of teaching a topic, ask the students to write their own questions on it. This allows you to assess what they have understood. It may take some time at the start, but once you and the students are familiar with this method, you will find that you can pick out what the students have found straightforward and what they found difficult by the questions they write.

Students need time to know what constitutes a good question, as this could be where misconceptions lie rather than in the content knowledge. Sometimes it is best to ask the students to write the questions at home, perhaps five questions each. The lesson can then be spent looking at the questions and working out which seemed to be good questions and why. The students will probably agree that a good question was one that was challenging, fair and based on their own experience where possible.

Questions written in this way will be the result of students thinking hard about what they know about a topic and therefore the range of questions was a good indicator of what the students understand and where there are still misconceptions.

Last five minutes – students saying what they know now but didn’t before

The last five minutes of a lesson can be used to allow the students to tell the class, including you as teacher, what they have learned during the lesson. This can encourage students to reflect on their learning and to self-assess what they have learned. One student could be appointed as a spokesperson for each lesson. (Use a register to make sure that everybody is given a turn.) The teacher goes to the back of the class and the appointed person comes to the front and tells the class what they have learned in that lesson, often using the objectives that the teacher has written on the board at the start as prompts.

The job of the rest of the class is to listen and say if anything is left out. They are also encouraged to ask the spokesperson questions about the topic. The questions from the class can be very revealing and may help you to plan the next lesson. The necessity to explain to the class helps some students to grasp ideas more fully and the reflection prompted by the need to ask questions helps others become sure of the learning from the lesson.

Each of the above ideas, when integrated into lessons, assesses the learning intentions of the lesson, assesses individual students and allows the teacher to assess their own planned lesson.

If you are interested in learning more about these ideas, read Embedded Formative Assessment by Dylan Wiliam.