Having stated on Twitter that I think that maths has it easy in many ways and concurrently ready ‘Making Good Progress‘ and the chapter on using tests, I thought I’d share an adaptation of what I do in GCSE RS and show how it could be used in maths.
Getting students to think about what they got right/wrong and why will help them to understand it and learn from it in the future. This process of ‘meta-cognition’ seems to have a high potential impact on learning.
How I do this in GCSE Religious studies
Once students have done a test, they complete an online form about the test. Example, here. It is a record of their marks for each question and a reflection. This collates all their responses and I get a pre-populated spreadsheet of their results and their individual targets. I can quickly analyse which topics/questions the students have done well or struggled on. I’m also an uber-geek and mail merge their results onto a reflection sheet for their next test.
Possible model for maths
I thought the same could be done in maths but with a reflection for each question after a test.
In order to support the process, you could add a box below each question for them to comment whilst doing the test. This might be particularly useful if they don’t answer a question.
The teacher then needs to create a form that has the questions and the possible pitfalls. It is also a record of what answer they all put.
Here is a sample part of a form.
You have to go through the test with them in some way before they input their data to help them understand why they got things right/wrong.
Alternatives to this might be to not give them options but require them to explain in their own words or only focus on particular questions for feedback.
You might also put the correct and the common incorrect answers as a drop down on the form for them to select. Google forms then has the ability to ‘mark’ the correct answers so your spreadsheet would also have marks e.g 14/20.
They make time to construct but there are ways to save time. Maths teams tend to be quite big; share the load. Or, commit to writing the form as they sit the test. 1 hour test = 1 hour to write the quiz. You can also, to some extent copy and edit these in Google forms. Other platforms have the opportunity to have tagged question banks so you could make generic responses that can easily be reused. Or only get them to reflect on specific questions based on your judgement on what might be useful.
You will need access to electric devices during the lesson for them to access the form. If this is problematical you can get them take turns in class with the devices you do have, whilst the others do their corrections or to do it for homework on their own devices. ( you just need to give them the URL link). I prefer it to be done in class.
Once you’ve established this routine with the students then it becomes easier and second nature to them. They know they will do this after each test.
Potential activities after this are:
- make corrections in class showing an understanding from where they went wrong
- to redo the exact same test at a later date (then you can compare outcomes)
- focus on their incorrect answers for homework and use a programme such as My Maths to watch how they should be done, then re-do the questions
The power of these forms are they are useful for info on:
- how they answered each question ( you get a copy of their answer as they’ve inputted it
- how the class did on each question
- what they need to ‘revise’/ do further practice
- what you may need to re-teach
- their thought process as they answered
- common misconceptions
- misconceptions that you might not have thought of
Overall, these forms make tests even more valuable in terms of their formative use.
As you can see I do a similar thing in Religious Studies, so this idea can be adapted fairly simply across all subjects.
2 thoughts on “A simple model for meta-cognition in maths (and all other subjects)”
I love this I use a simple similar version for feedback on lots of mini tests it really encourages strong reflection which is meaningful I have seen students make less simple mistakes in subsequent tests.
I’m uncertain of the benefits of the form.
I know what my students did wrong. I can see it when I mark their tests. Generally I know what they are going to do wrong before they even sit the test (as do you, since you have listed all the common errors in expansion — except you left out, “I panicked, like I always do in tests” and “I hate algebra”.).
The students have to know what they did wrong, or they can’t fill in the form. Does filling in the form make them understand their errors any better? Because that’s the only thing that would be different from what teachers normally do.
We already go over tests to point out common errors, we redo the test if we need to, and we give homework to hone skills. The paperwork doesn’t change that.
You say the benefits are:
how they answered each question
how the class did on each question
what they need to ‘revise’/ do further practice
what you may need to re-teach
Yeah, I marked them. I already know that.
their thought process as they answered
A form won’t help me read their minds.
misconceptions that you might not have thought of
I know the common misconceptions — tey are common, after all. The ones I haven’t thought of are not within the scope of a student of that age to be able to self-analyse.
It seems a lot of work to look like you are analysing, rather than sitting down and actually analysing from the evidence you have directly in front of you.