Reflective Journals and Developing Metacognition in Maths

In my school’s dedicated professional learning time on Friday afternoons, I recently read about the techniques that Gianfranco Conti plans on using over the coming year in order to enhance and develop his students’ metacognitive abilities.. The original article is a must read and can be found here but I was particularly taken by two of his strategies which I think have could prove particularly powerful in the Maths classroom.

The first of these is an error log. The idea is simple and one I have used (inconsistently and sporadically) before. When students get back a marked piece of work they read through their feedback and pick out the errors made. They then record these and make a note of their mistake, along with an explanation. When using this with my classes this year, I will not sum up their ‘WWWs’ and ‘EBIs’ for students and will only mark on a question by question basis to ensure that students have to engage in the process of working out their mistakes for themselves. To do otherwise may turn a cognitive exercise into a copying exercise.
The second of these techniques is encouraging students to keep a reflective journal in which students are presented with a stimulus question each week (e.g. ‘which aspects of Maths do you think are causing you the most worry?’) and are then encouraged to respond with a short paragraph.
I have decided to combine these strategies. Students will always be required to produce a written log of errors on each piece of marked work and will be given a stimulus question less frequently (perhaps every other week).
In addition to the metacognitive benefits that Gianfranco mentions, the error log in particular will hopefully have other positive impacts. Specifically it will ensure that students have read in detail the marking and corrections that I have made to their work. Students will therefore gain the benefits of acting upon individualised feedback as well as the metacognitive benefits of reflection.
I plan on introducing this to my Year 10 ‘core’ IGCSE class who I believe will benefit significantly from the increased confidence these metacognitive strategies will have and my Year 12 A-Level group, many of whom achieved a grade B or a low grade A at IGCSE.
All the journals will entries will be made on a Google Document that both myself and the student have access to and upon which I can comment directly. Here is a verbatim entry from two of my year 12 students.
Student 1
“I have to be more careful when multiplying with negatives because one of my first mistakes was that I had multiplied √2 by -√2 and said it equaled to 2 which is wrong. The right answer was negative √2. Moreover, when dealing with surds that are in fractions, and finding the value of P and Q which are numbers in front of the surd, I should not times the denominator by the numerator because the fraction would no longer be equivalent. I should continue to draw a graph when dealing with quadratic inequalities because they helped me a lot in finding which part of the graph is needed. When using difference of squares, I can times back to see if the equation is exactly the same as how it started. If it’s different, then I know that something must have gone wrong which I can then check through the working again.”
This student has clearly given a considerable amount of thought to his journal entry and has picked up on my feedback. I think that by ‘difference of squares’ he means ‘completing the square’ and I added a note to the document highlighting this. The student is using the language that I would expect from an A Level student and this has been a useful way of confirming that the student is responding to my feedback and ensuring the time I spent marking wasn’t wasted!

Student 2
“I feel that the the effort grade you gave me was a fair one as I actually spent quite a bit of time on this homework. Overall I felt that most of my homework was well done by me as I got the marks I felt I deserved however about the marks I didn’t get, I understand how I did not get those marks. I need to work on the discriminant questions that include inequalities in them as well as having to remember to draw the graph when working with inequalities.”

This student has commented on the effort grade I have given him as well as mentioning some of the topic areas he has lost marks on and how he can improve (drawing a graph to help solve quadratic inequalities). However, he doesn’t seem to have engaged with the reflective process in as much depth as he is capable of and the quality of his written English could be much better. Given this was his first entry I responded very positively and thanked him for his reflections so as not to put him off the reflective process. In future I will encourage him to be more reflective than he has been on this occasion, but that is a job for another day.
Key to the whole process will be consistency on my part in keeping this up over a long period of time, as well as ensuring that students really ‘buy into’ the idea of a reflective journal. Initially I expect the journal to be focused on the errors made rather than student perceptions of their Mathematical education. However, with some well-placed stimulus questions, I envisage this becoming will become more and more reflexive over time. I have also made a point of periodically checking the documents and as soon as I have read a completed entry emailed the student thanking them for their contributions and giving personalised feedback on their entry (perhaps encouraging meta-meta-cognition?!).

I really look forward to reading the reflections of my students, especially my low-confidence year 10 group. As always, comments welcome either below or @NWMaths

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