Effective Note Taking in Mathematics

This post relates to my very first blog post, how to study mathematics.

I don't think there is a single perfect way for students to take effective maths notes, I think they need to be given the freedom to develop what works best for them. Even if it was "for my own good" I hated being told that I must take notes in one specific way and no other. If you do a Google search for "how to take maths notes" you'll come up with a few different examples. What is considered a good strategy seems to vary between every individual. However that doesn't mean that teachers can't show their students multiple possible strategies that they could use.

I mentioned in that first blog post, the idea of ruling a line vertically down the page, leaving roughly a 5cm gap (or about 1/4 of the page) for the right hand column and then using that smaller column for explaining your steps. I also found I perfer to have two note books for maths classes. One for theory notes and one for practice. I started doing this because when it came time for revision, I got tired of flipping through pages and pages of practice work to find the theory notes I had taken which were interspersed within. The small right hand column can be used for the theory notes section, in the same or similar way as in the 'Cornell note taking system' (pdf). Here is a great blog post I found about using the Cornell system for maths notes (pdf).

Previously I wrote a post about mathematics teaching in Japan. While I was researching that, I came across a website which sold Japanese mathematics textbooks translated into English. These was a brochure (pdf) about the books, which contained a sample page teaching students a good way to set out their maths notes in their notebooks. It suggested that students have several headings for each lesson:

• Date
• Problem
• My Idea
• Friends' Idea
• Summary
• Reflection

It also had several suggestions to students, such as not erasing mistakes, but neatly crossing out the mistake and writing the corrected answer.  In the reflection section students are asked to record such things as, what they've learned, what the noticed, what they want to examine next (what I notice, what I wonder), and what they thought of their friends' ideas. They're asked to share their reflections with each other as well. Furthermore, the textbook will model good practice by showing solutions in 'down the page' format.

Still on the Japanese theme, I came across another pdf through a Google search which gave the characteristics of the ways that Japanese teachers often use blackboards that the authors believe contribute to promoting mathematical understanding among students. One point was that it should "provide a footprint of the lesson" which means no (or minimal) erasing of stuff written on the board during the lesson.

The pdf about the use of blackboards also mentioned the use of colour, and as a student I did find it useful to colour code my notes, for example using black pen for examples, blue pen for explanations, green pen for summaries, highlighting for lesson title, etc.

One final thought about notes, especially in high school, is the problem of worksheets. Unless students have a folder/binder, worksheets almost always end up lost, or scrunched up at the bottom of school bags. In primary school we were always required to glue our worksheets into our books. I hated it, because after one or two weeks of school, my books would be all wrinkly and uneven to write on. This is probably one of the main reasons I'm not a fan of "foldables" in notebooks. Personally, unless it can be lost or destroyed with no great loss to the student, I'm still not sure that worksheets are a good idea.

How do you take good maths notes? Do you have any other ideas?