At a recent Maths faculty meeting, we had time to share teaching ideas and strategies. It was fantastic that, even amongst very experienced teachers, there was this desire to learn especially from each other.
I really liked what @markmikulandra shared. He shared some mnemonics, a good learning strategy.
DAD – Draw A Diagram
This is a fantastic problem-solving strategy and it is easy to remember.
FSC – Factorise, Substitute, Calculate
This is really useful for equations. It is true that most equations are easier to ‘attack’ when you factorise first. There were some discussion on some students’ reluctance on this quasi-trial-and-error approach. That is, for these students they want to solve it on the word go. Anyway, I think this works because the fundamental skill involved in factorising is identifying the building blocks. Abstracting from this, factorising is an important problem-solving strategy not just in maths, ie if you can identify the factors that make up the problem, solving it is easier because you can focus on each factor (eliminate, mitigate or fix)….but, I digress.
N.ATEL – Number, Algebra, Trigonometry, Exponents, Logarithms
@markmikulandra introduced N.ATEL to his students (and us, his colleagues) as a metaphor for Avatar’s Na’vi. So, N.ATEL is like an avatar to the world of mathematics. When these elements mix in higher mathematics, students sometimes struggle with their strategies as in using algebra in solving trigonometric problems (eg differentiating x sinx, x is algebraic and sin x is trigonometric). Problem is, most of junior maths are taught in strand-approach and it’s rare for students to see the elements together. Mix them together, as they do in real life and higher maths, and confusion often arises. This mnemonic can help make sense. I think N.ATEL can be introduced in junior maths to provide a real-life context (the irony of an avatar doing this is quite amusing 🙂 ), a big picture.
In the spirit of sharing and mnemonics, I also shared my own – GGSC – Goal, Given, Solve, Check for approaching word problems (see older post).
All these mnemonics are learning strategies. They are frameworks to help make sense of mathematical ‘blobs’. These frameworks are forms of, even as they develop, mathematical thinking.