MASTERY LEARNING IN MATHEMATICS

Simple to complex, part to whole, concrete to abstract
& known to unknown

Mathematics in all branches is very well suited by teaching through Mastery Learning. This applies to algebra, trigonometry and geometry.

Many problems involve a number of processes. Knowns in process A are used to calculate the unknown. The new known becomes part of calculating the unknown in process B. This then becomes the known in calculating the final answer in process C.

It can all be too difficult for many students. Brilliant students can look at a problem and immediately recognise the progression of steps from process to process. The average students may not be able to do this. But they can easily be taught to do so.

In grade 12, I had a mathematics teacher who would walk into class and write a problem on the blackboard. He would then spend the rest of the period working through the problem with his back to the students. The brilliant students worked with him.

The rest of the students copied the working down in the hope of having the lights come on some time in the future. He was the most brilliant mathematician I had ever met. But he was the worst teacher on the planet.

He could have set up sequences in Mastery Learning to teach mathematics. I think I learned nothing from him. There was no rhyme nor reason to his problems that covered the blackboard. All problems seemed to go from complex to complex. There was no progression in difficulty. It was all difficult.

Mastery Learning involves a sequence of A process problems (one step). Once mastered, the students complete a sequence of A+B process problems (two step). It is followed by A+B+C process problems (three step) that leads to the solution.

Then the average students will learn to identify the total process in any problem given to them. I passed Grade 12 mathematics 1 and 2. So something must have stuck.

I once took a class in mathematics as a high school teacher in Queensland. We worked by sequences of Mastery Learning and most students passed the final exam. I am a terrible mathematician but a brilliant Mastery Learning designer. I still do not understand the purpose of dy/dx.