I recall a video I once saw. It was made by an elementary math teacher and it consisted of her campaigning against a new relational-based math curriculum. She explained how the simple algorithms for addition, subtraction, multiplication, and division that we all learned in school were being replaced by an aggregation of methods meant to target every conceivable learning style. There were visual-based multiplication tables, auditory methods, tactile methods, and word problems. It all seemed like a good idea that would help students to fully understand mathematics.
The new curriculum was a complete disaster. Test scores plummeted. Universities complained that high school graduates couldn’t do problems by hand. Basic arithmetic skills were lost in a maze of “understanding”. And so, this math teacher campaigned for a return to the simple algorithm-based approach that had successfully taught the basic skills for decades.
I sympathize with her. I am a relational learner myself. I strive for holistic understanding and reject easy memorization. But I was brought up in an instrumental system, and I thrived in it. I am aware that I should not extend my experience to the school system as a whole. Perhaps if the system was relational-based, then a different person would have thrived in it and would now be taking this class while I mop floors for a living.
But let us consider instrumental learning to be the ‘How’ and relational learning to be the ‘Why’. Mathematics are a tool of science. For most people, it is enough to be able to use a tool without knowing why it works. For example, it takes only one man to invent a circular saw; thousands then can use it to great benefit. Should we not simply teach everyone how to use the tool, and let only the truly self-motivated bother with asking why?
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