Conceptual understanding in math has served as a dividing line between those who teach in a conventional or traditional manner (like myself), and those who advocate for progressive techniques. The progressives/reformers argue that understanding of a procedure or algorithm must precede the procedure/algorithm itself; failure to do this results in what some call “math zombies”.
I will state that I, like many teachers, do in fact teach the underlying concepts for algorithms, procedures and problem solving strategies. What I don’t do is obsess over whether students have true understanding nor do I hold up a student’s development when they are ready to move forward.
For many concepts in elementary math, understanding builds from procedures. The student practices the procedure until it is realized conceptually through familiarity and tactile experience that forges pathways and connections in the brain. (Efrat, 2018). Daniel Ansari (2011), maintains that procedures and understanding provide mutual support…
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