Conceptual understanding is knowing more than isolated facts and methods. The successful student (with conceptual understanding) understands mathematical ideas and can transfer their knowledge into new situations and apply it to new contexts.
Now here’s something to think about … You can’t teach conceptual understanding !!
What I mean by ‘You can’t teach conceptual understanding’ is that it is not possible to directly impart our understanding of a concept into a student.
To explain: Using direct instruction we can teach a child to calculate the mean of a data set, or the length of a side of a right-triangle side using ‘Pythagoras' or trigonometry. We can drill students so they are able to replicate any mathematical procedure. But, we can’t teach, via direct instruction, the concept which underpins, for example, place value … or decimal rounding … or the formula for gradient. We can use direct instruction to teach the rules associated with place value, decimal rounding and gradient but we cannot directly impart the understanding of those concepts to students.
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