# Deepening conceptual understanding in mathematics by creating mathematical story picture books

Dr. Natthapoj Vincent Trakulphadetkrai explores how students could deepen their mathematical understanding by creating their own mathematical story picture books.

## Setting the scene

When Jane (pseudonym), a 9-year-old pupil, was asked by me what 4 x 7 equals to, she was able to give me the correct answer (28) effortlessly within a second. When asked to show me how she got her answer, she was also able to quickly and correctly use the column method to do so. Then, when she was asked to (contextually) represent 4 x 7 using a word problem, this is what she came up with: “A girl goes to the park, she finds these coins, 10p, 5p, 5p. She goes to the ice cream van. She wants one, one ice cream costs 20p, does she have 20p? Yes.” How Jane’s word problem is related to 4 x 7 remains a mystery.

What Jane demonstrates here is a classic example of pupils whose procedural fluency (i.e. the mechanic aspect of mathematical learning) in relation to multiplication is good, but have yet to fully grasp what multiplication means conceptually. As many mathematics education scholars have argued, in order to demonstrate conceptual understanding in mathematics, pupils must be able to represent mathematical concepts in different ways. One creative way to help pupils develop such ability is by getting them to create their own mathematical story picture books!