The Importance of Multiplicative Thinking
According to research completed by Terezinha Nunes, Peter Bryant, Rossana Barros and Kathy Sylva (2011), “Mathematical reasoning and arithmetic did make independent contributions to the prediction of mathematical achievement; mathematical reasoning was by far the stronger predictor of the two. These predictions were specific in so far as these measures were more strongly related to mathematics than to science or English.”
Multiplicative Thinking isn’t limited to students answering multiplication and division questions correctly.
According to the Elementary Mathematics Professional Learning website, “multiplicative thinking is
- a capacity to work flexibly with the concepts, strategies and representations of multiplication and division as they occur in a wide range of contexts. (mathematical reasoning)
- going beyond memorization of basic arithmetic skills
- the means to communicate multiplicative understanding effectively in a variety of ways (for example, words, diagrams, symbolic expressions, and written algorithms).”
There are several prevalent misconceptions students hold around multiplicative thinking. As you read the misconception statements below, can you determine when and why these misconceptions
- are developed?
- are interfering with developing new understandings?
Multiplication is repeated addition.
Multiplication means “groups of”.
Multiplication makes the answer bigger. Division makes the answer smaller.
You must divide the larger number b y the smaller number.
Division is commutative. ie. 5 / 4 is the same as 4 / 5.
Students need to understand
You can manipulative numbers in order to make solving problems easier.
Nunes, T., Bryant, P., Barros, R., & Sylva, K. (2011). The relative importance of two different mathematical abilities to mathematical achievement. British Journal of Educational Psychology, 82(1), 136-156. doi:10.1111/j.2044-8279.2011.02033.x
Operations – Multiplicative Thinking. (n.d.). Retrieved December 15, 2020, from https://learning.arpdc.ab.ca/mod/page/view.php?id=9212