# Multiplicative Thinking

# 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).”

# Misconceptions

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?

##### Misconception 1:

Multiplication is repeated addition.

##### Misconception 2:

Multiplication means “groups of”.

##### Misconception 3:

Multiplication makes the answer bigger. Division makes the answer smaller.

##### Misconception 4:

You must divide the larger number b y the smaller number.

##### Misconception 5:

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.

# High Leverage Strategies

Find strategies here. These are not yet full developed but are a work in progress.

# Further Learning

Watch the webinar “Multiplicative Thinking” (ARPDC) and use their Webinar Guide to think about Multiplicative Thinking.

Explore ARPDC’s Elementary Mathematics Professional Learning site, focusing on its “Multiplicative Thinking” section.

# More Readings

Explore the progression of multiplication with Graham Fletchy. Please note that his grade level alignment is not connected to Alberta’s program of studies.

# References

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