Week 4: Multiplication

Big ideas

This week, the focus was on the concept of multiplication and the skills and strategies involved. Multiplication is often viewed as a special case of addition with equal sized groups, or simply, repeated addition of equal groups (Reys et al., 2020). As a teacher, I will need to ensure my students have full understanding of the concept of addition before starting multiplication, and I also need to expose them to the four different ways multiplication can be pictured.

Concept, Skill or Strategy

As we know, a concept is a picture we form in our heads about a particular thing. The concept of multiplication can be pictured in four different ways:


Language Model


Misconception

For many children, zero represents nothing. Because of this, a common mistake involving zero in multiplication, is the failure by many students to realise that multiplying any number by zero yields zero (Lokanath, 2020). As zero represents nothing to some students, many believe that a multiplication by zero just leaves the number unchanged. As a teacher, I will need to instil in my students that anytime they see the number zero in a multiplication story, the answer is always zero. I can model this by using any of the 4 models of multiplication. To avoid further confusion, I will need to make it explicit that this only works for multiplying, and is not to be used when adding or subtracting.


ACARA

Multiplication is first seen in the Australian curriculum in year 2 (ACMNA031)

Strand: number and algebra
Sub-strand: number and place value

(ACARA, 2021)

Scootle


The array resource is a useful digital resource for students who are at the mathematics and symbolic stage of the language model. This is because it includes numbers, multiplication symbols and pictures of grids instead of concrete materials. It gives students an opportunity to explore commutative property or turnarounds, as it demonstrates this at the beginning, and then after students can experiment with this themselves.



(Education Services Australia, 2016)

Teaching Resource

Resources and ideas for teaching multiplication and more specifically arrays, can be found on ‘Miss Giraffe’s Class’ blog. These ideas are excellent for students in the materials or mathematics stage of the language model as they involve lots of hands-on activities with concrete materials. The puzzles and painting activities would be particularly helpful to students who may not have grasped that multiplication is repeated addition.

(Miss Giraffe' Class, 2015)

References

ACARA. (2021). Mathematics. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/

Education Services Australia (2016). The array. https://www.scootle.edu.au/ec/viewing/L106/index.html

Lokanath, M. (2020). Conception and misconception in teaching arithmetic at primary level. Journal of Critical Reviews, 7(5), 936-939. https://www.researchgate.net/profile/Lokanath-Mishra-2/publication/344066409_CONCEPTION_AND_MISCONCEPTION_IN_TEACHING_ARITHMETIC_AT_PRIMARY_LEVEL/links/5f50576692851c250b8b4454/CONCEPTION-AND-MISCONCEPTION-IN-TEACHING-ARITHMETIC-AT-PRIMARY-LEVEL.pdf

Miss Giraffe’s Class. (2015). How to teach arrays. https://missgiraffesclass.blogspot.com/2015/07/how-to-teach-arrays.html

Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Cooke, A., Ewing, B., & West. J. (2020). Helping children learn Mathematics (3rd Australian ed.). Milton: John Wiley & Sons





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