Big Ideas Covered
Before a student can understand the concept of multiplication, they must first understand the concept of addition. This is because the concept of multiplication is the repeated addition of equal groups. For example, 4 + 4 + 4 + 4 = 4 x 4.
There are four ways to picture multiplication being: the set model, the array model, the length model and the combinations model.
Prior to Week 4, I have never really thought about the direct relationship between addition and multiplication, in which I did not understand that a student must be taught addition first. As a future educator, I will ensure that each student has as a strong understanding of the concept of addition before teaching the concept of multiplication.
Concept, Skill or Strategy
As identified, the concept of multiplication is the repeated addition of equal groups. When teaching this concept and/or identifying the different ways to picture multiplication, an educator may first read a story book. An example of a story book which uses children’s language to identify the combinations model is Shirts and Skirts written by Calvin Irons.
Misconception
A misconception that a student may develop is that when multiplying a number by a power of ten, only zeros need to be added.
For Example: 5 x 10 = 50 – Only zero needs to be added to five.
Although the correct answer can be obtained from simply adding zero, it will only be obtained if the number is a whole number (Dabell, 2018). If zeros are simply added to an equation which requires a decimal to be multiplied by a power of ten, the incorrect answer will be obtained.
For Example: 11.25 x 10 = 112.5. Yet if a zero is simply added, the answer obtained would be 11.250 which is incorrect.
As a future educator, I could remediate this misconception through clearly demonstrating to each student that simply adding a zero does not always obtain the correct answer, in which I would use a whiteboard to write clearly, similar the the one above.
ACARA + Scootle
Year Level: 2
The Array is a scootle resource which could be used to reinforce the concept of multiplication at either the mathematics or symbolic language stage. This resource uses the array model to represent multiplication equations, in which each student is required to count the numbers of rows and columns, and then solve the related equation. A limitation of The Array is that the instructions are not read aloud, so a student must be able to read.
Resource or Teaching Strategy
An Array Puzzle is a fantastic resource which could be used to teach the concept of multiplication. Although this resource uses images to represent each array, it mostly aligns with the symbolic language stage. A possible limitation is that it may take a student quite a while to independently complete each set of puzzles, in which an educator could instead allow each set of puzzles to be completed in small groups.
Concept, Skill or Strategy: Textbook
Reys et al, p 290, explains the thinking strategy of repeated addition. This strategy could be taught in Year 2 when multiplication is first taught (Reys et al, 2017). When teaching this strategy, it is important that resources such as grids, number lines and groups of objects are used. Through this, each student is able to develop their understanding of both the thinking strategy and the concept of multiplication (Reys et al, 2017).
Resources
Australian Curriculum, Assessment and Reporting Authority. (2015). Mathematics: Sequence of Content. Retrieved from: https://www.australiancurriculum.edu.au/media/3680/mathematics_-_sequence_of_content.pdf
Dabell, J. (2018). Maths Misconceptions: Multiplying By Ten. Retrieved from: https://mathsnoproblem.com/maths-misconceptions-multiplying-ten/
Education Services Australia. (2016). The Array – Scootle. Retrieved from: http://www.scootle.edu.au/ec/viewing/L106/index.html
Irons, C. (1999). Shirts and Skirts: A Story about Simple Combinations. Shortland Publications.
Jamison-Proctor, R. (2019). EDMA241, Week 3 – Part 1 [PowerPoint Slides]. Retrieved from: https://leo.acu.edu.au/mod/book/view.php?id=2406568&chapterid=189998
Miss Giraffes Class. (2015). How to Teach Arrays. Retrieved from: 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., Robson, K & Bennett, S. (2017). Helping Children Learn Mathematics. (2nd ed.). Milton: John Wiley & Sons.
EDMA Reflective Journal 