Week 9: Early Algebra and Patterning

Big ideas

For many, algebra revolves around equations and finding ‘x.’ This is exactly the image I used to have in my head when I thought of algebra. This week, we learnt that even some of the youngest learners are using early algebraic thinking, as algebra is the ability to understand relationships and patterns, with algebraic equations being statements of relationships (Jamieson-Proctor, 2021).

I was initially hesitant to engage with this week’s topic as algebra is something I really struggled with in high school. Due to this, my belief before participating in this unit was that algebra was something that was only introduced in high school (except for simple missing element equations e.g. 5 + ? = 11). 



Concept, Skill or Strategy

The patterning skills we were introduced to in week 6 that also apply to early algebra are:

1. Recognising the pattern (What’s happening?)
2. Describing the pattern (What’s repeating?)
3. Repeating or copying the pattern (need to be able to see the relationships to do this)
4. Growing or extending or continuing the pattern 
5. Replacing missing elements of the pattern
6. Translating the pattern
(Jamieson-Proctor, 2021)

Repeating and growing patterns are essential building blocks for algebraic ideas (Reys et al., 2020).


(Jamieson-Proctor, 2021)



The Language Model


Misconception
 
Reys et al. (2020), identify the equal sign as something that children sometimes misunderstand. Often children believe ‘=’ means ‘the answer’ or the solution. However, simply explained, it actually is the mathematics symbol to indicate equality or the balance between each side of the equation. As a teacher, I can remediate this misconception by demonstrating a state of equilibrium using scales myself, or online resources such as the video below:



ACARA

Algebra (patterns) is first seen in the Australian curriculum in foundation year (ACMNA005)

Strand: number and algebra
Sub-strand: Patterns and algebra



Scootle

(University of Cambridge, 2021)

This is only a small activity, but these dominos are a good way for children to practice patterning. Teachers can use this to model patterns with dominos to the class and then extend this activity and create their own pattern questions for the children to answer.

Teaching Resource

(Pittman, n.d.)

This activity is a great way for students in the student language stage of patterning to practice their skills. Students can recognise, identify and re-create patterns by type. This can help students comprehend that patterns can be copied with any materials, with the example in this one being an AAB pattern. This is essential knowledge moving forward in the understanding of mathematical relationships (Pittman, n.d.).


References

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

Jamieson-Proctor, R. (2021). EDMA241/262. Mathematics Learning and Teaching 1: Week 9 Part 1 (slide 7-9). Australian Catholic University

Jamieson-Proctor, R. (2021). Week 9 learning activities: Part 1a lecture. Australian Catholic University. https://vimeo.com/user36828324/review/200614369/0a699008ad

Pittman, J. (n.d.). Mrs Pittman’s patterns. https://mrspittmanspatterns.weebly.com/station-2---same-pattern-different-items.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.

University of Cambridge. (2021). Next domino. NRICH. https://nrich.maths.org/168

Visual Musical Minds (2016). The equal song: What does this mean [Video]. https://www.youtube.com/watch?v=3FDIXz0AFCA&ab_channel=VisualMusicalMinds


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