- Skills that apply to both geometry and number patterns include:
- Recognising the pattern
- Describing the pattern
- Repeating the pattern
- Growing the pattern
- Replacing missing elements of the pattern
- Translating the pattern (Jamieson-Proctor, 2016a) - "Use a pronemtal to symbolise the step number so that you are not restricted to any one value" (Jamieson-Proctor, 2016a, p. 15)
- When finding a number pattern in a linear sequence the key is to look for a relationships between the numbers (Jamieson-Proctor, 2016b, p. 3)
- Different number theories include:
- Odds and evens
- Prime and composite
- Multiples and factors
- Positive and negative
- Whole and fraction (part/whole)
- Place value (Jamieson-Proctor, 2016b, p. 9) - There are three different concepts related to algebra:
- Patterns and functions
- Equivalence and equations
- Patterns, sequences and generalisations (Jamieson-Proctor, 2016c)
 |
| Figure 1.28: Terms and Symbols of Algebra Jamieson-Proctor, R. (2016c). EDMA202/262 mathematics learning and teaching: Week 7 Part 3. Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1238194&chapterid=36563 |
- "An algebraic equation is a statement of a relationship" (Jamieson-Proctor, 2016c, p. 9)
- A repeating pattern has a core element that has been repeated over and over (Reys et al., 2012)
- Growing patterns are when each successive term changes by the same amount of the preceding term (Reys et al., 2012)
- Functions are a way of expressing a relation (Reys et al., 2012)
- Algebra has always been a favourite maths concept of mine, and it is an area that I was good at in high school. However I did not realise, before this week, that algebra began so early in school. I was under the idea that algebra begun in the later primary years and early high school
Demonstrate your understanding of the mathematical concept and related skill and strategies children need to assimilate and be able to use, that are related to the topic of early algebra
Language model for concept- The concept for this week was algebra. Algebra is "...a study of patterns and relationships, [and] a language that uses carefully defined terms and symbols" (Reys et al., 2012, p. 351)
- The skill in regards to the concept of algebra include:
- Recognising the pattern
- Describing the pattern
- Repeating the pattern
- Growing the pattern
- Replacing missing elements of the pattern
- Translating the pattern (Jamieson-Proctor, 2016a) - The thinking strategies for the concept of algebra include:
- concrete materials to map out the equation
 |
| Figure 1.29: Language model for algebra Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1238194&chapterid=36561 |
- Different teaching strategies to assist children in understanding a key mathematical concept related to early algebra include the following videos:
- Algebra video
- Algebra basics
- There is a misconception among children, in relation to pre-algebra, that algebra is maths that uses letters instead of numbers (Jamieson-Proctor, 2016c)
- A way to re-mediate this specific misconception is to ensure that children understand that "Letters are only a symptom of algebra just like a runny nose is a symptom of a cold. Primary students in Years F-7 need to create patterns and describe the relationship between the steps in the pattern" (Jamieson-Proctor, 2016c, p. 18)
- Algebra can first be seen in the Foundation year, ACMNA005, Number and Algebra strand, patterns and Algebra sub-strand (ACARA, 2016)
- The content descriptor for ACMNA005 is "sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings" (ACARA, 2016, p. 1)
- The elaborations for ACMNA005 are:
- "observing natural patterns in the world around us;
- creating and describing patterns using materials, sounds, movements or drawings" (ACARA,
2016 , pp. 2-3). - Scootle resources to support the teaching of ACMNA005 include:
 |
| Figure 1.30: Scootle Resource One Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA005&userlevel=(0) |
 |
| Figure 1.31: Scootle Resource Two Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA005&userlevel=(0) |
 |
| Figure 1.32: Scootle Resource Three Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA005&userlevel=(0) |
Provide appropriate links to resources and ideas you have sourced personally to assist students to develop concepts, skills and/or strategies related to early algebra
Resources for students to understand the concept of pre-algebra:
Resources for students to understand the skills in algebra:
Resources for students to understand the teaching strategies in algebra:
- Concrete materials such as those shown in the lecture can help children understand the teaching/thinking strategies behind algebra
 |
| Figure 1.33: Jamieson-Proctor, R. (2016c). EDMA202/262 mathematics learning and teaching: Week 7 Part 3. Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1238194&chapterid=36563 |
Chapter 15 - Algebraic Thinking
- Algebra is a study of patterns and relationships (Reys et al., 2012)
- The teaching of algebra in primary school should build on ideas that are an essential part of the curriculum (Reys et al., 2012)
- Both routine and non-routine types of problem provide good opportunities for developing algebraic concepts of thinking (Reys et al., 2012)
- A repeating pattern has a core element that has been repeated over and over (Reys et al., 2012)
- Growing patterns are when each successive term changes by the same amount of the preceding term (Reys et al., 2012)
- Functions are a way of expressing a relation (Reys et al., 2012)
- There are four different properties of numbers:
- Commutative
- Associative
- Distributive
- Identity (Reys et al., 2012) - Children can learn the language and symbols associated with algebra as they are learning about numbers (Reys et al., 2012)
- There are 3 different uses of variables:
- Place-holder
- Generalisations
- Formulas and functions (Reys et al., 2012) - Modelling helps students to organise their thinking (Reys et al., 2012)
- Justifying allows students to explain their thinking (Reys et al., 2012)
References
Australian Curriculum Assessment and
Reporting Authority. (2016). Mathematics.
Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1
Education Services Australia. (2016).
Scootle: Mathematics. Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA005&userlevel=(0)
Funza Academy. (2014). Algebra made easy: Math concepts for kids.
Retrieved from https://www.youtube.com/watch?v=OU87O69sTLM
Jacknjellify. (2008). X finds out his value. Retrieved from https://www.youtube.com/watch?v=J2TYyUftI8k
Jamieson-Proctor, R. (2016a). EDMA202/262 mathematics learning and
teaching 1: Week 7 Part 1. Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1238194&chapterid=36561
Jamieson-Proctor, R. (2016b). EDMA202/262 mathematics learning and
teaching 1: Week 7 Part 2. Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1238194&chapterid=36562
Jamieson-Proctor, R. (2016c). EDMA202/262 mathematics learning and
teaching 1: Week 7 Part 3. Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1238194&chapterid=36563
Maths Online. (2013). Kindergarten lesson: Shape patterns.
Retrieved from https://www.youtube.com/watch?v=wHzjLsTadVk
Reys, R., Lindquist, M., Lambdin, D.,
Smith, N., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn mathematics. Queensland,
Australia: John Wiley & Sons Australia, Ltd.
Scratch Garden. (2014). The patterns practice song: Scratch garden. Retrieved
from https://www.youtube.com/watch?v=MBjjxSx45-Q
Zaaxa.com. (2014). Algebra basics. Retrieved from https://www.youtube.com/watch?v=YVJAdfE-L68
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