The concept of algebra is introduced in the foundation years through recognising patterns, shapes and symbols, being able to build and describe the patterns created. At this stage in early algebra children may familiarise themselves with the words: Isolating, getting on its own and strip it down as it is the terms used in the Children's language stage when describing algebra. Algebra is a statement between two variables. An algebraic equation needs to be consistent all the way through. Simply put, algebra is the ability to understand patterns and order.
Concepts, Skills and Strategy:
Concepts- It is multiplicative, using bases 2 and 10. Although it is often Base 2. Algebra is referred to as an abstract number understanding, it consist of repetitive patterns, relationship equality and equilibrium ( balance). In algebra letters take the place of numbers and are represented as such these are often based on a repeating pattern. All patterns in algebra have to be consistent for it to be defined as a pattern.
Skill- The importance of pattern and order in Mathematics is vital in the understanding of algebra. A skill needed is to be able to recognise patterns and words ( letters) relating to the pattern, creating basic sentence problem to find a missing element or to grow a pattern. For example:
3XS+1=N.S
3 X number of sticks + 1= Number of sticks
Strategy- Useful strategies used in Early Algebra can include summing, multiplication as it is key to algebra, knowledge of patterns and sequences, the ability to problem solve independently and understanding symbols.
Misconceptions:
It is easy for misconceptions to occur especially when learning algebra. It is automatically presumed that algebra will make mathematics more complex as it combines both numbers and letters as well as different operations to find the total. As well as this a very early misconception that occurs when beginning to learn algebra is that students' may confuse the letter " X" with the variable " x". Finally, another misconception combining non-like terms in an equation can further confuse a student for example : 5x + 4= 9x. This may confuse them as mentioned previously at this stage as they are not yet familiar with " x" being used as a variable.
Resources:
In ACARA under the Foundation Year Mathematics section subheading " Patterns and Algebra" the content description discussed how early references to algebra should be taught in the classroom with specific references to numeracy to be able to recognise and use patterns and relationship by observing natural patterns in the world around us and describe these patterns through material, sound, movement and drawings.
Sourced Teaching Strategy:
( Pintrest: https://www.pinterest.com.au/pin/157626055681170752/ )
Textbook Concept, Skills and Strategy:
The main concepts in algebra which the textbook discusses is that algebra is the study of patterns and relationships, it is a way of thinking, it is characterised by order and internal consistency, it is known as a language that is carefully designed to define terms and symbols and lastly algebra is a tool. The skills that will be essential in the early years when students start to develop algebraic thinking and being to progress are the abilities to understand patterns in numbers, using language and symbols appropriately. Finally being able to work out problems, understand patterns and relations are all critical in early and primary school mathematics. A general strategy that applies to algebra is to number the terms, this can help students' to recognise and generalise a pattern ( Reys, R. 2012)
References:
Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406589&chapterid=190027
Mathematics. (2019). Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/?strand=Number+and+Algebra&strand=Measurement+and+Geometry&strand=Statistics+and+Probability&capability=ignore&priority=ignore&year=11751&elaborations=true
Reys, R. (2017). Helping children learn mathematics (2nd ed., pp. 485,487,488). Milton, Qld: Wiley.
Search - Scootle. (2018). Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA005
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