This week the main focus was on Addition and the importance of informing students that Addition does not necessarily mean that the total is going to be greater than as this is a misconception which will be elaborated on further on in this blog. It is also important to note the use of language at a Materials Language Stage as the students have yet to gain a clear understanding of the Mathematic Language and Symbols used to express a form of equation. Hence why, avoiding the words " add" and " equals" at a Materials Language Stage is crucial. Simply put, Addition is joining groups to find a total.
Concepts, Skills and Strategy:
The C/S/S when it comes to the process of Addition are as followed:
Concept- The use of objects when explaining the concept of Addition, by joining numbers together. Developing a story-board or games with different themes (eg. counters, mats, MAB blocks) as well as learning through song by using well-known simple songs that children easily identify with to keep them engaged in the topic providing them with the opportunity to discuss the topic.
Skill- Knowledge of the concept and the ability to follow through. A skill is knowing what to do with the concept and how to do it properly. An ability to perform a simple " sum" is considered a skill. Such as 3+8= 11.
Strategy- Method used to complete a task effectively. A strategy which has proven to be ineffective when teaching children is the " finger counting" strategy as it is a distraction for children. The 3 main strategies used for Addition are the : Count-on strategy used for numbers ( 1-3) beyond that this method is proved to be ineffective, Double-up strategy ( used with larger numbers and numbers which are the same) and Use 10 strategy or Build Up strategy ( used for adding numbers that are close to the number 10. An example would be : 5+5= 10 or 10+0=10)
Misconceptions:
As mentioned briefly, a misconception when it comes to Addition is that the total is always going to be a greater number. However, this is not the case. Children should not be taught that by adding two numbers together the total is going to be greater the reason for doing so is that as they mature and learn more about different uses and different forms of equations they will come in contact with negative numbers and how a negative number + a positive number will equal a negative number and a positive + a positive equals a positive same way as a negative + a negative will equal a positive. That is why installing the idea of Addition will always be equal to a greater number is a false assumption and should not be taught to students that way.
Resources:
According to the QCAA and Australian Curriculum ( ACARA) under the section titled Number and Algebra students should establish an understanding of language and the process of counting numbers in sequences (Qcaa.qld.edu.au, 2014). Students should be taught how to connect and join numerals and quantities which also includes the number zero to ten. The goal by the end of the Foundation Year in terms of Addition is that the students should be able to analyse and read numbers up to ten and knowing the simple process of addition. ACARA states that in the Foundation level students learning Number and Algebra should be able to:
Understand- Connect names, numerals and quantity by addition
Fluency- Counting numbers in sequence or patterns
Problem Solving- Using materials to come up with a solution for the problem by using familiar counting sequences
Reasoning- Creating patterns and explanation of the process
( Australiancurriculum.edu.au, n.d)
Sourced Teaching Strategy:
( Amsi.org.au, 2011)
Mentioned previously, the use of counters is a very effective method when it comes to teaching Addition is it gives children a visual representation of the process and how it is presented.
Textbook Concepts, Skills and Strategy:
This text summarises the Big Idea related to C/S/S in Addition. Before start schooling it is generally assumed that all children will have the basic idea of Pre-number these will help build an understanding of the early number concept and the foundations of basic skills needed later on in their Mathematic journey ( Reys, R. 2012). The ability for a child to know how to count correctly is a skill however, in some cases a child may know how to count and the process involved but are unable to establish the last number is an indication of how many they are. It is encourage for students to organise their objects for a clearer understanding, this will also reduce the amount of errors a child makes such as accidentally double counting. Therefore, they will gradually improve on their skills as they are able to sort out the numbers efficiently and without hesitation. Furthermore, some of the key strategies mentioned in the textbook that are used in counting are the Count-On strategy which was mentioned previously and the Count-back strategy. Both of theses strategies are useful when it comes to teaching the children Addition and the basic principles of Counting. This strategy is critical when developing Addition. It teaches children to recognise different numbers and how the starting number differs from the next number ( 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=2406552&chapterid=189986
Mathematics. (2019). Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/?
Reys, R. (2017). Helping children learn mathematics (2nd ed., pp. 281,285,343). Milton, Qld: Wiley.
Search - Scootle. (2018). Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA002
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