Week 1 - Addition

ADDITION!

This week the focus was to allow me to understand how children learn mathematics through the 4 language stages (demonstrated below) allowing me to model and build an understanding of how to teach mathematics.

Concept, Skills and Strategies

The concept of addition is modeled through activities and concrete materials that allow student to join and separate collections and quantities 3. I'll aim to model to the children the joining of groups together, providing them with real life situations to give the students experience at their language stage with the concept of addition.

The skill follows on from what we do with the concept, so in the classroom we could model addition by using a place value map and using MAB blocks and joining the sets of blocks together to get the total.

There are 3 main thinking strategies for basic addition facts including count on for 0-3, the use of doubles and the use of 10 for numbers close to 104.


Language Model

We use this triangle to replicate the language model representing the 4 stages of language. Examples of addition that can be used when teaching in the classroom to check where the students are at in the language stage to get them to the symbolic stage include 5:

1. Student language (three birds put with two birds makes five birds altogether)
2. Materials (three counters with two more counters, makes five counters altogether) transfer to them to the materials of mathematics rather than objects such as teddy bears 
3. Mathematics language (three add two equals five) 
4. Symbolic language (3 + 5 = 8) ⁵ 

Teaching strategy - Resource

An excellent teaching resource to be used to model addition in the classroom is using learning mats. We can create one of these relevant to the topic and it gives the children a real life situation to move materials around to understand addition and can be reversed to also teach subtraction5.








Misconceptions
Some misconceptions that might occur include the children not understanding the concept of the operation or failing to understand the place value of the number. The use of place value mats is an excellent way to understand the place value of the numbers and where they should lie in the operation2.


ACARA
The earliest link to addition is found in foundation year of the curriculum1:

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References

1. Australian Curriculum and Assessment Reporting Authority. (2014). Foundation to Year 10 Curriculum: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1#cdcode=ACMNA004&level=F 

2. Harris, Andrew. (2000) Addition and Subtraction  Retrieved from http://ictedusrv.cumbria.ac.uk/maths/pgdl/unit5/A&S.pdf 

3. Jamieson-Proctor, R., & Larkin, K. (Week 1). "Mathematics as a Language”: A Theoretical Framework for Scaffolding Students’ Mathematical Understanding. Brisbane, Australia: ACU LEO EDMA202/262.

4. Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn Mathematics (1st Australian ed.). Milton: John Wiley & Sons. 

5. Week 1 lecture