Concept of addition

Piaget believed that students are creators of their own knowledge, rather then a blank slate. This theory suggests relating addition concepts, skills, and strategies to real-world facts will encourage students to construct their own web of thoughts and ideas around addition as they interact with concrete materials, math symbols and story problems (Hiebert and Lindquist, 1990).

The concept of addition is developed differently from one student to the next, depending on their experience with addition. Generally there are several patterns that most can visualise when they ‘think addition’. Firstly addition is commutative and associative. Although, in year one students learn to add numbers using the decimal system, starting from the ‘ones’ column up (right to left) (Jamison- Proctor, R 2010, wk 1 slides). In the early years addition also requires students to recognise whole numbers in symbolic form, and/or groups of numbers. This can often lead to students visualising a symbolic picture of two or more groups being placed together (smith, 2006).

Addition closely relates to the other operations significantly and is therefore a fundamental skill that needs to be mastered before students can be introduced to subtraction. In subtraction one strategy is ‘think addition. Missing addend subtraction relates – to +. As well as, using the three addition strategies, in reverse for subtraction. Multiplication requires addition strategies when adding groups or group totals, and division requires ‘think addition’ strategies when separating a number into equal parts (Jamison- Proctor, R, 2010, Edx1280 wk 2, 3 & 4 slides).

Skills and strategies for addition

As mentioned before counting sets of physical objects is one of the very first skills of addition. This process involves gathering two sets of objects, then counting them altogether to find the sum. For example, using toy farm animals, 4 chickens in one pen, and 3 in the other, count how many chickens there are altogether to find the sum. As simple as this task may seem, some students, particular those with learning difficulties may struggle with the task and end up not grasping concept or skills to addition (Jamieson-Proctor, 2009).

Counting on is an idea that relates to the student's ability to recite number names. To ensure students are able to recognise and known and understand the meaning behind a number, questions such as “what number is before the 3?” or “what number is after 7?” Questions such as these are equivalent to addition questions such as 1 + 1 and assist students to build the link between the notions of addition and number. Using these and similar strategy prepares student to use number tracks, and gives them the confidence to solve problems in their head. Once students know how to respond to similar problems out loud, it is suggested to present them the question written down. This will allow the student to see counting and addition as fundamentally related (S. Currigan, 2009).

For most people the ability to solve addition in their head is based on facts they have memorized. Having the ability to remember a range of number facts lets students approach mathematic tasks with confidence. Board games, songs and nursery rhymes that incorporate numbers are just some of the primary resources that can assist student s to memorise mathematic facts in a fun and inviting way.  As student progress, flashcards with basic addition facts will allow students to see the link between real-world addition in their language and the materials language stage of the mathematics language model (Jamieson-Proctor, 2009). Flash cards are also able to demonstrate all three of the addition strategies.

• Count-on – 0,1,2,3….
• Use doubles- 1+1,  2+2, 3+3
• Use ten- 9+8=  9+1=10 , 10+7=17

The Australian curriculum (2011). Australian curriculum, Assessment and reporting Authority. Version 1.2. Retrieved August 16 2011, from Foundation_to_year_10_curriculum[1]pdf

Bhattacharya, K.& Han, S. (2001). Piaget and cognitive development. In M. Orey (Ed.), Emerging perspectives on learning, teaching, and technology. Retrieved August 12, 2011, from http://projects.coe.uga.edu/epltt/

Bay-Williams, J. M., Karp, K. S., &  Van de Walle, J. A. (2010). Elementary and Middle School Mathematics: Teaching Developmentally, (7th ed.). Pearson, Sydney

Evans, D., Bell, D., Bryant, P., Nunes, T., & Hallett,D., (2008). Teaching Children About the Inverse Relation between Addition and Subtraction, Mathematical Thinking and Learning, Vol. 11,No. 1-2, November 2008: pp 1-42

Jamieson-Proctor, R. (2010). EDX1280: wk4 slides. Retrieved August 16 2011, from http://usqstudydesk.usq.edu.au/mod/resource/view.php?id=405688

Hiebert and Lindquist, (1990). Developing Spatial abilities in the early grades. Teaching Children Mathematics. Retrieved August 9 2011 from http://www.highbeam.com/doc/1G1-17724540.html

Queensland Studies Authority. (2010). Mathematics essential learnings by the end of year three. Retrieved August 16 2011from http://www.qsa.qld.edu.au/downloads/early_middle/qcar_el_all_yr3.pdf

Digital and concrete resources:

Creative Academics (1998). Mathematics: Base Ten. Place value mats. Retrieved August 12 2011 from http://www.creativeacademics.com/mathbaseten.htm

IXL Learning (1997) Addition word problems. Retrieved August 14 2011 from: http://au.ixl.com/math/year-1/addition-word-problems-sums-to-10

Leah, K (1997) Coolmath-Games.com. Feed Fribbit the Frog addition games. Retrieved August 17 2011, from http://www.coolmath-games.com/0-feed-fribbit-addition/index.html

Peek, M (1998) Roll Over. A counting song.