Week 2: Addition

Big Ideas

This week, we looked at the difference between concepts, skills and strategies, and then applied these to the concept of addition. As a teacher, when teaching mathematics, I first need to make sure my students understand a concept before teaching about skills and strategies. Without an understanding of a concept, students may not understand why and how they are performing skills and strategies.



Concept, Skill or Strategy: Addition

The concept of addition is the joining of groups and sets together to find a total. By working with a range of different objects, children will develop a concrete understanding of addition, and will use counting and grouping strategies to find the total number of objects (Reys et al., 2020). Initially with addition, children may only re-count all the objects, but later this will develop into more efficient strategies such as counting on, using doubles and using 10 for adding to 8 and 9. The language and materials that can be used at each stage of the language model to facilitate students’ learning can be seen below in figure 2:

Language Model


Misconception

As children start to work with larger numbers, a common misconception or error that arises is the understanding of zero’s place value. A study of addition error patterns among young children highlighted misconceptions arising in incorrect sums when zero is addend 

(Muthukrishnan et al., 2019)

When teaching mathematics, I would remediate this by using MABs and place value mats to help children understand the concept of place value, particularly with zero. Handling zero is difficult for young children as many believe one is the smallest number, which hinders their mathematical operations (Muthukrishnan et al., 2019).

ACARA

Addition is first seen in the Australian curriculum in the foundation year (ACMNA004)

Strand: number and algebra
Sub-strand: number and place value

(ACARA, 2021)

Scootle

This Scootle resource is appropriate for foundation and year 1. Counting beetles should be used for students who are at the student language stage of the language model, as the addition game requires students to count the beetles on their screen, then count on more as they move through addition questions. The game is from a series of ‘counting beetles’ resources, with this particular one only including questions that require counting, and allows students to use two addition strategies count on and doubling. There are 3 levels for different capabilities, and the game reads out the question and instructions, ensuring reading would not be a constraint.

One small issue with this resource, is that it occasionally has some beetles crawl away, to include one or two subtraction questions. While the majority of questions are related to addition, there is no choice for the player to select only addition. This could also be a great resource for beginners with subtraction as it slowly introduces the player to simple subtraction.



(Education Services Australia, 2016)

Teaching resource

Following on with the insect theme, the lady beetle addition activity, is a resource that can assist children who are at the student language, materials or mathematics stage in addition. In figure 6, the activity is depicted using the ‘+’ symbol. The design of the activity would need to be tweaked as in the picture, there is a combination of more than one stage of learning. As the students would be using a picture of a lady beetle and its spots as the materials, the ‘+’ and ‘=’ would need to be replaced with words, such as ‘joined with, altogether, add, and equals’ depending on what learning stage they are up to (see figure 2). If this activity was to be used as is, the teacher would need to have ensured the children had moved through all four stages.

(Holly, 2016)


References


ACARA. (2021). Mathematics. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/

Education Services Australia. (2016). Counting Beetles. https://www.scootle.edu.au/ec/viewing/L8280/index.html

Holly. (2016). 10 easy, simple addition activities for kids. https://www.teachstarter.com/au/blog/10-easy-simple-addition-activities-kids/

Muthukrishnan, P., Kee, M.S., & Sidhu, G.K. (2019). Addition error patterns among the preschool children. International Journal of Instruction, 12(2), 115-132. https://doi.org/10.29333/iji.2019.1228a

Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Cooke, A., Ewing, B., & West. J. (2020). Helping children learn Mathematics (3rd Australian ed.). Milton: John Wiley & Sons.









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