WEEK ONE: Addition
- Cassie-Jaye Simmons
- Mar 4, 2016
- 4 min read
1. Mathematics as a Language: From lecture One and the subsequent reading 'Mathematics as a Language: A Theoretical Framework for Scaffolding Students' (Jamieson-Proctor & Larkin, n.d.), I found the 'Four Levels of Mathematical Language' very interesting. Although, I had never put much thought into why educators used certain mathematical terms (or lack thereof) with their students, I can now understand the ideologies and methodologies which substantiate Maths as a language.
Language of Addition:
Thinking Strategies: Count up - From 1, count up 1 / Doubles - Double 1 is 2
2. The Dimensions of Disciplinary Understanding - Addition: (Ron Ritchhart, 1999) Method - Is the student using a method to assist them in finding the answer to an addition problem?
Purpose - Can they clarify the purpose of why they are using addition to find an answer?
Forms - Are they using appropriate forms to communicate their ideas?
Content - Are they correctly identifying the content to use in each situation?
3. Concept, Skill and Strategy: Maths Concept: The concept that addition is the bringing together of two numbers to find a total.
Maths Skills: How we act upon turning our concepts into answer - Such as, using addition algorithm and knowing to work right to left in our workings.
Strategies: Mathematical strategies are tactics used to help one answer questions efficiently.
Strategies for Addition
(Math Coachs Corner. (2014). Anchor chart [Photograph]. Retrieved from http://www.mathcoachscorner.com/2014/07/trendinginmath-6/)
Unit Learning Resource:
"Blank Addition number facts grid to 9 + 9 that children can colour in as they learn a new strategy and can use that strategy to work out the answers" - Lecture 1: Learning Activities
"Research has shown that the most effective way for students to learn number facts is to organise the facts into clusters. Each cluster is based on a thinking strategy that students can use to help them learn all of the facts in that cluster. For addition, the clusters are 'count on', 'use doubles' and 'use ten'. Similar clusters are used for subtraction." (Burnett & Irons, 2002)
How has this week changed my understanding of addition?
Without having any placements as yet, I reflect on this week as a parent that becomes (regrettably) frustrated whilst helping my six year old with his homework. At times when he seems fidgety or vacant, I feel like saying "It’s not hard, you are just adding 4 and 7, count it out!” But, through this week’s teachings, it is clear my lack of student language is impending his ability to create concepts within himself, stalling him at the basic level of comprehension. I must be mindful to engage language that helps him form concepts in his mind, allowing him to confidently start exploring skills and methods. It makes sense that students will be unable to progress to symbolic language in addition (or Maths in general), if they do not first understand what addition is and the purpose of finding answers. In creating this deep understanding with children, it is fundamental to create Maths contextual to the individuals, and I can now appreciate why.
MISCONCEPTION: A big struggle for my son with addition, was that we were not adding the numbers together ( 4 + 4 = 44) we were adding their value together (4 + 4=8).
Strategies to avoid misconception - Use tokens or blocks to show the physical joining of amounts. Visual/ Concrete as below, help foster conceptual understandings of addition and avoid misconceptions:
Additional Resources:
Teaching Strategy - Working in pairs, the cup addition activity (pictured above) is a fantastic way for children to role play a problem. For Example, You could have two students (Sarah and Steve) and give them each 5 lollies. You can then have them enact this following problem which you will share in student language - "If Sarah had five lollies to put in a cup and Steve had 5 lollies to put in a cup, how many would they have together".
(Fig 1: Teaching in Progress. (n.d). Ladybug mat [photograph].
Retrieved from https://www.pinterest.com/pin/353462270730573361/)
(Fig. 2: Sweet Sounds of Kindergaten. (2014). Math - addition cups [photograph]. Retrieved from http://sweetsoundsofkindergarten. blogspot.com.au)
(Fig. 3: Pladough to Plato. (2015). Lego addition [photograph]. Retrieved from https://www.pinterest.com/pin/9577192955280 1549/)
ACARA Links to Addition in the Foundation Year:
http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?y=1&s=NA&layout=1
(Australian Curriculum, n.d.)
Scootle Resources:
- The below is an interactive digital resource, where students are given a question, for example "2 groups that make 4 altogether. Then, students click the tile that answers the question. In a class that utilises iPads, this could be a great morning rotation activity
(http://worksheets.mathsbuilder.com.au/games/selector/Addition_and_Subtraction/0/)
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- The below interactive digital resource helps student visualise the strategy of counting on, using a number line. In a class that utilises iPads, this could be a great morning rotation activity.
(http://www.scootle.edu.au/ec/viewing/L8285/index.html)
Idea Summaries from the Textbook:
Chapter One: School mathematics in a changing world
* The three strands of maths are - Number and algebra, measurement and geometry, and statistic and probability
* Educators must consider the needs of the subject (Maths is continually in flux, must embrace new technologies), child (children must be developmentally ready to reach levels of understanding) and society (assessment, accountability and equity).
Chapter Nine: Operations meanings and basic facts - addition
- Thinking strategies for addition - Communitive (a + b = b + a), Doubles and near doubles, counting on, 10 facts
Chapter Eleven: Solving mathematical problems with standard and alternative written strategies - addition
- Teachers must ensure students gain conceptual understandings to algorithms, couterpart to procedual understanding - Ensure students are not learning by rote. Using materials helps consolidate the gap between student language and mathematical/symbolic language.
-Addition is the first goal of early years.
- Standard addition algorith - Systematic right to left approach, trading and place value.
- Alternative partial-sum algorithm - Add the hundreds, then the tens and then the ones, then add the 3 sets of numbers together.
(Reys, Lindquist, Lambdin, Smith, Rogers, Falle, Frid & Bennett, 2012)
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