In week one the following big ideas were covered:
- The four language models for mathematics are a framework that can be used to underpin
mathematics learning. These four language models can be seen below:
1. Student language - the language used in this level is at the students level and reflects the real
world. An example is three birds put with four birds makes seven birds altogether (Jamieson-
Proctor, 2016, p. 10).
2. Materials language - the language used in this level is still at the students level but replaces
the language used in their world with materials language, for example counters (Jamieson-
Proctor, 2016, p. 11).
3. Mathematics language - the language used in this level uses proper mathematics, such as add,
subtract, equals, but does not used the symbols yet (Jamieson-Proctor, 2016, p. 12).
4. Symbolic language - this is the final language level and involves students using the
mathematics symbols, for example 3 + 4 = 7 (Jamieson-Proctor, 2016, p. 13).
- The language model for mathematics, which can be seen below (figure 1.1). This language model
is a way to break down the four stages of mathematics language. On the right hand side is where
the four stages go (see figure 1.2), and on the left hand side is where the different materials for
each stage belong (see figure 1.3). This is a very useful diagram in breaking down the four
language model for mathematics, which is crucial in teaching mathematics to people of any ages.
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| Figure 1.1: Jamieson-Proctor, R. (2016). EDMA202/262 Mathematics Learning and Teaching 1: Week 1 Part 1. Brisbane, Australia: Australian Catholic University. |
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| Figure 1.2: Jamieson-Proctor, R. (2016). EDMA202/262 Mathematics Learning and Teaching 1: Week 1 Part 1. Brisbane, Australia: Australian Catholic University. |
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| Figure 1.3: Jamieson-Proctor, R. (2016). EDMA202/262 Mathematics Learning and Teaching 1: Week 1 Part 1. Brisbane, Australia: Australian Catholic University. |
1. Count On - this is a strategy that can be used for 0, 1, 2 and 3. The child would start at the
larger number and then count on to the final answer (Reys, Lindquist, Lambdin, Smith,
Rogers, Falle, Frid & Bennett, 2012).
2. Use Doubles - doubles are a basic concept which children can learn quickly (Reys et al., 2012)
3. Use Tens - in the early years children learn how to make combinations of ten, often described
as 'rainbow facts', and this can then be used as a strategy for addition (Reys et al., 2012).
These big ideas have changed my understanding on the weekly topic in two ways;
1. Due to the four language models of mathematics I now have a greater understanding of how to
teach mathematics to students of any age.
2. I also have a greater understanding of addition and effective strategies that can be used to teach
children.
Demonstrate your understanding of addition and related skills and strategies children need to assimilate and be able to use
- The concept this week was addition, addition is the joining of two or more numbers to find a total
(Jamieson-Proctor, 2016).
- The concept of addition is applied using the skill of addition algorithm. An example of an addition
algothrim being used can be seen in figure 1.4.
- There are three strategies that can be used for addition; count on, use double and use tens. This
strategy has been explained in section one of this post.
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| Figure 1.4: Jamieson-Proctor, R. (2016). EDMA202/262 Mathematics Learning and Teaching 1: Week 1 Part 1. Brisbane, Australia: Australian Catholic University. |
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| Figure 1.5: Language Model for Addition |
Describe/demonstrate a specific teaching strategy and appropriate resource/s that could be used to assist children to understand the concept of addition
- A specific teaching strategy that could be used for children to understand the concept of addition
is the count on strategy. "In counting on, the child gives correct number names as counting
proceeds and can start at any number and begin counting" (Reys et al., 2012, p. 152). Children
would be taught to start at the highest number given and then count on.
- An example of using the count on strategy would be "Sally has 6 biscuits and was given 3 more
by her mother." 6, 7, 8, 9.
- When practising addition in the children and materials language stage I would use resources, such
as pictures, counters, toys, MAB blocks and other concrete materials. By using these concrete
materials students are able to physically count on to reach their final answer. An example of how
this would work can be seen in the Matholia Channel video.
Describe/demonstrate a specific misconception children might have in relation to addition. How would you avoid or remediate this misconception?
- A common misconception that children might have in relation to addition is that the '+' sign means
'and' not 'plus' or 'add' (Harris, 2000). One way that this misconception can be avoided is to make
sure that when writing for the students the '+' sign is never used as short-hand for 'and', as this
may confuse matters for children. A way to remediate this misconception would be to make sure
that when practising addition with students to use the correct terminology 'plus' and 'add', and to
make a point that students know the reason behind this use of terminology.
Provide appropriate URL links to the ACARA year, strand, sub-strand, content description, elaborations and Scootle resources for the earliest mention of addition
- Addition can be first seen in the foundation year, number and algebra strand and the number and
place value sub-strand.
- The content description for ACMNA004 is "represent practical situations to model addition and
sharing" (ACARA, 2016)
- The elaborations are "using a range of practical strategies for adding small groups of numbers,
such as visual displays or concrete materials" and "using Aboriginal and Torres Strait Islander
methods of adding, including spatial patterns and reasoning" (ACARA, 2016).
- Scootle resources for addition
Provide appropriate links to resources and ideas you have sourced personally to assist students to develop concepts, skills and/or strategies related to addition
- Resources for students to understand the concept of addition
* Addition Song
* Concept of Addition
- Resources for students to understand the skill of addition
*Addition Algorithm
- Resources for students to understand the strategies for addition
* Counting On
* Use Doubles
* Use Tens
Provide a concise synthesis of the textbook chapter/s related to the weekly topic
- Reys et al. (2012) described six different thinking strategies for addition:
* Commutativity is the task of learning that by changing the order of the addends. this does not
affect the outcome of the sum, i.e. 5 + 6 = 11, 6 + 5 = 11.
* Adding 1 and 2, i.e. 5 + 1 = 6, 6 + 1 = 7.
* Adding doubles and near doubles, i.e. adding doubles 4 + 4 = 8. i.e. adding near doubles 7 + 8 =
15, because 7 + 7 = 14, plus 1 is 15.
* Counting on, i.e. 2 +6 = 8. Start at 6 then count on i.e. 6, 7, 8
* Combinations to 10, i.e. 4 + 6 = 10, 3 + 7 = 10.
* Adding to 10 and beyond, i.e. 8 + 5 = 13, 8 +2 = 10, plus 3 is 13.
- A goal for basic addition is a goal for the early years (Reys et al., 2012).
- Reys et al. (2012) described three different skills for addition:
* Standard addition algorithm,
i.e. 27
+35
-------
62
* Partial-sum addition algorithm,
i.e. 437
+ 25
--------
12
50
400
--------
462
* Higher-decade algorithm,
i.e. 9 + 5 = 14, the sum will have a 4 in the ones place and the tens place will always have 1 ten
References
Australian Curriculum and Assessment, Reporting Authority [ACARA].
(2016). Mathematics.
Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1
Boney4th. (2012). Doubles and near
doubles. Retrieved from https://www.youtube.com/watch?v=7PRIBdFtRNA
Boney4th. (2012). Make 10 addition
strategy. Retrieved from https://www.youtube.com/watch?v=E4Kq28ayZiU
Education Services Australia. (2016). Scootle: Mathematics.
Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA004&userlevel=(0)#backToTop
Harris, A. (2000). Addition and subtraction.
Retrieved from http://ictedusrv.cumbria.ac.uk/maths/pgdl/unit5/A&S.pdf
Harry Kindergarten Music. (2014). When you add with a pirate.
Retrieved from https://www.youtube.com/watch?v=WT_wvvEvkw4
Jamieson-Proctor, R. (2016). EDMA202/262 Mathematics
learning and teaching 1: Week 1 part 1. Brisbane, Australia: Australian
Catholic University.
Matholia Channel. (2013). Addition by Counting On.
Retrieved from https://www.youtube.com/watch?v=PUY072JHE4g
Professor Pete's Classroom. (2014).
Teaching the addition algorithm with regrouping. Retrieved from https://www.youtube.com/watch?v=F9mnIXEbTNI
Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn mathematics. Queensland, Australia: John Wiley & Sons Australia, Ltd.
Walkin, K. (2013). Teaching concept of
addition. Retrieved from https://www.youtube.com/watch?v=JZh298VpdhY
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