In week two the following big ideas were covered:
- That mathematics is what teachers teach and students develop numeracy (Jamieson-Proctor,
2016).
- There are three different types of subtraction:
1. Take-away - i.e. "I had 5 lollies and I ate 2. How many do I have left?".
2. Difference/Comparison - i.e. "I have 5 lollies and you have 10 lollies. How many more do you
have than me?" or "How many less do I have than you".
3. Missing addend - i.e. "I have 3 lollies but I need 7 for all my friend. How many more lollies do
I need?" (Jamieson-Proctor, 2016).
- There are three different strategies for subtraction:
1. Count back,
2. Use halves,
3. Use tens (Jamieson-Proctor, 2016).
- Storybooks are a great way to teach subtraction.
- At a primary school level teachers need to consider that children's ability to learn mathematics can
depend on their reading ability (Reys, Lindquist, Lambdin, Smith, Rogers, Falle, Frid & Bennett,
2012).
- Students learn mathematics with understanding by actively building new knowledge from their
personal experiences and prior knowledge (Reys et al., 2012).
These big ideas have changed my understanding on the weekly topic in the following ? ways;
1. I now have a greater understanding of subtraction after this week. Prior to this week I didn't
realise that there was more than one type of subtraction.
2. This week has also given me a greater understanding of different strategies for teaching children
subtraction
Demonstrate your understanding of the mathematical concept and related skills and strategies children need to assimilate and be able to use, that are related to subtraction
- The mathematical concept this week was subtraction. Subtraction is where the overall
total and one part of the sum is known and you need to find the missing part.
- The concept of subtraction is applied using the skill of subtraction algorithm. This can be seen in
figure 1.6.
- There are three strategies for the concept of subtraction; count back, use halves and use tens.
 |
| Figure 1.6: Jamieson-Proctor, R. (2016). EDMA202/262 Mathematics Learning and Teaching 1: Week 2 Part 2. Brisbane, Australia: Australian Catholic University. |
 |
| Figure 1.7: Language Model for Subtraction |
Describe/demonstrate a specific teaching strategy and appropriate resource/s that could be used to assist children to understand the mathematical concept of subtraction
- A specific teaching strategy that could be used for children to understand the concept of
subtraction is the count on strategy. Children struggle to count backwards and therefore there
should be learning experiences available for children to learn to count backwards (Reys et al.,
2012). Children would be encouraged to count back from the highest number.
- An example of the count back strategy would be "Max had 12 eggs and broke 4 eggs. How many
eggs does Max have left?" 12, 11, 10, 9, 8.
- When practising subtraction in the children and materials language stage I would use resources,
such as pictures, toys, MAB blocks, counters 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 subtraction. How would you avoid or remediate this misconception?
- A common misconception for subtraction is that it is only 'take away', when in fact there are
three kinds of subtraction. A way to remediate this misconception is to make sure that the proper
subtraction language is used, such as 'subtract' or 'minus', instead of 'take away' to avoid
confusion (Harris, 2000).
Provide appropriate URL links to the ACARA year, strand, substrand, content description, elaborations and Scootle resources for the earliest mention of subtraction
- Subtraction can first be seen in Year One of the Australian Curriculum, in the number and algebra
strand, and the number and place value sub-strand.
- The content description for ACMNA015 is "represent and solve simple addition and subtraction
problems using a range of strategies including counting on, partitioning and rearranging parts"
(ACARA, 2016).
- The elaboration is "developing a range of mental strategies for addition and subtraction problems"
(ACARA, 2016).
- Scootle resources for subtraction
Provide appropriate links to resources and ideas you have sourced personally to assist students to develop concepts, skills and/or strategies related to subtraction
- Resource/s for students to understand the concept of subtraction
* subtraction song
- Resource/s for students to understand the skill of subtraction
* subtraction algorithm
- Resource/s for students to understand the strategies of subtraction
* counting back strategy
* use tens strategy
* use doubles strategy
Provide a concise synthesis of the textbook chapter/s related to the weekly topic
- Teachers can support the diverse learners in the classroom by:
* Creating a positive learning environment;
* Avoiding negative experiences that increase anxiety;
* Establishing clear expectations;
* Treating all students as equally likely to have aptitude for mathematics;
* Helping students improve their ability to retain mathematical knowledge and skills (Reys et al.,
2012).
- At a primary school level teachers need to consider that the children's ability to learn mathematics
can depend on their reading ability (Reys et al., 2012).
- There are three types of subtraction:
1. Separation problems - "...involves having one quantity, removing a specified quantity from it
and noting what is left" (Reys et al., 2012, p. 200). i.e. "Wan had 7 balloons. She gave 4 to
other children. How many did she have left?" (Reys et al., 2012, p. 200).
2. Comparison problems - "...involves having 2 quantities, matching them 1 to 1 and noting the
quantity that is the difference between them" (Reys et al., 2012, p. 200). i.e. "Wan had 7
balloons. Richard had 4 balloons. How many more balloons did Wan have than Richard?"
(Reys et al., 2012, p. 200).
3. Part-whole problems - "...a set of objects can logically be separated into 2 parts. You know
how many are in the entire set and you know how many are in one of the parts. You need to
find out how many must be in the remaining part" (Reys et al., 2012, p. 200). "Wan had
7 balloons. Four of the were red and the rest were blue. How many were blue?" (Reys et al.,
p. 200).
- There are two different skills for subtraction:
* Standard subtraction algorithm
91 11 - 4 = 7 ones
- 24 8 tens - 2 tens = 6 tens
-------
67
* Partial-difference subtraction algorithm
523
- 385
-----------
200
- 60
- 2
-----------
140
- 2
----------
138
- There are four thinking strategies for subtraction facts:
1. Subtracting 1 and 2
2. Doubles
3. Counting back
4. Counting on (Reys et al., 2012).
References
Australian Curriculum and Assessment, Reporting Authority [ACARA].
(2016). Mathematics.
Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1
Beams, H. (2013). Subtraction
with the make ten strategy. Retrieved from https://www.youtube.com/watch?v=n3fY7DbyEUo
Education Services Australia. (2016). Scootle: Mathematics.
Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA015&userlevel=(1)
Gray, S. (2011). Using
doubles and building on doubles: A mental math subtraction strategy.
Retrieved from https://www.youtube.com/watch?v=E9_oZ3ew56I
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 subtract with a pirate. Retrieved from https://www.youtube.com/watch?v=QkPa9V2wtZs
Jamieson-Proctor, R. (2016). EDMA202/262 Mathematics
learning and teaching 1: Week 2 part 2. Brisbane, Australia: Australian
Catholic University.
Mathantics. (2012). Math
Antics: Multi-digit subtraction. Retrieved from https://www.youtube.com/watch?v=Y6M89-6106I
Matholia Channel. (2013). Subtract
by counting back. Retrieved from https://www.youtube.com/watch?v=QhR1SEK49qM
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.
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