Talk:Cognition and Instruction/Learning Mathematics

Explain any major decisions that led to your choice of sub-topics or content.
Mathematics is an abstract and complex subject to many people. Therefore, our group decided to elaborate more teaching strategies for mathematics. The definition of mathematics in relation to the knowledge on the student's performance are misused and mistaken by many teachers today. For instance, the western school curriculums are focusing more on procedural and declarative knowledge rather than conceptual knowledge. Hence, it is important that we discuss the definition of mathematics and what knowledge is required in learning mathematics in the introduction. In addition, we decided to briefly mention arithmetic and algebra because they are two major mathematical concepts that are influential to other mathematical areas.

We believe that we need to include arithmetic problem solving as one of our topics in learning to mathematics is because we use arithmetic regularly in our daily lives. Although this is considered to be one of the basic parts of mathematics, we must have this conceptual knowledge in order to develop further in learning new materials.

We believe that we should include algebra in our chapter because it is a board topic in math. Also, the knowledge of algebra is applied to other areas in mathematics too. Therefore, it is essential and fundamental knowledge in higher level of math. Since this chapter is about cognitive and instruction of mathematics, we decided to confuse on the teaching side of algebra, so we have sub-topics like problems with algebra teaching/learning, ways to solve these problems/errors, Instructions to teach algebra and Important factors that teachers should focus on.

We all experience and use math every day yet the majority of people don’t seem to feel confident using math. In my experience at university, it is a subject which is frequently avoided. I wanted to include math in the book because we need to make a point of learning math, learning to teach math and becoming confident with math. I especially wanted to include a section on word problems because this type of math is often considered to be more difficult. With word problems it is not just about understanding algorithms and functions. It is also about comprehending the text itself. For this reason there are other implications for teaching mathematics. Topics were chosen for the following reasons: Difference and Relationship between Arithmetic and Algebra: Word problems are found in both arithmetic and algebra. These types of problems are similar in both areas of mathematics and can be taught with similar strategies. Issues with learning word problems: Syntax and semantics are important, as well as learning inference. These topics are taught in English Language Arts but not generally taught in math. This has some implications on instruction. Instructions to teach word problems: Solving a word problem is more than just plugging in the right algorithm. What are the necessary steps for solving a word problem. Are these steps generally taught to students? Important factors that teachers should focus on: Why is it so hard for students to solve word problems? Let’s identify the most common mistakes and consider ways to correct these in future instruction.

Learning is closely related to the students’ level of self-efficacy and self-confidence. Therefore, we decided to look closely at the relationship between self-efficacy and learning. After discussing the importance of self-efficacy, we believe that it is critical to recommend some assessments on how to identify the students’ level of self-efficacy because many school curriculums overlook the measurements of self-efficacy. Nevertheless, the main point is to increase students’ self-confidence so that students’ learning performance will also enhances. This is definitely important in teaching mathematics since many people believe that they are not skilled at mathematics due to past challenges or failures. Hence, it is a good idea to first improve their self-confidence level which will then engage them in learning in mathematics in the future.

Describe your plans for developing the chapter.
There seems to be a relationship between working memory capacity and learning mathematics. We might discuss this important relationship later as a major factor to learning mathematics. If possible, we might put it as a second-level heading under a top-level heading or putting it as its very own top-level heading. In addition, there is a relationship between arithmetic and algebra. If we can find enough information and studies about this relationship, we can move it back to its own top-level heading. We also noticed that the importance of conceptual, procedural, and declarative knowledge play a big role in learning mathematics. We did not mention thoroughly enough in the wikibook. Hence, if we noticed more connections in the arithmetic, algebra and word problem area, then we will add these knowledges as a second-level heading under arithmetic, algebra and word problem. Since mathematics is such a big component of science, we might add a section that is called, implications of teaching science. In this section, we will discuss the relationship between mathematics and science. However, we will have to gather enough information to elaborate more on this relationship.

links for article reviews
Hi everybody,

I have added all the topics for our chapter. As you go through the papers, if you find one that you think would be good for one of our headings, just copy the link and paste it under the right heading. Then whoever is researching that topic will be able to use info from the paper if they think it is good info. I have added a section entitled "Other Studies" for papers that look interesting but may not relate specifically to the topics we have listed. I've put some links to studies in the "other" category. They seem interesting and we could consider them if we have room and feel they would be helpful or relevant.

I have added some links but I think that I will try to search using different key words, tomorrow.

Corrine

EDUC320CLB (discuss • contribs) 00:21, 8 November 2015 (UTC) 2 Arithmetic Problem Solving

2.1 Definition of Arithmetic

2.2 Problems with Arithmetic teaching and learning http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=10&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2014-15851-001&db=psyh http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=14&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2013-35352-004&db=psyh http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=23&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2010-03040-004&db=psyh http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=27&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2009-00839-009&db=psyh http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=33&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=1994-39146-001&db=psyh

2.3 Ways to solve these problems http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=37&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2013-02439-012&db=psyh

2.4 Teaching strategies for arithmetic http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=12&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2009-00156-003&db=psyh

2.5 Important factors that teachers should focus on

3 Algebra Problem Solving

3.1 Definition of Algebra

3.2 Problems with algebra teaching and learning http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?sid=d87b97c9-c243-4140-b70a-da033e24ed78%40sessionmgr4002&vid=139&hid=4107&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2011-11779-010&db=psyh

3.3 Ways to solve these problems

3.4 Teaching strategies for algebra http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=8&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2015-01041-009&db=psyh

3.5 Important factors that teachers should focus on

4 Word Problems

4.1 Relationship between Arithmetic and Algebra

4.2 Issues with learning to solve word problems http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=11&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2005-02182-004&db=psyh

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4.3 Teaching Strategies for word problems http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?sid=d87b97c9-c243-4140-b70a-da033e24ed78%40sessionmgr4002&vid=147&hid=4107&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2004-17602-026&db=psyh

http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?sid=d87b97c9-c243-4140-b70a-da033e24ed78%40sessionmgr4002&vid=163&hid=4107&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2010-01017-007&db=psyh

4.4 Important factors that teachers should focus on http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?sid=d87b97c9-c243-4140-b70a-da033e24ed78%40sessionmgr4002&vid=155&hid=4107&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=1996-90591-001&db=psyh

5 Development in self-efficacy and self-confidence

5.1 How students' psychological states can impact their success in learning http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?sid=d87b97c9-c243-4140-b70a-da033e24ed78%40sessionmgr4002&vid=151&hid=4107&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2012-11985-002&db=psyh

5.2 How to measure self-efficacy and self-confidence

5.3 How to develop self-efficacy and self-confidence http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=105&sid=d87b97c9-c243-4140-b70a-da033e24ed78%40sessionmgr4002&hid=4107&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2010-07571-004&db=psyh

5.4 Mathematical skills are applicable in their real-life situations

Other studies

http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?sid=d87b97c9-c243-4140-b70a-da033e24ed78%40sessionmgr4002&vid=134&hid=4107&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=1982-31222-001&db=psyh

http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?sid=d87b97c9-c243-4140-b70a-da033e24ed78%40sessionmgr4002&vid=142&hid=4107&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=1989-06691-001&db=psyh

http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?sid=d87b97c9-c243-4140-b70a-da033e24ed78%40sessionmgr4002&vid=153&hid=4107&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2006-06439-041&db=psyh

http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?sid=d87b97c9-c243-4140-b70a-da033e24ed78%40sessionmgr4002&vid=172&hid=4107&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2008-04999-007&db=psyh

http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=7&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2012-04592-000&db=psyh

http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=16&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2012-22068-002&db=psyh

http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=19&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2006-08778-004&db=psyh

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http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=25&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2007-02586-006&db=psyh

http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=30&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2004-11650-008&db=psyh

http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=32&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2008-07541-003&db=psyh mathematic disability?

http://web.a.ebscohost.com.proxy.lib.sfu.ca/ehost/detail/detail?vid=43&sid=02119bd6-1ad2-4dbd-855b-f95547e6065d%40sessionmgr4003&hid=4109&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=2007-14999-002&db=psyh low achieving EDUC320CLB (discuss • contribs) 06:09, 10 October 2015 (UTC)

Personality and the Learning of Mathematics (attitudes towards Mathematics)

http://www.jstor.org.proxy.lib.sfu.ca/stable/3482335

Teaching Strategies: problem solving

Reconceptualizing Mathematics problem solving for low-achieving students

http://rse.sagepub.com.proxy.lib.sfu.ca/content/22/2/102.full.pdf+html

Cognitive process in learning Mathematics http://aer.sagepub.com.proxy.lib.sfu.ca/content/21/3/487.full.pdf+html

Applying Piaget’s Theory of Cognitive Development to Mathematics Instruction  http://files.eric.ed.gov/fulltext/EJ841568.pdf

1.introduction 2.cognition theory in math

3. Problems with mathematic learning and teaching problem with learning problem with teaching

4. teaching strategies

5.summary

EDUC320CLB (discuss • contribs) 00:21, 8 November 2015 (UTC)

Revamping the Chapter
Hi Everybody,

As per our discussion in class today, we are revamping the chapter. Based on John's feedback and availability of relevant articles, we have come up with a new outline which looks like this:

Introduction

Cognitive Theory and Math

Problems with Learning and Teaching Mathematics Problems for Learning Problems in Teaching Word Problems: A special case (maybe we want to do this in a text box as a special feature?)

Teaching Strategies

Summary

I think we'll probably need a couple of other headings and sub-headings but I think they might come about naturally if we start reading the articles.

We didn't have time to finish strategizing about how to organize the chapter for writing but we had started talking about reviewing the articles we had found before, with each of us reorganizing our set of articles for these new headings. It was suggested that we include the title of the article as well as the link for articles we find helpful. As you go through the articles, if you see any potential new headings for our chapter, I suggest that you add the heading and the relevant article. We can discuss pros and cons of each heading the next time we get together. Also, is anyone interested in meeting outside of class time so that we can get more organized? I am available on Fridays after class (most times) and also Mondays between 11 am and 130 pm. I can come other days by special arrangement.

Have a good weekend.

Corrine EDUC320CLB (discuss • contribs) 23:02, 16 October 2015 (UTC)

EDUC320CLB (discuss • contribs) 00:21, 8 November 2015 (UTC)

New Headings
Hi everybody,

On Friday John asked us to work more in our groups. Since Sylvia and I were the only ones there, we talked about each person choosing a topic from those that are already listed for our chapter. We have updated the headings for the chapter. We also talked about the fact that many of the articles are taking a long to to review and thought we should just each choose the articles for the headings we want to write about. So, as it stands now, we have edited the headings on the math chapter. Choose the heading you would like to write about, find your articles and edit directly into the wikibook math chapter. We are short of sub-headings so add some to your topic as appropriate.

Corrine

EDUC320CLB (discuss • contribs) 00:21, 8 November 2015 (UTC)

Peer Reviews
First Peer Review

I think the strongest feature of this chapter is the clear connection between mathematics and cognition. The paragraphs always go back to the main point (learning mathematics) which I find it easy to follow. The chapter uses research studies effectively, especially the paragraphs on cognitive domain. I like how multiple studies are compared and used to come to a conclusion. Good choice of articles. I think the chapter covers important aspects of the topic like Piaget's stages of cognitive development. Some topics need more evidence to support the argument. Since the chapter mentions cultural differences, make sure the studies you picked is somewhat universal. The chapter has a good flow so the readers can understand the overall picture.

The weakest feature is writing mechanics and style. Now, I understand that this is a draft but you can go over the chapter again and fix some sentences. Some sentences are redundant, there are spelling and grammar mistakes. Be careful with words like critics and critiques, formal operational stage, pre-operational (don't forget the bar). You can read each other's work and create a similar tone. Also, I feel like “findings on self-regulated learning in mathematics” can be combined with other paragraphs. For example, mathematics self-regulated learning program research. Overall, the chapter has very good components with interesting research, and the structure looks good. Rumi Hasegawa (discuss • contribs) 00:29, 7 November 2015 (UTC)

Second Peer Review

Overall, this chapter was well structured and written with relevant information. I think one of the strongest features of this chapter is how all the new information introduced was done in context to learning and education. Though theories were discussed in terms of the research they produced, it did not take away from the educational approach, as all research discussed added more to the explanation of how the information related to teaching. This is important as the goal of the wikibook is to provide a clear understanding of how to use these different areas of cognition in an educational setting. I also liked how the popular criticisms of different researchers and theories were discussed, as it helped broaden exactly how and how not to use the theory in terms of teaching.

However, the main criticisms of the chapter can be found in grammatical errors, especially in terms of singular/plural grammar and sentence structure. This is important because the chapter is presented well, but the frequency of grammatical errors takes away from the overall clarity and message of the chapter. Having each author closely edit everyone’s contributions may help in this. Also, as the chapter does a good job of linking theories and strategies to learning throughout the chapter, having a section titled Implications for Instruction can seem a bit repetitive. Nevertheless it is a useful section, so simply renaming it could be a good solution. As a whole, the content and research provided in this chapter is relevant and informative, and with some close editing will be a strong chapter.

Edu320acb (discuss • contribs) 06:09, 8 November 2015 (UTC)

Friday discussion
Hi everybody,

As you may be aware, John has asked each group to give a bit of a presentation about our chapter. Does anybody have any ideas about what we would like to discuss regarding this topic. As you may remember, I already gave a presentation about some of the material which I submitted for the text book. Do we want to use that as a jumping off point? Do you all know what part of the chapter you would like to discuss in the presentation? Are we doing a slide show?

I would be interested in discussing some of the implications for teaching.

Please let me know what you would like to do so that I can prepare some materials.

Corrine EDUC320CLB (discuss • contribs) 22:33, 1 December 2015 (UTC)EDUC320CLBEDUC320CLB (discuss • contribs) 22:33, 1 December 2015 (UTC)

I read your message, Corrine. I have emailed everyone as well about the presentation. Nicole Hui (discuss • contribs) 00:14, 2 December 2015 (UTC)

working memory
Hi everybody,

I just wanted to let you know that I am editing the section on the importance of working memory and I have added information from a brand new study (Aug 2015).

Corrine EDUC320CLB (discuss • contribs) 23:04, 2 December 2015 (UTC)