Assignments

RUME 1 Fall 18 Public

**RUME I Fall 2018 Assignments**

Dates are **meeting dates**. Assignments are due the next class meeting or on a specified date, if given.

Aug 21 | Aug 28 | Sep 04 | Sep 11 | Sep 18 | Sep 25 | Oct 02 | Oct 09 | Oct 09 | Oct 16 | Oct 23 | Oct 30 | Nov 06 | Nov 13 | Nov 20 | Nov 27

Note: You can find any article on which I am author or coauthor at Pat's Publications. Hard-to-find articles are at Hard to Find Articles

- Introductions and introduction to the course
- Purchased and have read chapters 1-5 of
*The Teaching Gap*by Stigler & Hiebert (for 08/28) - Download Zotero, the (free) bibliographic management software.
*Install both the desktop application and the browser plugin.* - Enter
*The Teaching Gap*into your Zotero database - Discussion of chapters 1-5 of
*The Teaching Gap*

* Directed reading and reflection questions:*

- What is the
*problematique*that this study addresses? - Describe two “gaps” the authors identify (first chapter) and explain their ostensible importance/significance given the problem this study addresses.
- What are some of the authors’ rationales for conducting a cross-cultural study of mathematics teaching in light of their framing of the problem of mathematics teaching in American classrooms?
- In what ways might the use of classroom video described in this study be an appropriate broad method for researching the problem?
- Describe the dimensions (both broad and more fine grained) considered by the Math Group in the video study. What implicit or explicit assumptions about what it means to do and learn mathematics might underlie the choice of these dimensions? How appropriate is attention to these particular dimensions given the purpose of the video study?
- What might be the potential value of the authors’ focus of inquiry on teach
*ing*rather than teach*ers*?

Discussion page for this assignment is at Aug 21 Discussions

- Read chapters 6-10 of
*The Teaching Gap*for next week (Sep 4) - Discussion leaders: Stu 9, Stu 3
- Post discussions at Aug 28 Discussions.

* Directed reading and reflection questions (come prepared to discuss them on 09/04):*

- The authors view teaching as a “cultural activity” (TACA). Discuss what they mean by this. A suitable discussion should entail a description of the central characteristics of TACA, as well as an articulation of its significance and important implications. What makes TACA a potentially productive/useful view of teaching (wherein lies its potential power)?
- In their discussion of TACA, the authors introduce the construct of a
*script.*Describe what they mean by this in the context of TACA, and how they propose using it as an explanatory construct. W*hat*phenomena do scripts purportedly explain and*how*do they purportedly explain them? - A core component of Japanese Lesson Study is teachers’ development of “research lessons”. Given the authors’ description of the steps in the lesson study process, what features of the process speak to the
*research*aspect of “research lessons”? That is, wherein lies the*research*in the development of such lessons? - The authors propose, and provide a fairly specific outline of, an “American-style” of lesson study that they assert is a potentially viable means of improving teaching nationwide:

- What are the core criteria upon which their assertion is based?
- Discuss ways in which Stigler and Hiebert’s vision of an American-style lesson study is deeply rooted in their image of teaching as a cultural activity. In other words, how is their image of teaching as a cultural activity reflected in core features of their overarching vision of an American-style of lesson study?

*Follow these links to US graphing equations and Japan solving inequalities.*

*Hear James Stigler's interview on the issue of cultural differences and mathematics learning *. (Click the **play** button in top-left corner to hear the interview.)

*The next four assignments are designed to give you an opportunity to analyze the raw data upon which a research article is based, then compare your analysis with the published analysis. The aim of this activity is to give you a foundational experience to reverse-engineering a published article so that you can imagine the data an article reports.*

*Due noon, Sep 11*

- Complete
**Part 1**of the assignment at this website. - Post comments or questions at Over & Back 1 Discussion.
- Upload documents to your Projects page.
*No late assignments accepted due to the nature of the next assignment.*- Discussion leaders: Stu 10, Stu 1

*Due 6p, Sep 17*

- Complete
**Part 2**of the assignment at this website. - Post comments, questions, or replies at Over & Back 2 Discussion.
- Upload documents to your Projects page.
*No late assignments accepted due to the nature of the next assignment.*- Discussion leaders: Stu 4, Stu 2
- 1994Talking about Rates 1.pdf

*Due 6p, Sep 24*

- Complete
**Part 3**of the assignment at this website. *No shared comments or discussion for this assignment*.- Upload documents to your Projects page.
*No late assignments accepted due to the nature of the next assignment.*- Discussion leaders: Stu 7, Stu 8

*Due 6p, Oct 1*

- Complete
**Parts 4 and 5**of the assignment at this website. *No shared comments or discussion for this assignment*.- Upload documents to your Projects page.
- Discussion leaders: Stu 6, Stu 5
- 1996Talking about Rates 2.pdf

- Locate, acquire, and enter the following 2 articles into your bibliographic system:

- Thompson, P. W. (1994). The development of the concept of speed and its relationship to concepts of rate. In G. Harel & J. Confrey (Eds.),
*The development of multiplicative reasoning in the learning of mathematics*(pp.179–234). Albany, NY: SUNY Press. - Moore, K. C., & Carlson, M. P. (2012). Students’ images of problem contexts when solving applied problems.
*The Journal of Mathematical Behavior*, 31, 48-59. doi: 10.1016/j.jmathb.2011.09.001

- Regarding the Thompson article:

- What does Thompson mean by
*quantity*? Why is it important that he define it as he does? - In what way is a rate of change a quantity as Thompson defines quantity?
- Summarize JJ's development of speed as a quantity (including subsidiary quantities) and her general notion of rate of change as a quantity.

- Regarding Moore and Carlson

- What is the thesis proposed by M & C?
- What do M & C mean by "quantity"? Do they employ this meaning consistently?
- In what ways do M & C add to Thompson's theory of quantitative reasoning?

- Post your responses to these six questions as a Word file in your Projects page by 6p on
**Oct 10**. Use the standard format to name your file.

(*Yes, there is no class, but you have an assignment for Oct 16.*)

- Locate and acquire
*Thompson, P. W. (1993). Quantitative reasoning, complexity, and additive structures. Educational Studies in Mathematics, 25, 165-208.*Enter it into your bibliographic system. - Read the article
- How does this article, together with what we learned about JJ's development of speed and rate, provide insight into calculus students' difficulty with slope as a rate of change?
- Discussion leaders: TBA
- This question is for discussion on Oct 16.

NO CLASS -- FALL BREAK

*In subsequent assignments, do this when requested to respond to "the five questions".*

- Identify the main constructs used/developed in the article;
- Describe the constructs in your own words and in a manner that is faithful to the authors' intended meaning;
- Provide at least one example from the article for each construct that illustrates its use and usefulness;
- Explain how the examples illustrate the use and usefulness of each construct. That is, describe how the constructs constitute a system for explaining the article's phenomena of interest.
- Explain what you learned from this article. Use the article's constructs and others you bring in.

- Locate, acquire, and enter the following articles into your bibliographic system:

- Hackenberg, A. J. (2010). Mathematical caring relations in action.
*Journal for Research in Mathematics Education.*41*(3)*, 236-273. - Proulx, J. (2013). Mental mathematics, emergence of strategies, and the enactivist theory of cognition.
*Educational Studies in Mathematics*. April, 2013.

- Read the articles
- Post questions, comments, or replies about each article at Oct 16 discussions.
- Discussion leaders: TBA

*This is an "experimental" assignment to emphasize how different researchers bring different perspectives to researching the same body of ideas.*

You will, as a group, read all of the following articles and hold a discussion about students' learning of trigonometry--what it means to understand trigonometry and sources of students' difficulties with trigonometry. Your discussion will simulate what happens when a group of experts on a subject hold a mini-conference to flesh out "what is known" about an area.

- Locate, acquire, and enter the following articles into your bibliographic system:

- Bressoud, D. M. (2010). Historical reflections on teaching trigonometry. Mathematics Teacher, 104, 107-112 (plus six pages of supplementary material).
- DeJarnette, A. F. (2018). Students’ conceptions of sine and cosine functions when representing periodic motion in a visual programming environment. Journal for Research in Mathematics Education, 49, 390-423.
- Martínez-Planell, R., & Cruz Delgado, A. (2016). The unit circle approach to the construction of the sine and cosine functions and their inverses: An application of APOS theory. The Journal of Mathematical Behavior, 43, 111-133. doi: 10.1016/j.jmathb.2016.06.002
- Moore, K. C. (2012). Making sense by measuring arcs: A teaching experiment in angle measure. Educational Studies in Mathematics, 83, 225-245. doi: 10.1007/s10649-012-9450-6
- Moore, K. C. (2014). Quantitative reasoning and the sine function: The case of Stu 9. Journal for Research in Mathematics Education, 45, 102-138.
- Tallman, M. A., & Frank, K. M. (2018). Angle measure, quantitative reasoning, and instructional coherence: an examination of the role of mathematical ways of thinking as a component of teachers’ knowledge base.
*Journal of Mathematics Teacher Education*(online first). doi: 10.1007/s10857-018-9409-3 - Thompson, P. W. (2008). Conceptual analysis of mathematical ideas: Some spadework at the foundations of mathematics education. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. Sépulveda (Eds.), Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol 1, pp. 31-49). Morélia, Mexico: PME.
- Thompson, P. W. (2013). In the absence of meaning. In K. Leatham (Ed.), Vital directions for research in mathematics education (pp. 57-93). New York: Springer.
- Thompson, P. W., Carlson, M. P., & Silverman, J. (2007). The design of tasks in support of teachers’ development of coherent mathematical meanings. Journal of Mathematics Teacher Education, 10, 415-432.
- Weber, K. (2005). Students' understanding of trigonometric functions. Mathematics Education Research Journal, 17, 91-112.

- Read the articles assigned to you
- Post questions, comments, or replies about each article at Oct 23 discussions
- Prepare to debate these questions
- What is the difference between understanding triangle trigonometry and understanding trigonometric functions?
- What ideas are central to understanding triangle trigonometry? Trigonometric functions? What does it mean for students to understand them?
- What difficulties do students have with these ideas and what are sources of their difficulties?
- Implications of research on teaching/learning trigonometric ideas for improving students' trigonometric understandings?

- You will pretend to be the author(s) of articles assigned to you and represent their views in the discussion.
- Panel Assignments.docx

- Locate, acquire, and enter the following articles into your bibliographic system:

- Tall, D., & Vinner, S. (1981). Concept Image and Concept Definition in Mathematics with Particular Reference to Limits and Continuity.
*Educational Studies in Mathematics, 12*(2), 151-169. - Roh, K. H. (2010). An empirical study of students' understanding of a logical structure in the definition of limit via the epsilon-strip activity.
*Educational Studies in Mathematics, 73*, 263-279.

- Read the articles
- Post a question about the content of each article on the Oct 30 discussions page.
- Discussion leaders: TBA
- Write-up: Respond to the five questions for both articles, but you need only write a précis for Roh's article.

- Enter the following two articles into your bibliographic system:

- Sfard, A. (1992). Operational origins of mathematical notions and the quandary of reification - the case of function. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy. Washington, D. C. : Mathematical Association of America.
- Thompson, P. W., & Sfard, A. (1994). Problems of reification: Representations and mathematical objects. In D. Kirshner (Ed.),
*Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education — North America, Plenary Sessions*(Vol 1, pp. 1–32). Baton Rouge, LA: Lousiana State University.

- Read the articles
- Post question, comment, or reply about each article on the Nov 6 Discussions page.
- Discussion leaders: TBA
- Write-up: Respond to the five questions for both articles, and submit these by noon, Nov 13 on your Projects page.

- Locate, acquire, and enter the following 2 articles into your bibliographic system:

- Confrey, J., & Smith, E. (1995). Splitting, Covariation, and Their Role in the Development of Exponential Functions.
*Journal for Research in Mathematics Education*, 26(1), 66-86. - Ellis, A. B., Özgur, Z., Kulow, T., Dogan, M. F., & Amidon, J. (2016). An exponential growth learning trajectory: Students’ emerging understanding of exponential growth through covariation.
*Mathematical Thinking and Learning*, 18, 151-181. doi: 10.1080/10986065.2016.1183090

- Read each article
- By the noon of Nov 20 post questions, comments, or replies about each article on the Nov 13 Discussions page.
- Contrast the two articles on whatever features stand out to you. Post your paper to your Projects page by noon, Nov 20.
- Discussion leaders: TBA

- Locate, acquire, and enter the following articles into your bibliographic system:

- Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function.
*Educational Studies in Mathematics*, 23(3), 247-285. - Carlson, M. P., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study.
*Journal for Research in Mathematics Education, 33*(5), 352–378. - Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. In J. Cai (Ed.),
*Compendium for research in mathematics education*(pp. 421-456). Reston, VA: National Council of Teachers of Mathematics.

- Read each article for discussion on Nov 27. Pay special attention to differences among ways of characterizing key constructs.

*Ignore the following. I thought we had one more week than we actually have.*

- Locate, acquire, and enter the following articles into your bibliographic system:

- Zazkis, D., & Villanueva, M. (2016). Student Conceptions of What it Means to Base a Proof on an Informal Argument.
*International Journal of Research in Undergraduate Mathematics Education, 2*, 318-337. doi: 10.1007/s40753-016-0032-3 - Hub, A., & Dawkins, P. C. (2018). On the construction of set-based meanings for the truth of mathematical conditionals.
*Journal of Mathematical Behavior, 50*, 90-102. doi: 10.1016/j.jmathb.2018.02.001