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

Aug 21

           Directed reading and reflection questions:

  1. What is the problematique that this study addresses?
  2. Describe two “gaps” the authors identify (first chapter) and explain their ostensible importance/significance given the problem this study addresses.
  3. 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?
  4. In what ways might the use of classroom video described in this study be an appropriate broad method for researching the problem?
  5. 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?
  6. What might be the potential value of the authors’ focus of inquiry on teaching rather than teachers ?

Discussion page for this assignment is at Aug 21 Discussions

Aug 28

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

  1. 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)?
  2. 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. What phenomena do scripts purportedly explain and how do they purportedly explain them?
  3. 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?
  4. 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:

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.

Sep 04

Due noon, Sep 11

Sep 11

Due 6p, Sep 17

Sep 18

Due 6p, Sep 24

Sep 25

Due 6p, Oct 1

Oct 02

  1. 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.
  2. 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
  1. What does Thompson mean by quantity? Why is it important that he define it as he does?
  2. In what way is a rate of change a quantity as Thompson defines quantity?
  3. Summarize JJ's development of speed as a quantity (including subsidiary quantities) and her general notion of rate of change as a quantity.
  1. What is the thesis proposed by M & C?
  2. What do M & C mean by "quantity"? Do they employ this meaning consistently?
  3. In what ways do M & C add to Thompson's theory of quantitative reasoning?

Oct 09

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

Oct 09


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

  1. Identify the main constructs used/developed in the article;
  2. Describe the constructs in your own words and in a manner that is faithful to the authors' intended meaning;
  3. Provide at least one example from the article for each construct that illustrates its use and usefulness;
  4. 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.
  5. Explain what you learned from this article. Use the article's constructs and others you bring in.

Oct 16

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

Oct 23

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.

  1. Bressoud, D. M. (2010). Historical reflections on teaching trigonometry. Mathematics Teacher, 104, 107-112 (plus six pages of supplementary material).
  2. 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.
  3. 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
  4. 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
  5. Moore, K. C. (2014). Quantitative reasoning and the sine function: The case of Stu 9. Journal for Research in Mathematics Education, 45, 102-138.
  6. 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
  7. 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.
  8. 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.
  9. 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.
  10. Weber, K. (2005). Students' understanding of trigonometric functions. Mathematics Education Research Journal, 17, 91-112.

Oct 30

  1. 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.
  2. 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.

Nov 06

  1. 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.
  2. 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.

Nov 13

  1. 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.
  2. 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

Nov 20

  1. Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23(3), 247-285.
  2. 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.
  3. 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.

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

Nov 27

  1. 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
  2. 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