Assignments

RUME 2 Spr 19

**Assignments**

Dates are **meeting dates**. Assignments listed under a date are due 8:00pm the day prior to the **next** class meeting, or on a specified date if given. Articles are at Articles. *Enter all articles into your Zotero bibliographic library.*

A précis is a special type of summary. See this website for helpful guidance.

THEORY | Jan 08 | Jan 15 | METHODOLOGY | Jan 22 | Jan 29 | Feb 05 | EMERGENCE | Feb 12 | QUANTITATIVE REASONING | Feb 19 | Feb 26 | Mar 05 | Mar 12 | DNR | Mar 19 | AMT | Mar 26 | Apr 02 | Apr 09 | Apr 16 | Apr 23 | Apr 30

**Read**- diSessa, A. A. (1991). If we want to get ahead, we should get some theories. In R. Underhill & C. Brown (Eds.), Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Plenary Addresses (Vol. 1, pp. 220–239). Blacksburg, VA: PME-NA.
- Thompson, P. W. (1991). Getting ahead, with theories: I have a theory about this. In R. Underhill & C. Brown (Eds.), Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Plenary Addresses (Vol. 1, pp. 240–245). Blacksburg, VA: PME-NA.

- Write (and submit) essay:
*My View of the Role of Theory in Mathematics Education Research and Practice*. Cite diSessa, Thompson, or others (e.g., RUME 1) when you draw from them

**Read**- Cobb, P. (2007). Putting philosophy to work: Coping with multiple theoretical perspectives. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 3–38). Charlotte, NC: Information Age Pub.

- Prepare for 1/22 discussion of connections (or lack thereof) among diSessa, Thompson, and Cobb.
- Write a précis of Cobb (2007).
**Due: 1/29**

**Read**- Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 547–589). Mahwah, NJ: Lawrence Erlbaum.
- Hunting, R. (1997). Clinical interview methods in mathematics education research and practice. Journal of Mathematical Behavior, 16(2), 145–165.

- Prepare for 1/22 discussion of comparisons and contrasts between Clement's and Hunting's stances regarding clinical interviews

**Read**- Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 267–307). Mahwah, NJ: Erlbaum.
- Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.

- Prepare for 2/5 discussion of connections between
*Theory*and*Methodology* - Write précis of Steffe/Thompson (
**due 2/12**) - Write précis of Cobb, Confrey et al (
**due 2/12**)

**Read**- diSessa, A. A., & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments. Journal of the Learning Sciences, 13(1), 77–104.
- Thompson, P. W. (2016). Researching mathematical meanings for teaching. In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed., pp. 435–461). New York: Taylor & Francis.

- Prepare for 2/12 comparison and contrast among diSessa/Cobb, Thompson, and prior readings.

**Read**- Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31, 165–190. https://doi.org/10.1080/00461520.1996.9653265
- Cobb, P. (1999). Individual and collective mathematical development: the case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5–43. https://doi.org/10.1207/s15327833mtl0101_1

- Essay: Explain Cobb's meaning of an
*emergent*perspective. How does this perspective align with the theoretical perspectives he outlines in Cobb (2007)? (**Due Feb 19**; will count as one précis)

**Read**- Thompson, P. W. (2011). Quantitative reasoning and mathematical modeling. In L. L. Hatfield, S. Chamberlain, & S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education (Vol. 1, pp. 33–57). Laramie, WY: University of Wyoming. Retrieved from http://bit.ly/15II27f

- For discussion on 2/19:
*Create an example of quantitative reasoning in university-level (calculus or above) mathematics.* - Write précis of Thompson (2011). (
**Due: 2/26**)

**Read**- Vergnaud, G. (1994). Multiplicative conceptual field: What and why? In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 41–59). Albany, NY: SUNY Press.
- Thompson, P. W., Carlson, M. P., Byerley, C., & Hatfield, N. (2014). Schemes for thinking with magnitudes: A hypothesis about foundational reasoning abilities in algebra. In L. P. Steffe, L. L. Hatfield, & K. C. Moore (Eds.), Epistemic algebra students: Emerging models of students’ algebraic knowing (Vol. 4, pp. 1–24). Laramie, WY: University of Wyoming. Retrieved from http://bit.ly/1aNquwz

**For discussion on 3/12:**

- In what ways does the idea of magnitude exemplify Vergnaud's construct of multiplicative reasoning?
- In what ways does the idea of magnitude fit within the theory of quantitative reasoning?

- Spring Break (yay!)

**Read**- Thompson, P. W., Hatfield, N. J., Yoon, H., Joshua, S., & Byerley, C. (2017). Covariational reasoning among U.S. and South Korean secondary mathematics teachers. Journal of Mathematical Behavior, 48(1), 95–111. https://doi.org/10.1016/j.jmathb.2017.08.001
- Byerley, C., & Thompson, P. W. (2017). Secondary teachers’ meanings for measure, slope, and rate of change. Journal of Mathematical Behavior, 48(2), 168–193.

- Explain what you take to be the central points of Thompson et al. (2017) and Byerley & Thompson (2017). (
**Document to share with classmates on 3/19**)

*Duality, Necessity, and Mathematical Reasoning*

**Read**- Harel, G. (1998). Two dual assertions: The first on learning and the second on teaching (or vice versa). Mathematical Monthly, 105(6), 497–507.
- Harel, G. (2013). Intellectual need. In K. Leatham (Ed.), Vital directions for research in mathematics education (pp. 119–151). New York: Springer.

- One essay on both articles, with the theme of how Harel's ideas developed from 1998 to 2013. (
**Due Mar 26; counts as one précis**)

*Advanced Mathematical Thinking*

'* **Read**

- Carlson, M. P., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58(1), 45–75.
- Selden, A., & Selden, J. (2005). Perspectives on advanced mathematical thinking. Mathematical Thinking and Learning, 7(1), 1–13. https://doi.org/10.1207/s15327833mtl0701_1
- For discussion on Mar 26: Explain how Carlson and Bloom (2005) address issues of advanced mathematical thinking even though the content of their focus was 8th-grade mathematics.

**Read**- Edwards, B. S., Dubinsky, E., & McDonald, M. A. (2005). Advanced mathematical thinking. Mathematical Thinking and Learning, 7(1), 15–25. https://doi.org/10.1207/s15327833mtl0701_2
- Harel, G., & Sowder, L. (2005). Advanced mathematical-thinking at any age: its nature and its development. Mathematical Thinking and Learning, 7(1), 27–50. https://doi.org/10.1207/s15327833mtl0701_3
- Rasmussen, C., Zandieh, M., King, K., & Teppo, A. (2005). Advancing mathematical activity: a practice-oriented view of advanced mathematical thinking. Mathematical Thinking and Learning, 7(1), 51–73. https://doi.org/10.1207/s15327833mtl0701_4

- For discussion on Apr 02: Compare and contrast these three perspectives on
*Advanced Mathematical Thinking*.

- Work on course project

- Project presentations

- Project presentations

- Final Exam/Qualifying Exam (Part 2)