Math 506A: Research on the Learning of Mathematics: Fall 2006
Tuesdays 5:15  7:45 pm Math East 143/141
Cynthia Anhalt Marta Civil Javier D’ez Palomar
canhalt@math.arizona.edu civil@math.arizona.edu jadiez@math.arizona.edu
Math East 244 Math 203 Math East 240B
6261522 6216873 6218306
This course has two main objectives (breadth and depth):
1) To familiarize students with some of the key pieces of research in mathematics education (with particular attention to research on student learning). So, in this sense, it is a survey course into main areas of research on learning.
2) To allow for students to go in depth in an area of their interest through a series of assignments during the semester, culminating in a poster presentation.
Required Text
Carpenter, T. P., Dossey, J. A., & Koehler, J. L. (2004) (Eds.). Classics in Mathematics Education Research. Reston, VA: NCTM
There will several other readings handed out during the semester either via email as PDF attachments or as photocopies.
About the course
This course will be run as a seminar with a pair of students each week facilitating the discussion of the articles. To ensure the flavor of a seminar, studentsÕ participation is crucial. A major part of this course is reading and discussing ideas/issues related to teaching and learning mathematics as they relate to the readings; therefore adequate time spent preparing for each class period is expected of every student Ð read assigned material thoroughly and take some notes as you read.
There will be three main ÒactivitiesÓ in this course
Inclass work: as discussion facilitators you will be expected to prepare some questions and / or activities related to the readings assigned for your session. As a participant, your responsibility will be to have carefully read the articles to help your colleagues as they facilitate the discussion.
PROJECT I: Each student will become knowledgeable with some of the literature in a particular area of student learning of mathematics (e.g., childrenÕs understanding of the concept of area). This knowledge will be built as students collect, read, interpret, compare, synthesize, and write about a set of research articles/chapters related to a topic of their choosing (to be agreed upon by the student and instructors). This project will be broken down into two smaller pieces as follows:
Assignment 1 Ð Project I: A two to three page write up on the topic of your choice that includes: rationale (why did you choose this topic) and a review of one research article related to your topic. The review should 1) briefly describe the research subjects and methods, (2) summarize key findings and recommendations, and (3) offer your personal commentary / critique. [Due September 26]
Assignment 2 Ð Project I: A 68 page review of three research articles related to your topic (the article used for assignment 1 can be one of them). These articles must be OKÕd by the instructors in advance. Students will bring two copies of their paper to class on Tuesday October 17 to exchange with other students as part of a peer discussion of each otherÕs papers that will take place the following Tuesday (October 24).
Final Review of the Literature Paper Ð Project 1: The paper for assignment 2 will be revised (according to instructorsÕ and peersÕ feedback) and expanded to a 1014 page review of 6 to 7 articles, due Tuesday December 5. There should be one section on recommendations for further research (based on both your readings and your own study (see Project 2)).
PROJECT II (can be done in pairs): This will be a mini research project in which you explore further the topic of your choice for project 1 by carrying out a small research study. The main goal is for you to develop some experience doing a research project in an area of studentsÕ understanding of a topic. Although there are many approaches possible, in this course we will emphasize the use of taskbased interviews as the research approach. So, for example, if you topic of interest is ÒchildrenÕs understanding of area,Ó your research project may consist of a taskbased interview to explore 2 or 3 childrenÕs understanding of area. Replication of methods used by other researchers is acceptable. On November 7th we will have an in class session where you exchange your research ideas / instruments for peer and instructor feedback. Bring 2 to 3 copies of a draft to this meeting to be shared with a small working group.
You will present this research project as a poster the day of the final exam (Tuesday December 12). In addition to the poster, you will turn in a final writeup that describes methods and results and situate findings within the literature on the topic. Expected length for this writeup is approximately 5 to 7 pages.
Format for Papers
APA style (fifth edition) is required for all writeups. All writeups should be doublespaced with 1 inch margins on all sides. Block quotes should be singlespaced and indented. Use a 12point font and a standard font style (i.e., CG Times, Arial, or Times New Roman).
JOURNAL LIST
Educational Studies in Mathematics (ESM)  http://www.springerlink.com/content/15730816/
Focus on Learning Problems in Mathematics (FLPM)
For the learning of Mathematics (FLM)  http://flm.educ.ualberta.ca/
Journal for Research in Mathematics Education Ð Monograph  http://www.jstor.org/journals/08839530.html
Journal for Research in Mathematics Education (JRME) Ð
http://my.nctm.org/eresources/journal_home.asp?journal_id=1
Journal of Mathematical Behavior [JMB] Ð
http://www.elsevier.com/wps/find/journaldescription.cws_home/620200/description#description
Journal of Mathematics Teacher Education [JMTE]  http://springerlink.metapress.com/content/15731820/
Mathematical Thinking and Learning (MTL) (ItÕs published by Lawrence Erlbaum; http://www.erlbaum.com
Mathematics Educator [ME]  http://math.coe.uga.edu/tme/tmeonline.html
Day: 
Topic: 
Readings (due on date indicated on far left column): 
Assignments: 
Facilitators: 
Aug 22^{nd} 
Course Overview ÒCombining Cognitive and Sociocultural approaches in mathematics education researchÓ 



Aug 29^{th}

Intro to research (interviewing) The role of cognition 
á Brenner, M.E. (2006), (In Green, Camilli & Elmore) á Brenner, M. E. (1998), (AEQ) á Erlwanger, S. H. (1973), (ch. 5, Classics...) 


Sept 5^{th} 
Student Thinking /Arithmetic 
á Lampert, M. (1990), (ch. 12, Classics...) á Carpenter el al. (1997), (JRME) 


Sept 12^{th} 
Geometry Measurement 
á van Hiele, P. M. (1959/1985), (ch. 6, Classics...) á Barrett, Clements, Klanderman et al. (2006), (JRME) á Battista, M.T. (2004), (MTL) 


Sept 19^{th} 
Fractions 
á Cramer et al (2002), (JRME) á Empson, S.B. (2003), (JRME) á Mack, N.K. (2001), (JRME) 


Sept 26^{th} 
Algebraic thinking

á Chazan, D. & Yerushalmy, M. (2003), (ch.9, Research companion...) á Carraher et al. (2006), (JRME) á Knuth et al. (2006), (JRME) 
Project I Assignment 1 due (1 article) 

Oct 3^{rd}

Reasoning & proof 
á Yackel, E., Hanna. G. (2003), (ch. 15, Research companion...) á Reid, D.A. (2002), (JRME) á Healy, L. & Hoyles, C. (2000), (JRME) 


Oct 10^{th} 
Constructivism / Emergent/ Sociocultural/ Ethnomathematics 
á Steffe, L. & Kieren, T. (1994), (ch.7, Classics...) á Cobb, P. & Yackel, E. (1996), (ch. 17, Classics...) á DÕAmbrosio, U. (1985), (ch. 15, Classics...) 


Oct 17^{th} 
Research methods 
á Doyle, W. (1988). (Educational Psychologist) á Pirie, S. (1997). (JRME Monograph, 9) 
Project I Assignment 2 due (3 articles) (papers to exchange with peers) 

Oct 24^{th} 
Paper discussion / Peer feedback 
Working Groups 


Oct 31^{st} 
Representation 
á Smith, S. P. (2003), (ch. 18, Research companionÉ) á Goldin, G. & Shteingold, N. (2001), (Cuoco & Curcio) 


Nov 7^{th} 
Research proposal discussion / peer feedback 
Working Groups 
Project II Research proposals duebring drafts to class 

Nov 14^{th} 
Multiplicative Structures / Proportional Reasoning 
á Vergnaud, G. (1988), (ch.8, Classics...) á Lesh, R., Behr, M., Post, T. (1987), (In Janvier). 


Nov 21^{st} 
Mathematics & cultural context 
á Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985), (ch. 14, Classics...) á Bishop, A. J. (1988), (ch. 16, Classics...) 
Project II Informal report on progress of research project 

Nov 28^{th } 
Mathematics & language 
á OÕConnor, M. (2001), (ESM) á Lampert, M. & Cobb, P. (2003), (ch. 16, Research companion...) á Moschkovich, J. (2002), MTL

Project II Informal report on progress of research project 

Dec 5^{th} 

TBA 
Project I Final review of literature due (67 articles) 

Dec 12^{th} 
Final Exam 
Poster Presentations 
Final Research Project II writeup due 

Reference / Resource List [Partial; more references will be added during the semester]
Barret, J. E., Clements, D.H., Klanderman, D., Pennisi, SJ., & Polaki, M.V. (2006). StudentsÕ coordination of geometric reasoning and measuring strategies on a fixed perimeter task: developing mathematical understanding of linear measurement. Journal for Research in Mathematics Education, 37(3), 187221.
Battista, M. T. (2004). Applying cognitionbased assessment to elementary schools studentsÕ development of understanding of area and volume measurement. Mathematical thinking and learning, 6(2), 185204.
Bishop, A. J. (1988/2004). Mathematics education in its cultural context. In T.P. Carpenter, J.A. Dossey, & J.L. Koehler (Eds.), Classics in mathematics education research, (pp. 2002007). Reston, VA: NCTM.
Bihop, A. J., Clements, K., Keitel, C., Kilpatrick, J., & Laborde, C. (Eds.) (1996). International handbook of mathematics education. Boston, MA: Kluwer.
Brenner, M. E. (1998). Adding cognition to the formula for culturally relevant instruction in mathematics. Anthropology & Education Quarterly, 29(2), 214244.
Brenner, M.E. (2006). Interviewing in educational research. In J. l. Green, G. Camilli, & P. B. Elmore (Eds.), Handbook of complementary methods in education research (pp. 357370). Mahwah, NJ: Lawrence Erlbaum.
Carpenter, T. P., Franke, M.L., Jacobs, V.R., Fenema, E., & Empson, S.B. (1997). A longitudinal study of invention and understanding in childrenÕs multidigit addition and subtraction. Journal for Research in Mathematics Education, 29(1), 320.
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Carpenter, T.P., Dossey, J.A., & Koehler, J.L. (Eds.) (2004). Classics in mathematics education research. Reston, VA: NCTM.
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Carraher, T.N., Carraher, D.W., & Schliemann, A.D. (1985/2004). Mathematics in the streets and in schools. In T.P. Carpenter, J.A. Dossey, J.L. Koehler (Eds.), Classics in mathematics education research, (pp. 186193). Reston, VA: NCTM.
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Chazan, D., & Yerushalmy, M. (2003). On appreciating the cognitive complexity of school algebra: research on algebra learning and directions of curriculum change. In J. Kilpatrick, G. Martin, D. Schifter (Eds.), A research companion to principles and standards for school mathematics, (pp. 123135). Reston, VA: NCTM.
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Cramer, K.A., Post, T.R., & delMas, R.C. (2002). Initial fraction learning by fourth and fifth grade students: a comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33(2), 111144.
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