LAKEHEAD UNIVERSITY
Faculty of Education
2011 Tuesdays 3:30 – 6:30 p.m.
ED 5435 Curriculum Studies in Mathematics Education
Instructor: Alex Lawson PhD
Office: BL-1029
Email:
Course Website: http://flash.lakeheadu.ca/~ed4050
TENTATIVE OUTLINE
COURSE DESCRIPTION
Curriculum Studies in Mathematics Education is designed to immerse students in the research theory and methods in mathematics education at the Primary, Junior and Intermediate level. The course will focus primarily on conducting and reporting on informal action research in mathematics education. Students will need to have access to one or two adults, or, school age students (18 years old and up) who will be willing to participate in your action research assignments. In addition to informal action research we will be examining the student development of mathematical concepts using video data. The course is open to MEd and PhD students. You do not need to have a mathematics background to take the course.
The course objectives are:
· to offer a first-hand experience of elementary and intermediate mathematics education research procedures and methods;
· to survey and to analyse some of the theoretical and, some of the empirical research on mathematical cognitive development in school children; and,
· to survey and to analyse some of the theoretical and empirical research on effective teaching methods in mathematics at the K-8 level.
Classes and Assignments
The classes will typically be conducted in two-week blocks. In the first week you will read the pertinent literature on your topic, conduct action research in the field and orally report on your findings in class. In the second week of the topic you will incorporate the findings of fellow students to write a report for submission.
Evaluation
Each assignment will be worth 20% of the final grade.
Attendance
Full attendance is a course requirement, as much of the course work will take place during class time.
Alex Lawson Math 5435 Page 5 6/29/10
COURSE OUTLINE*
There will be some changes to the readings; expect three readings a week.
Class / Date / Topic / Readings / Assignment /1 / Jan. 4 / History of Reform
Action Research / Battista, M. (1999). The mathematical miseducation of America's youth. Phi Delta Kappan, 80(6), 425-433. [online]
2 / Jan 11 / Multiplication & Division
- analyzing typical difficulties
- beginning strategies
- prominent models / Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah: Lawrence Erlbaum Associates. Chapter on Multiplication, pp. 28-54 [hard copy]
Simon, M. (1993). Prospective elementary teachers' knowledge of division. Journal for Research in Mathematics Education, 24(3), 233-254. [online]
______
PhD Students only: Silver, E., Shapiro, L., & Duetsch, A. (1993). Solution processes and their implications. Journal for Research in Mathematics Education, 24(2), 117-135. / Assignment 1a: Action Research Division (Oral Report)
3 / Jan. 18 / Multiplication and Division Video Analysis
-beginning strategies
-invented strategies / Carpenter, T.; Fennema, E., Loef Franke, M., Levi, L., Empson, S. (1999). Children’s Mathematics: Cognitively Guided Instruction Portsmouth: Heinemann (pp. 1-4, 33-53). [hard copy]
Fosnot, C. T., & Dolk, M. (2001). Young mathematicians at work: Constructing numbers sense, constructing multiplication and division Portsmouth: Heinemann. 15 – 71 [on reserve in library, you may wish to purchase this book]
4 / Jan. 25 / Numeracy (Invented Strategies) / Anglieri, J. (2001). Intuitive approaches, mental strategies and standard algorithms. In J. Anghileri (Ed.) Principles in arithmetic teaching: Innovative approaches for the primary classroom (pp. 79-94). Buckingham: Open University Press. [hard copy]
Clark, F., & Kamii, C. (1996). Identification of multiplicative thinking in children in grades 1-5. Journal for Research in Mathematics Education, 27(1), 41-51. [online library]
Mulligan, J., & Mitchelmore, M. (1997). Young children's intuitive models of multiplication and division. Journal for Research in Mathematics Education, 28(3), 309-330. [online library] / Assignment 1b: Action Research Analysis (Short Paper)
(20%)
5 / Feb. 1 / Models & Algorithms
(Melissa at Ministry conference) / Fosnot, C. T., & Dolk, M. (2001). Young mathematicians at work: Constructing numbers sense, constructing multiplication and division Portsmouth: Heinemann pp. 73-103
Fuson, K. (2003). Developing mathematical power in whole number operations. In J. Kilpatrick (Ed.), A research companion to Principles and Standards for School Mathematics (pp. 68-94). Reston: National Council of Teachers of Mathematics. [hardcopy] / Assignment 2a: Developing a landscape of students’ multiplication and division methods
6 / Feb.8 / Addition, Subtraction & Models / Anghileri, Julia; Beishuizen, Meinert, and Van Putten, Kees (2002) From Informal Strategies to Structured Procedures: Mind the Gap! Educational Studies in Mathematics 49(2):149-170. [online library]
van Putten, C., van den Brom-Snijders, P., & Beishuizen, M. (2005). Progressive mathematization of long division strategies in Dutch primary schools. Journal for Research in Mathematics Education, 36(1), 44-73. [email]
Fosnot & Dolk’s CDs
The big dinner: A context for multiplication
The soda machine: A context for division
[loaded up in class or downloaded from idisk.
Discuss Fractions action research.
7 / Feb.15 / Assessment
Margaret and
Sarah away / Atlas workshop with elementary math data. (Meet in the lab.) I will do a second one in April in Toronto with Margaret and Sarah.
Verschaffel, L., Greer, B., & De Cote, E. (2007). Whole number concepts and operations. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557-592 or pp. 593-619). Reston: National Council of Teachers of Mathematics. [hard copy] / Written Assignment 2b: Landscape or Continuum of Multiplication and Division Development (20%)
8 / Feb. 22 / Fractions
- analyzing typical difficulties
- prominent models / Ball, D. (1990) The mathematical understandings that prospective teachers bring to teacher education The Elementary School Journal 90:4 pp. 449-466 [online]
Empson, S. (2001) Equal sharing and the roots of fraction equivalence. Teaching Children Mathematics, 7(7), pp 421-425 [email]
Fosnot & Dolk (2002) Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents. Heinemann: Portsmouth 55-71 [hard copy]
Sharp, J., Garofalo, J., & Adams, B. (2002). Children’s development of meaningful fraction algorithms: A kid’s cookies and a puppy’s pills. In B. Litwiller (Ed.), Making sense of fractions, rations, and proportions (pp. 18 -28). Reston: NCTM. [hard copy]
______
PhD Students:
Charles & Nason 2000 Young children’s partitioning strategies Educational Studies in Mathematics 43: 191-221 / Oral Assignment 3a: Fractions Action Research
9 / Mar. 1 / Assessment / Black, P. (1998a). Inside the black box. Phi Delta Kappan, 80(2), 139-148. [on website]
Kohn, A. (2000). The case against standardized testing. Portsmouth: Heinemann. [hard copy]
Lawson, A. & Suurtamm, D. (2006). Aligning large-scale testing with mathematical reform: the case of Ontario. Assessment in Education 13(30) [onwebsite] / Written Assignment 3b: Analysis of Fractions Action Research Short Paper (20%)
10 / Mar.8 / Measurement: Area, perimeter and volume / Battista, M., Clements, D., Arnoff, J., Battista, K., & Van Auken Borrow, C. (1998). Students; spatial structuring of 2D arrays of squares. Journal for Research in Mathematics Education, 29, 503-32. [online]
Battista, T. M. (2003). Understanding students' thinking about area and volume measurement. In NCTM Yearbook: Learning and teaching measurement (pp. 122-142). NCTM. [hard copy]
Barrett, J., Jones, G., Thorton, C., & Dickson, S. (2003). Understanding children's developing strategies and concepts of length. In NCTM Yearbook: Learning and teaching measurement (pp. 17-30). NCTM. hard copy
Stephan, M., & Clements, D. (2003). Linear and area measurement in prekindergarten to Grade 2. In NCTM Yearbook: Learning and teaching measurement (pp. 3-16). NCTM. [hard copy] / Oral Assignment 4a: Action Research in Measurement Oral Report
Possible readings depending upon items:
Baturo, A., & Nason, R. (1996). Student teachers' subject matter knowledge within the domain of area measurement. Education Studies in Mathematics, 31, 235-268. [Online]
Kamii, C., & Clarke, F. (1997). Measurement of length: The need for a better approach to teaching. School Science and Mathematics, 97. [online]
Carpenter, T., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra. Portsmouth: Hienemann.
. / Assignment 4b: Action Research in Measurement Short Paper (20%)
Mar.
15 / March Break: No class
11 / Mar. 22 / Math Wars / Verschaffel, L., Greer, B., & De Cote, E. (2007). Whole number concepts and operations. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557-628). Reston: National Council of Teachers of Mathematics. / Assignment 5: Final Short Paper due April 12: negotiated (20%)
12 / 29 / Mighton, J. (2007). The end of ignorance. Toronto: Anansi. (on reserve)
Alex Lawson Math 5435 Page 5 6/29/10
Informal Action Research Procedures
When you are carrying out a piece of research I suggest the following procedures.
1. Answer the questions yourself. You need to know what to expect and what to look for. Try and anticipate what is likely to happen in your interview so that you will be able to respond appropriately, obtain the most information and most importantly, put your participant at ease. Your participant may need to sign a release form; this will be addressed in the first class.
2. Find a participant who is willing to answer your questions. Explain that the questions will take between 30 and 45 minutes, further that you will be sharing the results with your class but not their name or any identifying marks.
3. Be ready to share your data with the class by either copying it onto an acetate sheet or photocopying it for the rest of the class. We will be compiling the data and examining it in class in light of the pertinent research.
ED 5435 Curriculum Studies in Mathematics Education
Action Research Assignment 1
Oral Report Due Jan. 15, 2009
______
Items 1 and 2 adapted from Simon, M. (1993). Prospective elementary teachers' knowledge of division. Journal for Research in Mathematics Education, 24(3), 233-254.
Simon used the following items to assess the connections students made between their procedural or arithmetic knowledge and their conceptual and real world knowledge of division. Ask your participant to answer the following questions.
1. Story Problems: Write three different story problems that would be solved by dividing 51 by 4 and for which the answers would be, respectively:
a) 12 ¾ b) 13 c) 12
2. Long Division: In the long division carried out in the example below, the sequence divide, multiply, subtract, bring down is repeated. Explain what information the multiply step and the subtract step provide and how they contribute to arriving at the answer.
59
12 ) 715
-60
115
- 108
7
Item 3 Adapted from Ma Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah: Lawrence Erlbaum Associates.
3. Multiplication: A student was calculating the following problem and wrote the solution as follows:
123
x645
615
492
738 Is this inaccurate? Explain why or why not and what you
1845 might say to the student.
ED 5435 Curriculum Studies in Mathematics Education
Assignment #1 Action Research Analysis
(2 – 4 pages typed double-spaced with AR attached)
1. Read the Simon (1993) article and Ma (1999) chapter. How did the results of your action research for questions 1 and 2 compare to those of Simon and Ma’s results? Compare and contrast your findings with those of your fellow students?
2. Would you make any changes to your action research method in the future?
3. Do you consider his and her findings to be important? Explain.
4. How do Simon and Ma’s results fit into the call for mathematical reform as outlined by Battista and discussed in class?
ED 5435 Curriculum Studies in Mathematics Education
Assignment #2: Developing a Multiplication and Division Landscape
CDs on reserve in the library or on the .mac account
If children use their own methods for solving multiplication and division problems they will typically use a variety of increasingly sophisticated methods to solve single-digit and then multi-digit problems. Look at Fosnot and Dolk’s Landscape of Learning for Multiplication and Division as described in the Young Mathematician series. Use this lens to analyse the strategies, underpinning Big Ideas, and attendant models you see in the videos of children solving multiplication and division problems throughout the their elementary years.
First describe what Fosnot and Dolk mean by big ideas, strategies and models. Then describe the strategies children use to solve the problems, the big ideas that underpin a particular strategy and, if visible, the model in use for each video clip. Include any pertinent research from the other articles you have read.
For your continuum I would like you to look at the problem the teacher poses on the second day under ‘continuing the investigation: cooking the turkey’. Watch her present the problem, think about what students might do and then have a look at the following to build your own continuum of children’s multiplication and division development. Look at: Cassandra and Scarlett, Kenneth and Marlon, Andrew and Leilei and Rose and Suzanne.
Then have a look at 4 pairs of children in the Soda Machine video:
ED 5435 Curriculum Studies in Mathematics Education
Assignment #3a: Action Research on Fractions
For Intermediate Students and Adults
1. Solve the submarine problem. (below)
2. Of the following fractions ¾, 5/12, 2/3, 3/2, 2/5, 5/8 which two fractions will add to less than 1? Show or explain your thinking. (Deck D)
3. Jeremy and Fiona were eating pizza. Fiona has ½ of a pizza and Jeremy has 1/3 of a pizza. Is it possible that Fiona has more pizza than Jeremy? Explain your reasoning. (TIMSS Gr. 8 item).
Optional:
4. Calculate 1 3/4 divided by ½. What does the answer mean? Explain in words and/or pictures. Can you generate a word problem which would require this calculation? (Ball 1990)
For Young Children:
Use the Sharp et al. article as a template to ask fractional questions of young children.
Sub problem from Fosnot
A fifth-grade class traveled on a field trip in four separate cars. The school provided a lunch of submarine sandwiches for each group. When they stopped for lunch, the subs were cut and shared as follows:
• The first group had 4 people and shared
3 subs equally.
• The second group had 5 people and shared
4 subs equally.
• The third group had 8 people and shared
7 subs equally.
• The last group had 5 people and shared