Teaching and Learning Algebraic Thinking
Weekly Course Outline and
Assignments
** Subject to change**
Last updated: 11/14/06
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Date |
In-Class Activities |
Assignments |
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1 |
Aug 28 |
Course Introduction What is Algebraic Thinking? How is it different or similar to Algebra? Identifying the Algebra and Potential for Algebraic Thinking in Tasks and Problems What is the Algebraic Thinking needed to complete these tasks? |
Read: 1) Driscoll, Ch1 p.1-19 and Ch2 p.20-46 2) Read from course reserves: Chazan, D. (2000). My algebra teaching autobiography. In
D. Chazan, Beyond formulas in mathematics and
teaching: Dynamics of the high school algebra classroom (pp. 1-36), Usiskin, Z. (1988). Conceptions
of school algebra and uses of variables. In A. F. Coxford
& A. P. Shulte, (Eds.) The Ideas of Algebra, K-12, 1988 Yearbook of the National Council of
Teachers of Mathematics (pp. 8-19). Write: 1-2 page reflection on your own algebraic learning and/or teaching in light of your initial thoughts about the readings from Driscoll and Chazan. Be prepared to share reflections during class and to discuss points made by Usiskin on Sept 11th. |
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Sept 4 |
Labor Day --- No Class |
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2 |
Sept 11 |
Building Algebraic Thinking on Number Operations, Algorithms and Patterns |
Submit: 1-2 page reflection. Due in Wolfware
by Sunday Sept 10th at Read: 1) Driscoll, Ch3 p. 47-63 2) Read from course reserves: Schoenfeld, A. H., & Arcavi, A. (1988). On the meaning of variable. Mathematics Teacher 81(6), 420-427. Booth, L. R. (1988). Children’s difficulties in
beginning algebra. In A. F. Coxford & A. P. Shulte, (Eds.) The
Ideas of Algebra, K-12, 1988 Yearbook of the National Council of Teachers of
Mathematics (pp. 20-32). Stacey, K., & MacGregor, M. (1997). Ideas about symbolism that students bring to algebra. Mathematics Teacher 90(2), 110-121. |
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3 |
Sept 18 |
Developing a Rich Understanding of Variable [Use of manipulatives and spreadsheets] Download the Sequence Generator |
Read: 1) Driscoll Ch 4 p. 64-72 only & Ch 5 p. 90-114. 2) Read from course reserves: English, L. D., & Warren, E. A. (1998). Introducing the variable through pattern exploration. Mathematics Teacher 91(2), 166-170. Lannin, J. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning 7(3), 231-258. |
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4 |
Sept 25 |
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· Read from course reserves: Verschaffel, L., Greer, B.,
& De Corte, E. (2002). Everyday knowledge and mathematical modeling of
school word problems. In K. Gravemeijer, R. Leher, B. van Oers, & L. Verschaffel (Eds.), Symbolizing modeling and tool use
in mathematics education (pp. 257-276). Nathan, M. J., & Koedinger, K. R. (2000). Teachers’ and researchers’ beliefs about the development of algebraic reasoning. Journal for Research in Mathematics Education 31(2), 168-190. |
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5 |
Oct 2 |
Student-led Algebraic Tasks (15 mins each) |
Work on specific topic for curriculum project! |
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6 |
Oct 9 |
Student-led Algebraic Tasks (15 mins each) |
Work on specific topic for curriculum project! By October 11th, submit a brief proposal for what you (or a small group--up to 3 people) intend to pursue for the curriculum analysis project. |
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7 |
Oct 16 |
No Class Meeting—small group work on curriculum project.
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8 |
Oct 23 |
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Read: 1)
Driscoll 2) Driscoll Ch 7, p. 141-164. |
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9 |
Oct 30 |
4-5pm Innovations in Research talk at Friday Institute 5-6:45 2 Doctoral level presentations: Discussion of Symbol Sense Discussion of Multiple Representations of Functions---Driscoll’s notes Using 5 different representations of a function FYI—discussed in Ryan’s presentation · Levels of Cognitive Demand for Mathematics Tasks Framework |
Read from course reserves: MASTERS
& PBS students read: Falkner,
K. P., Levi, L., & Carpenter, T. P. (1999). Children’s
understanding of equality: A foundation for algebra. Teaching
Children Mathematics, 6, 232–236. PHD students read: Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education 37(4), 297-312. ALL READ: Monk, S. (2003). Representation in school mathematics:
Learning to graph and graphing to learn. In J. Kilpatrick, W. G. Martin,
& D. Schifter, Research companion to
principles and standards for school mathematics (pp. 250-262). SOLVE the Hot Dog Task –use any tools you wish, bring your work and be prepared to discuss |
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10 |
Nov 6 |
Discussion of Hot Dog task and use of representations.
Students' Approaches to Solving an Equation Developing Understanding of Relationships and Functions with Multiple Representations Use of GC to Solve Phone
Bill Problem |
Read: EVERYONE Read from course reserves: Blanton, M. L., & Kaput, J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education 36(5), 412-446. Read one according to number assigned in class: 1) Report on Idaho policy 2005 2)
Algebra for All in Eighth Grade: What's the Rush?
3)
A
Formula for Failure in L.A. Schools EVERYONE READ NCTM 2000 Dialogues—read through all --pick 3 articles that you feel illustrate some of the beliefs you have concerning “Algebra for All” |
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11 |
Nov 13 |
Analyzing Students’ Algebraic Thinking during an Algebra lesson (video) · Phone Bill video · TIMSS 1999 video from a Japanese classroom Part I: Communicating with Parents & the Community about Algebraic Thinking |
Read: Start drafting ideas for your reflection
(Part I)—Algebra for All
reflection and position statement. Bring copy of draft of ideas for Part I to
class on Nov 20th. |
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12 |
Nov 20 |
Discussion of Issues surrounding Algebra for All Small group conversations Communicating with Parents & the Community about Algebraic Thinking Developing position statements |
Submit Parts I & II of Algebra for All assignment in a single document in Wolfware by Nov 27th at 4pm **************************** Spend at LEAST one
hour perusing the SimCalc website to become familiar with their connected classroom
project as well as simcalc software (Calculator MathWorlds
and Java MathWorlds) software. ************************************* Read from course reserves: Heid, M. K., Blume, G. W.,
Hollebrands, K., & Piez, C. (2002). Computer
algebra systems in mathematics instruction: Implications from research. Mathematics
Teacher 95(8), 586-591. **************************************** FYI: other CAS-related articles that may be of interest. Zehavi, N. (2004). Symbol sense with a symbolic-graphical system: A story in three rounds. Journal of Mathematical Behavior, 23, 183-203. Shaw, N., Jean, B., & Peck, R. (1997). A statistical analysis on the effectiveness of using a computer algebra system in a developmental algebra course. Journal of Mathematical Behavior, 16, 175-180. Heid, M.K. (2001). Theories
that inform the use of CAS in the teaching and learning of mathematics. In P.
Kent (Ed.), Proceedings of the 2nd Biennial Symposium of the
Computer Algebra in Mathematics Education Group: http://ltsn.mathstore.ac.uk/came/events/freudenthal/3-Presentation-Heid.pdf. |
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13 |
Nov 27 |
Use of Java MathWorlds or MathWorlds for the TI-83/84+ (FREE from TI) Use of Computer Algebra Systems for Developing Symbolic Understanding TI-92 or TI-89 |
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14 |
Dec 4 |
What is Algebraic Thinking?
Megan’s Curriculum Poster presentation |
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15 |
Dec 11 |
Curriculum Project Presentations at Math Education Research Symposium
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Submit 5 page Executive
Summary through Wolfware by |
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