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# Developing the MKT Through Analyzing and Deepening Tasks and Curriculum

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### Developing the MKT Through Analyzing and Deepening Tasks and Curriculum

1. 1. Developing the Mathematical Knowledge Needed for Teaching (MKT) through Analyzing and Deepening Tasks/Curriculum Nicole Miller Rigelman Portland State University Teachers of Teachers of Mathematics September 12, 2009
2. 2. Close to 100 The object of the game is to create double-digit numbers that sum as close to 100 as possible. Each game has five rounds. For round 1, deal six cards to each player. Players then choose any four of their six cards to make two two-digit numbers that, when added, come as close to 100 as possible. Wild cards can be assigned any value. Players record their numbers and total on their score sheets. The player’s score is the difference between the total and 100. (102 and 98 are both scored as 2.) The used cards are discarded and four new cards are dealt to each player. Each player will have 6 cards at the beginning of a round, two that are left from the previous round and four that are new. At the end of five rounds the player with the lowest total score wins.
3. 3. Close to 100 Strategies • • •
4. 4. About this Session  Doing some math; playing Close to 100.  Framing our Work  Examining the opportunities for student mathematical discourse within the curriculum as written.  Analyze video clip of students at work.  Considering general strategies for drawing out and deepening student thinking and reasoning.
5. 5. The Principles & Standards say…
6. 6. Mathematical Tasks of Teaching Ball, Thames, & Phelps, 2008  Presenting mathematical ideas  Responding to students “why” questions  Finding an example to make a specific mathematical point  Linking representations to underlying ideas and to other representations  Connecting a topic being taught to topics from prior of future years -
7. 7.  Explaining mathematical goals and purposes to parents  Appraising and adapting mathematical content of textbooks  Modifying tasks to be either easier or harder  Evaluating the plausibility of students’ claims (often quickly)  Giving or evaluating mathematical explanations  Choosing and developing useable definitions  Using mathematical notation and language and critiquing its use  Asking productive mathematical questions  Selecting representations for particular purposes  Inspecting equivalencies
8. 8. Mathematical Knowledge Needed for Teaching (MKT) Subject Matter Knowledge Common Content Knowledge (CCK) Horizon Content Knowledge Pedagogical Content Knowledge Knowledge of Content and Students (KCS) Specialized Content Knowledge (SCK) Knowledge of Content Curriculum Knowledge of Content and Teaching (KCT) Ball, Thames, & Phelps, 2008
9. 9. Why Student Mathematical Discourse?
10. 10. Why Student Mathematical Discourse?  The discourse of a classroom – the ways of representing, thinking, talking, agreeing, and disagreeing – is central to what and how students learn about mathematics. - NCTM, 2007, p. 46
11. 11. The Intended Curriculum Private Think Time  Imagine a group of 4th graders engaged in this activity. Predict the levels of math talk you would hear. Record examples of what you think students might say in the cells of the Discourse Analysis Tool. Deepening the Discourse  Recognizing the goal of promoting higher-levels of student mathematical discourse, what might you do to deepen the math talk?
12. 12. Mathematical Tasks of Teaching Ball, Thames, & Phelps, 2008  Presenting mathematical ideas  Responding to students “why” questions  Finding an example to make a specific mathematical point  Linking representations to underlying ideas and to other representations  Connecting a topic being taught to topics from prior of future years -
13. 13.  Explaining mathematical goals and purposes to parents  Appraising and adapting mathematical content of textbooks  Modifying tasks to be either easier or harder  Evaluating the plausibility of students’ claims (often quickly)  Giving or evaluating mathematical explanations  Choosing and developing useable definitions  Using mathematical notation and language and critiquing its use  Asking productive mathematical questions  Selecting representations for particular purposes  Inspecting equivalencies
14. 14. Close to 1000 Close to 1000 is similar, but the number of cards dealt is different. Players start with 8 cards, and lay out six of them to make two three-digit numbers that add as close to 1000 as possible. A game consists of 5 rounds and the player with the lowest score at the end of five rounds is the winner.
15. 15. What if we played…  Close to 10,000 with two four-digit numbers, Close to 100,000 with two five digit numbers, etc. Work to describe a general strategy for all games involving two addends whose sum is close to a power of 10 or list some components of such a general strategy.
16. 16. Principles & Standards remind us…
17. 17. Developing the Mathematical Knowledge Needed for Teaching  What ideas/tools are you taking away for developing the mathematical knowledge needed for teaching?  What questions remain … and what might you do to work on answering the questions?
18. 18. Building and Sustaining Student Mathematical Discourse  Teachers need to create an environment in which students build a “personal relationship” with mathematics. Three key elements need to be in this environment. 1. Students need to engage in authentic mathematical inquiries. 2. Students must act like mathematicians as they explore ideas and concepts. 3. Students need to negotiate. The meanings of, and connections among, these mathematical ideas with other students in the class. - D’Ambrosio, 1995
19. 19. Questions? Nicole Miller Rigelman rigelman@pdx.edu