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# Mathematical processes

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### Mathematical processes

1. 1. Mathematical Processes in Senior Math Cindy Smith Math 7-121
2. 2. 2Research-Based Practice “Human thinking is inherently social in its origins…” There is a “fundamental link between instructional practice and student outcomes”  -Marilyn Goos, Journal of Research in Mathematical Education, 2004
3. 3. 3 November 21, 2012What do weknow?
4. 4. 4 November 21, 2012Mathematical ProcessesThe outcomes in K-12 mathematics shouldbe addressed through the appropriatemathematical process as indicated by thebracketed letters following each outcome.Teachers should consider carefully in theirplanning those processes indicated asbeing important to supporting studentachievement of the respective outcomes.-Saskatchewan Renewed Math 9 Curriculum
5. 5. November 21, 2012Problem Solving  Build new mathematical knowledge through problem solving  Solve problems that arise in mathematics and in other contexts  Apply and adapt a variety of appropriate strategies to solve problems  Monitor and reflect on the process of mathematical problem solving  NCTM
6. 6. 6Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics Make and investigate mathematical conjectures Develop and evaluate mathematical arguments and proofs Select and use various types of reasoning and methods of proof  NCTM
7. 7. 7Representation Create and use representations to organize, record, and communicate mathematical ideas Select, apply, and translate among mathematical representations to solve problems Use representations to model and interpret physical, social, and mathematical phenomena  -NCTM
8. 8. Visualization  Being able to create, interpret, and describe a visual representation …Spatial visualization and reasoning enable students to describe the relationships among and between 3-D objects and 2-D shapes including aspects such as dimensions and measurements.  Saskatchewan Math 9 Curriculum
9. 9. 9Connections  Recognize and use connections among mathematical ideas  Understand how mathematical ideas interconnect and build on one another to produce a coherent whole  Recognize and apply mathematics in contexts outside of mathematics  NCTM
10. 10. 10Communication Organize and consolidate their mathematical thinking through communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others Analyze and evaluate the mathematical thinking and strategies of others; Use the language of mathematics to express mathematical ideas precisely.
11. 11. 11 November 21, 2012 Through communication, ideas become objects of reflection, refinement, discussion, and amendment. The communication process also helps build meaning and permanence for ideas and makes them public (NCTM, 2000). When students are challenged to think and reason about mathematics and to communicate the results of their thinking to others orally or in writing, they learn to be clear and convincing. Listening to others’ thoughts and explanation about their reasoning gives students the opportunity to develop their own understandings.  -Huang
12. 12. 12Tell Me!DescribeExplainJustifyDebateConvinceProove
13. 13. 13Partner Discussions Allow ALL students an opportunity to express their thinking, where calling on students allows only few to participate Allows debate, original ideas, conceptualizing Teaches to female modes of learning: Boys speak up in class more often, and we often direct our richest questions to boys.
14. 14. 14 November 21, 2012 Boys will argue longer for an answer they are not sure of than girls will argue for an answer they KNOW is right (Guzzetti & Williams, 1996).
15. 15. 15 November 21, 2012Connections and Communicationare inextricably linked
16. 16. 16Piagetknowledge is constructed as the learner strives to organize his or her experiences in terms of pre-existing mental structures or schemes
17. 17. 17 Communication works together with reflection to produce new relationships and connections. Students who reflect on what they do and communicate with others about it are in the best position to build useful connections in mathematics. (Hiebert et al., 1997, p. 6)
18. 18. 18Connections
19. 19. 19 Connections
20. 20. 20Group Activity: Tell me a Story! Communications/Connections
21. 21. 21 November 21, 2012Debate!
22. 22. 22 November 21, 2012Connections  Math to real life  Math to self  Math to Math
23. 23. 23 November 21, 2012
24. 24. 24 November 21, 2012Math to Math Solving single degree equations Arithmetic sequences Linear functions Slope Related rates Science End behaviours of polynomial functions Zero behaviour of polynomial functions Asymptotes
25. 25. 25 November 21, 2012
26. 26. 26 November 21, 2012Math to Math Factoring Quadratics Solving Quadratics Graphing Quadratics Completing the Square Quadratic Problems End Behaviour Models Zero Behaviours Asymptotes Curve behaviours Local min/max
27. 27. 27 November 21, 2012Place Value
28. 28. 28Assessment What we assess determines how we teach. What do we want students to learn?
29. 29. 29Formative Assessment Assessment AS learning List some formative assessments you use What do we do with the data?
30. 30. 30How does our summativeassessment reflect deeperlearning? 3 -2
31. 31. 31 November 21, 2012How does it all fit together DI RTI Formative Assessment Small Group Instruction Outcomes, Indicators Instructional Practices Pre/Post Assessment UbD Inquiry