Messages from Focus Groups

1. Messages from Focus Groups • Teaching must include providing opportunities for students to develop and demonstrate essential mathematical processes such as problem solving and communication. • Investigation and modelling play a critical role in learning mathematics through problem solving.

2. Messages from Focus Groups, cont’d The expectations are not clear. Difficult to understand and contain the processes of mathematics.

3. Existing Process Expectations • judge the reasonableness of answers produced by a calculator, a computer, or pencil and paper, using mental mathematics and estimation. From Grade 9 Measurement and Geometry • communicate solutions to problems in appropriate mathematical forms (e.g. written explanations, formulas, charts, tables, graphs) and justify the reasoning used in solving problems From Grade 9 Number Sense and Algebra

4. The Process Expectations Reasoning and Proving Representing Communicating Reflecting Problem Solving Selecting Tools and Computational Strategies Connecting

5. Clarity

6. Clarity

7. Use of “Through Investigation”

8. Use of “Through Investigation”

9. More Examples and Sample Problems

10. Mathematical Process Expectations • apply developing problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding • demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by explaining to others why they think their solution is correct.) • select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems

11. Mathematical Processes: • The actions of mathematics • Ways of acquiring and using the content, knowledge and skills of mathematics

12. Teaching Activity • At your table, there is a envelope that has 8 cards in it. Each card corresponds to a mathematical process. • Each person reads their card to themselves and attempts to identify the process that matches the statement. Depending on the number of people at your table, you may need to do this in partners • Selecting Tools & Computational Strategies • Problem Solving • Reasoning & Proving • Reflecting • Communicating • Connecting • Representing • Using the legend on the next slide, see how you did

13. How Did You Do? x Reasoning and Proving Representing Communicating x Reflecting Problem Solving x Selecting Tools and Computational Strategies Connecting

14. Teaching activity • On the back of file folders on each table the symbols from the previous slide are listed, find the table that matches your card and move to it. This is your expert group. • In this expert group • Each person reads their card • The group is to summarize the process using the template on the inside of the file folder • Prepare to share whole group

15. Response should include • Define the mathematic process • Provide an example • What does this look like in your classroom?

16. Culminating Statement The important thing about(insert process here)is(insert a statement that captures the essence of the process).