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.

•The expectations are not clear. Difficult to understand and contain the processes of mathematics.

Messages from Focus Groups, cont’d

Clarity

1997 CURRICULUM

Grade 7

SPRING 2005 DRAFT

Grade 7

• recognize patterns and use them to make predictions;

• make predictions, by extending patterns, through investigations with concrete materials; Sample Problem: Investigate the surface area of cube towers to predict the surface area of a cube tower that is fifty cubes high.

Clarity

1999 CURRICULUM

Grade 9 Academic

SPRING 2005 DRAFT

Grade 9 Academic

• expand and simplify polynomial expressions involving one variable

•multiply a polynomial by a monomial in the same variable to give results up to degree three (e.g….) using a variety of tools…

Use of “Through Investigation”

1997 CURRICULUM

Grade 8

SPRING 2005 DRAFT

Grade 8

• investigate the Pythagorean relationship using area models and diagrams;

•determine, through investigation, the Pythagorean relationship, using a variety of tools and strategies (e.g., dynamic geometry software, paper and scissors, geoboards)

Use of “Through Investigation”

1999 CURRICULUM

Grade 10 Academic

SPRING 2005 DRAFT

Grade 10 Academic

• describe the nature of change in a quadratic function using finite differences in tables of values, and compare the nature of change in a quadratic function with the nature of change in a linear function

•Determine, through investigation, that a quadratic relation of the form y = ax2 + bx + c can be graphically represented as a parabola, and that the table of values yields a constant second difference (Sample problem: Graph the relation…observe the shape…calculate first and second differences…Describe….)

More Examples and Sample Problems

1997 CURRICULUM

Grade 8

SPRING 2005 DRAFT

Grade 8

• investigate measures of circumference using concrete materials (e.g., use string to measure the circumference of cans or bottles);

• measure the circumference, radius and diameter of circular objects, using concrete materials; Sample Problem: Use string to measure the circumferences of different circular objects

Mathematical Processes:

• The actions of mathematics

• Ways of acquiring and using the content, knowledge and skills of mathematics

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

Existing Process Expectations

• 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

From Grade 9 Measurement and Geometry

• judge the reasonableness of answers produced by a calculator, a computer, or pencil and paper, using mental mathematics and estimation.

The Process Expectations

Reasoning and Proving

Communicating

Problem Solving

Connecting

Reflecting

Representing

Selecting Tools and Computational Strategies

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

How Did You Do?

x

x

xReasoning and Proving

Communicating

Problem Solving

Connecting

Reflecting

Representing

Selecting Tools and Computational Strategies

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

Response should include

• Define the mathematic process

• Provide an example

• What does this look like in your classroom?

Culminating Statement

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