TOChow

= How will Students Study Mathematics? = All learning of mathematics in the new curriculum involves the students using mathematical processes. All the processes are interrelated and provide the focus of mathematics education.

In addition to learning sound mathematics, students also will learn how to learn. They will learn how to think. This will improve understanding of mathematical concepts and reduce frustration and anxiety. These process thinking skills will serve students well in all areas of their lives. Thinking skills are life skills.

Problem solving is the focus of mathematics at all levels. It provides an opportunity for children to be active in constructing mathematical meaning, to learn problem-solving strategies, to practise a variety of concepts and skills in a meaningful context and to communicate mathematical ideas.

Mathematical Processes
Communication Connections Mental Mathematics and Estimation Problem Solving Reasoning Technology Visualization

Using the new common curriculum for mathematics:
 * problem situations can be used to introduce new topics
 * the problem-solving process is a continuous thread woven through all instruction, in every strand
 * problem situations can also be used at the end of a unit to check for student success in applying what has been learned about solving problems.

A goal in classrooms is to encourage a problem-solving “spirit” in all that is done. Together, students and teachers will experience the satisfaction of working hard toward solving a problem. Together they will become “hooked” on thinking.

A problem is something to be worked on when you don’t know the solution. The solution is not obvious to you. Problem solving is the action you take in such a situation.

Many “word problems” in texts are not true problems. They are often just factual mathematical exercises surrounded by words. The only thinking involved is deciding which number operation (+ – x ¸) is needed to solve the problem, then calculating the answer.

For example: Bob had $2. He bought a bottle of pop for $1.25. How much change will Bob get?

Two examples of problems involving more complex and higher level thinking are: {insert file of a net}
 * I have six coins worth $0.42. What coins do you think I have? Is there more than one correct answer?
 * Cut out each of the following nets (patterns). Fold each one to make an object. What object does each net make? Make a different net for the same object.

Students learn steps to solving problems, which help them to organize their thinking.

 * Make sense of the problem (understanding what you need to find out)
 * Attempt several strategies (what are possible ways of solving the problem)
 * Solve the problem (deciding on the best strategy, making a plan, carrying it out)
 * How did you do? (looking back, thinking, discussing how the problem was solved)

Students create their own set of problem-solving strategies.

 * draw a picture or diagram
 * solve a simpler, similar problem
 * guess and check
 * visualize the problem
 * organize information on a chart or table
 * talk out the problem
 * use concrete materials to show a problem
 * break down problem into smaller parts
 * act our problem (role play)
 * work backwards
 * look for a pattern

=Math Talk= Most of us remember our own mathematics classes as being a very quiet time of the school day. Teachers did most of the talking: explaining a concept, asking questions and giving instructions. Students worked independently and silently at their desks. There was little opportunity for Math Talk and student interaction.

The new curriculum recognizes that mathematics is a way to communicate. Communication is an important mathematical process that should be encouraged in all learning activities. Students need opportunities to talk to each other about mathematics. They need to feel free to ask questions of the teacher and of their peers. As children are busy doing their mathematics activities, they need to talk about what they are doing, why they are doing it, and what they are learning. When children verbalize their thinking, it helps them to internalize concepts successfully.

Talking about mathematics is not just giving answers to questions like 8 + 6 = ? It’s using language to make sense of things. It helps students clarify their ideas. It helps them to connect new concepts to what they already know. It helps them to solve problems. Teachers, parents and others can encourage Math Talk, first and foremost, by being good listeners. When we listen to children talk about how they arrived at particular solutions, we get a picture of how each child is thinking and that child’s level of understanding. We can encourage children to explain their ideas clearly. We can help them to organize their ideas by asking questions that focus their thinking. We can ask open-ended questions that promote Math Talk.

=Math Talk: Students, Parents and Teachers Communication=
 * when students discuss mathematics activities, it helps them to develop their thinking and to broaden their understanding
 * when students “talk through” their thinking to solve a problem, it helps them to clarify and make improvements to their thinking
 * sharing writing and records, such as diagrams or graphs, used in solving a problem
 * asking questions
 * sharing ideas, and clearly explaining thinking in solving a problem
 * demonstrating with concrete materials
 * as students talk about what they are doing during a mathematics task, it helps the teacher get a clear picture of their thinking and their understanding of the activity
 * discussing how to go about solving a problem: what should be done, what would be a reasonable answer
 * listening to and respecting the ideas of others
 * thinking aloud by talking to oneself