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Welcome to Module 1

Principles of Mathematics Instruction

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Getting Started

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Getting Started

 In these sessions, we will explore Chapters 2 to 9 of the Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3, 2004.

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Introduction to the Modules

Module 1 Principles of Mathematics Instruction Module 2 Teaching Through Problem Solving Module 3 Teaching About Problem Solving Module 4 Planning the Mathematics Program /

Instructional Approaches Module 5 Communication Module 6 Classroom Resources and Management Module 7 Assessment and Evaluation Module 8 Home Connections Module 9 Teaching Basic Facts and Multidigit

Computations

Module Topics

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Key Messages

Rich environments do not just happen; they are the result of insightful planning by a thoughtful teacher.

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Key Messages

Before a teacher can institute effective planning, he or she must have a firm grasp of the basic principles of teaching and learning.

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Key Messages

Of paramount importance for successful mathematics instruction is the promotion of positive attitudes in students.

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Key Messages

Instruction in mathematics must emphasize conceptual understanding and not just procedural knowledge.

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Key Messages

In an effective program, students must be allowed to ‘do’ mathematics; children learn mathematics primarily through doing, talking, reflecting, discussing, observing, investigating, listening, and reasoning.

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Key Messages

For learning to be effective, it must utilize and build upon the prior knowledge of the child.

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Key Messages

Students need to encounter concepts in an appropriate manner, at an appropriate time, and with a developmentally appropriate approach.

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Key Messages

The culture and climate in the classroom have a profound effect on the learning that takes place.

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Key Messages

Effective mathematics programs provide students with opportunities to have deep and sustained interaction with big ideas or key concepts of mathematics.

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Working on It

Principles of Mathematics Instruction

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Principles of Mathematics Instruction

“One thing is to study whom you are teaching, the other thing is to study the knowledge you are teaching. If you can interweave the two things together nicely, you will succeed.… Believe me, it seems simple when I talk about it, but when you really do it, it is very complicated, subtle, and takes a lot of time. It is very easy to be an elementary school teacher, but it is difficult to be a good elementary school teacher.”

- Ma, Knowing and Teaching Elementary Mathematics, Erlbaum, 1999, p. 136

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Principles of Mathematics Instruction

Work in groups of 3 or 4. Create a list of mathematical content (knowledge, skills, concepts) related to a topic in the mathematics program (e.g., multiplication, symmetry). Create a second list of instructional considerations for teaching the topic (e.g., manipulatives, teaching strategies, students’ prior knowledge).

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Principles of Mathematics Instruction

Discuss the complexity of decisions that teachers need to make as they develop their mathematics program.

your thoughts with the large group.

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Working on It

Investigating the Principles of Mathematics Instruction

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Investigating the Principles of Mathematics Instruction

Form groups of five. Use a JIGSAW strategy to learn about the principles of mathematics instruction. Record your ideas on BLM 1.3.

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Investigating the Principles of Mathematics Instruction

JIGSAW is a cooperative learning strategy.In Step 1, each home-group member chooses a different topic. In Step 2, home-group members join expert groups to study their topic. In Step 3, “experts” return to their home groups to share what they have learned.

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Investigating the Principles of Mathematics Instruction

Expert Group 1* foster positive mathematical attitudes* focus on conceptual understanding

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Investigating the Principles of Mathematics Instruction

Expert Group 2* involve students actively in their learning* acknowledge and utilize students’ prior knowledge

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Investigating the Principles of Mathematics Instruction

Expert Group 3* provide developmentally appropriate learning tasks

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Investigating the Principles of Mathematics Instruction

Expert Group 4* respect how each student learns * provide a culture and

climate for learning

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Investigating the Principles of Mathematics Instruction

Expert Group 5* recognize the importance of metacognition* focus on the significant

mathematical concepts

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Investigating the Principles of Mathematics Instruction

Return to your home groups and

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Investigating the Principles of Mathematics Instruction

Are there principles that:• are more important than others?• are often neglected because of

time limitations and interruptions in your program?

• are ones you would like to emphasize in your teaching?

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Reflecting and Connecting

In Your Classroom  Select a principle of mathematics

instruction that you would like to focus on in your classroom.

At our next session, be prepared to share a strategy you used to address the principle, and the impact of your efforts.