1 Welcome to Module 1 Principles of Mathematics Instruction

2 Getting Started

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

4 Introduction to the Modules Module 1Principles of Mathematics Instruction Module 2Teaching Through Problem Solving Module 3Teaching About Problem Solving Module 4Planning the Mathematics Program / Instructional Approaches Module 5Communication Module 6Classroom Resources and Management Module 7Assessment and Evaluation Module 8Home Connections Module 9Teaching Basic Facts and Multidigit Computations Module Topics

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

6 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.

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

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

9 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.

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

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

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

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

14 Working on It Principles of Mathematics Instruction

15 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

16 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).

17 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.

18 Working on It Investigating the Principles of Mathematics Instruction

19 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.

20 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.

21 Investigating the Principles of Mathematics Instruction Expert Group 1 *foster positive mathematical attitudes *focus on conceptual understanding

22 Investigating the Principles of Mathematics Instruction Expert Group 2 *involve students actively in their learning *acknowledge and utilize students’ prior knowledge

23 Investigating the Principles of Mathematics Instruction Expert Group 3 *provide developmentally appropriate learning tasks

24 Investigating the Principles of Mathematics Instruction Expert Group 4 *respect how each student learns *provide a culture and climate for learning

25 Investigating the Principles of Mathematics Instruction Expert Group 5 *recognize the importance of metacognition *focus on the significant mathematical concepts

26 Investigating the Principles of Mathematics Instruction Return to your home groups and

27 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?

28 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.