MODULE 1 –PRINCIPLES OF MATHEMATICS
INSTRUCTION
This module provides suggestions for an activity that session leaders can use in order to helpparticipantsget to know each other. As well, it presents an overview of session topics and provides a framework within which participants will be able to explore the key principles of mathematics instruction outlined in the Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3, 2004.
Materials: BLM 1.1, BLM 1.2, BLM 1.3, chart paper, markers
Getting Started
Introduction
Begin the session with an activity that allows participants to get to know each other (see BLM 1.1 and BLM 1.2).
Discuss the purpose of the sessions and show participants the overview of the nine sessions (PowerPoint slide 4).
Module 1 – Principles of Mathematics Instruction
KEY MESSAGES
Rich environments do not just happen; they are the result of insightful planning by a thoughtful teacher.
Before a teacher can institute effective planning, he or she must have a firm grasp of the basic principles of teaching and learning.
Of paramount importance for successful mathematics instruction is the promotion of positive attitudes in students.
Instruction in mathematics must emphasize conceptual understanding and not just procedural knowledge.
In an effective program, students must be allowed to ‘do’ mathematics; children learn mathematics primarily through a combination of doing, talking, reflecting, discussing, observing, investigating, listening, and reasoning.
For learning to be effective, it must utilize and build upon the prior knowledge of the child.
Students need to encounter concepts in an appropriate manner, at an appropriate time, and with a developmentally appropriate approach.
The culture and climate in the classroom have a profound effect on the quality of learning that takes place.
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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Module 1 –Principles of Mathematics Instruction
Working on It
“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
Discuss the complexity of teaching mathematics. Teachers need to possess an understanding of the mathematics they are teaching, and of instructional methods that help students develop their own understanding of mathematics.
Arrange participants in groups of three or four. Ask each group to identify a topic in the mathematics program (e.g., linear measurement, multiplication, symmetry) and to create a list on chart paper of mathematical content (knowledge, skills, concepts) related to the topic. Next, ask participants to make a second list of things teachers need to considerwhen teaching the mathematical content
(e.g., manipulatives, teaching strategies, students’ prior knowledge).
Have groups present their lists. Highlight the complexity of the decisions teachers make as they design and implement instructional activities.
Explain to participants that teachers need to understand the principles of mathematics instruction in order to make appropriate decisions about the mathematics program for their students.
Module 1 –Principles of Mathematics Instruction
Investigating the Principles of Mathematics Instruction
Arrange participants in groups of five. Use a jigsaw strategy to facilitate participants’ exploration of the principles of mathematics instruction.
Jigsaw is a cooperative learning strategy that allows participants to become “experts” on a topic, and to share their expertise with other members of their group.
Step 1 –Participants are divided into home groups. A different topic is assigned to each home-group member.
Step 2 –Home-group members each join the appropriate expert group to study their assigned topic.
Step 3 – The new “experts” return to their home groups to share what they have learned.
Ask the expert groups to study the following principles:
Expert Group 1–
Foster positive mathematical attitudes (p. 2.4)
- Focus on conceptual understanding (pp. 2.4–2.5)
Expert Group 2–
Involve students actively in their learning (pp. 2.5–2.7)
- Acknowledge and utilize students’ prior knowledge (p. 2.7)
Expert Group 3 –
Provide developmentally appropriate learning tasks (pp. 2.8–2.9)
Expert Group 4 –
Respect how each student learns (p. 2.10)
- Provide a culture and climate for learning (p. 2.11)
Expert Group 5–
Recognize the importance of metacognition (pp. 2.11–2.12)
Focus on the significant mathematical concepts (pp. 2.12–2.13)
Ask expert groups to record their ideas on BLM 1.3.
Provide extra copies so that participants can make notes when 'experts' share information with their home groups.
Module 1 –Principles of Mathematics Instruction
Discuss the following questions:
- Are some principles more important than others?
- Are there principles that are often neglected because of time limitations and interferences with your program?
- Are there principles that you would like to emphasize in your teaching?
Reflecting and Connecting
In Your Classroom
Ask participants to select a principle of mathematics instruction that they would like to emphasize in their classroom. At the next session, participants should be prepared to share the strategies they used when they addressed the principle,
and the impact of their efforts.
For Next Time
Ask participants to read the first three sections of Chapter 5 – Problem Solving (Introduction, Teaching Through Problem Solving, and The Teacher’s Role in Teaching Through Problem Solving) in A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3, 2004.
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