Prerequisites for Planning Lessons Effectively

1. Prerequisites for Planning Lessons Effectively Akihiko Takahashi Tad Watanabe Makoto Yoshida

2. Effective Teaching Effective teaching requires knowing and understanding: • content • students as learners • pedagogical strategies.

3. Important Ingredients for Preparing a Good Lesson • Subject content knowledge • Subject pedagogical knowledge • Knowledge about students’ thinking and learning process • Clear goals and outcomes

4. Frequently Asked Questions About Outcomes of Lesson Study • Can lesson study improve teachers’ subject content knowledge? • Can lesson study improve students’ test scores?

5. Yes, if lesson study includes the intensive study of instructional materials.

6. Necessity for Studying Instructional Materials Intensively • What does it mean to study instructional materials intensively? • Is it enough to study and understand how to solve problems in the textbook? • Is it enough to study and understand what teacher’s manual suggests for implementing lessons in the classroom?

7. Instructional Materials Investigation • Kyozaikenkyu • Understanding subject content and the scope and sequence • Establishing a clear understanding of the goals and outcomes • Preparing necessary instructional materials for the learning activities • Thinking and preparing instruction to help students to achieve the learning goals

8. What Do Japanese Teachers Say About Kyozaikenkyu? “Teachers can provide the richness of learning experiences for the students in the classroom only up to the level of teachers’ understanding of the instructional materials. Thus, it is important for teachers to conduct kyozaikenkyu every day through classroom practice.”

9. “Teachers can provide the richness of learning experiences for students in the classroom only up to the level of understanding of the students*” *Students’ thinking and learning process, common misunderstandings, etc.

10. Conducting Instructional Materials Investigation in Lesson Study • Lesson Study enhances the level of investigation • Collaboration helps deepen understanding of the instructional materials • Teachers can influence each other to grow together by sharing and contrasting different point of views

11. Instructional Materials Investigationin Mathematics

12. Learning Mathematics • Mathematics is a subject for which students need to build up their knowledge and skills based on the foundation of what they learned before.

13. (A) Investigating Scope and Sequence • Where does a topic fit within a content standard and how is it related to other topics within the content standard as well as to other content standard areas? • Why do students need to learn specific topics before learning a certain topic? • How do the topics they learn build upon other related topics they learned previously?

14. B A A B Cutting triangle A and moving it to B to make a rectangle Cutting trapezoid A and moving it to B to make a rectangle Area of Parallelogram Relating area of parallelogram to area of rectangle:

15. Making different shapes with two congruent triangles: • Composition and decomposition of shapes • Equivalent area transformation

16. A D B E C Area of a parallelogram where the height is located outside of its base: Can students understand why they still can use the formula “base times height” to find the area?

17. Square Rectangle Triangle Parallelogram Parallelogram Triangle

18. Area of a regular triangle:

19. Area of a triangle where the height is located outside of its base:

20. Understanding Scope and Sequence • Understanding scope and sequence helps teachers to: • Develop a clear understanding of mathematical concepts they are teaching to students • What concept will be taught? • When will the particular concept be taught? • What is the connection to other concepts? • How will understanding of the concept be developed using prior knowledge? • Determine clear goals for the lesson

21. (B) Investigating Problems & Activities • How does solving a particular problem or engaging in an activity help students understand important mathematical concepts? • What kind of knowledge and skills do students develop through the lesson, and what is our role in helping them achieve the goals?

22. 4 cm 4 cm 3 cm 8 cm 4 cm 7 cm Finding area of L-shaped figure

23. Understanding the structure of the figure by asking students to measure the sides instead of giving all the measurements • Students might discover they don’t need to measure all 6 sides

24. 4 cm 4 cm 3 cm 4 cm 7 cm Understanding multiple ways to solve this problem and finding similarity and differences among those ideas >>> Lead to discovery of other and better solutions A B C D E

25. Fostering expressive ability to describe their ideas for solving problem: • Manipulating the figures • Drawing diagrams • Explaining with words • Writing mathematical sentences

26. (C) Understanding Students • Think about students’ • state of learning • process of thinking and learning • anticipated reactions and solutions • common misunderstandings thoughout the instructional materials investigation

27. How Does Kyozaikenkyu Help Teachers to Conduct Lesson Study Effectively? • Enhances content knowledge (mathematics, mathematical concepts, scope and sequence, etc.) • Establishes clear goals of the lesson • Develops deeply thought out rationale, hypothesis, and instructional plan for the lesson • Evaluates the lesson effectively (clear objectives >> clear evaluation points) Greater Learning from Lesson Study

28. How does Teachers’ Practice of Kyozaikenkyu Help Students? • Develops a well thought out lesson • Identifies thoughtful questions (Hatsumon) for provoking students’ deep thinking • Increases understanding of students’ different perspectives • Develops insight into student misunderstandings • Supports individual student’s needs Improves Students’ Learning and Understanding