Thinking Differently about Middle School Teaching

1. Bill AtwehRetired Visiting Prof Philippines Normal University Retired Adjunct Prof Curtin University Thinking Differently about Middle School Teaching

3. Is way too complicated for me …. Its like a foreign language

4. I am not smart enough for mathematics

5. Passing the test is the most important thing in mathematics

6. Of course, for some students mathematics is fun/easy/useful But, they are in the minority (Sigh)

7. Aimsof this workshop … • Identify two problem in mathematics education for students around the world • Discuss Problem Based Learning and Project Based Learning to deal with these problems • Illustrate some example activities illustrating these approaches • Allow you to create activities in the elementary school based on these examples

8. Two Challenges for Mathematics Teaching • How to achieve QUALITY mathematics teaching? • How to achieve CONNECTIONS in learning?

9. Principle One: Intellectual Quality – Teaching through problem solving • Most of mathematics teaching focus on understanding and skills in basic concepts and procedures • Teachers may think that practice and regular tests (school and national) encourage this to happen 9

10. On Teaching problem solving • Problem solving means engaging in a task for which the solution and the solution method is not known in advance – • These are different from of exercises • Is this a problem: 2 x 4 = ? • Is this a problem: 45 x 43 = ? • Is this a problem: Factorise 4X2 + 16 X – 4 • Is this a problem: There are 20 people in a room, how many handshakes are there if each two people shake hands once?

11. Most problem solving in mathematics classes … • Are not realistic context • Have one (or best) known method of solution • Are done individually at the end of the lesson or homework • Are done after the teacher explains the content • Students solve many problems for practice

12. Make a distinction between • Teaching problem solving in mathematics, and • Teaching mathematics through problem solving • In some Asian countries they have successfully considered what it means to have problem solving as main teaching method • Typically one problem is taken in one lesson • Students work in groups to solve it in many ways • Teacher compare results and develop new mathematics Following few slides are taken from: Tom McDougal and Akihiko Takahashi (2014)

13. Problem Problem Problem Solution Solution Solution Problem Problem Problem Solution Solution Solution

15. From: Tom McDougal and Akihiko Takahashi (2014)

18. Idea 1: B and C have the same number of rabbits, but C has a smaller area, so C is more crowded. Unsure about A vs. C. • Idea 2: If you make 5 copies of A and 6 copies of C, they would have the same area (30 m2). A would then have 45 rabbits while C would have 48 rabbits, so C is more crowded. • Idea 3: If you make 8 copies of A and 9 copies of C, they would have the same number of rabbits (72). A would have an area of 48 m2 while C would have an area of 45 m2, so B is more crowded. • Idea 4: Divide: (area) ÷ (# of rabbits) = amount of area per rabbit • Idea 5: Divide: (# of rabbits) ÷ (area) = number of rabbits per unit area

19. Students explain their ideas and discuss questions such as • Which method is simple? • Which method is general? • Which method is hard to understand? Why?

20. Notes on Activity …. • Students working in groups obtained different solutions • Problem was used to teach ratios NOT to apply student knowledge • High order thinking was used to solve the problem and to evaluate possible solutions • Single problem took all lesson to develop deep engagement and mathematics knowledge

21. Principle Two: Make Connections • Knowledge is usually isolated from what was taught in past, other subjects and real world • Often connections are shallow and artificial and may not be meaningful to students • Establishing connections increases meaning, applications and engages students

22. Connections to be made with • Previous content studied • Other subjects • Real world – not only physical but also social world • Connections to the real world make students learn about the world as they learn mathematics and learn mathematics as they look at real world problems

23. Traditional teaching • Teachers follow curriculum • They think each lesson is needed for each outcome • Different school subjects have different curricula and time table

24. Sample Feed Me Project • (Available upon request from b.atweh@oneworldripples.com)

25. Notes on Activity • Uses simple resources from the internet • Teacher creativity in developing lessons based on local curriculum • Develop mathematics by interactions and working in groups – no single answer was preferred • Develop knowledge of students about real world in which we live in • Make connections across the curriculum • No artificial motivation was needed

26. Take home message … • Teaching Math has not progressed as deep as other subjects in the schools/and universities • Change is hard ….. • Take the challenge and think differently about teaching mathematics

27. Participants activity • Work in groups of 3-5 at same grade level • Develop some activities from these pictures in your class in different subject areas • Explain some of your activities with the rest of the group