Yeap Ban Har presented a regular lecture on second day of the conference.

1. The Emphasis of Primary-Level Textbooks in Singapore on Higher-Order Competencies Yeap Ban Har Marshall Cavendish Institute Singapore banhar@sg.marshallcavendish.com Slides are available for download at Marshall Cavendish Institute’s Facebook or at www.banhar.blogspot.com

2. Background Mathematics is “an excellent vehicle for the development and improvement of a person’s intellectual competence”. Ministry of Education Singapore 2006 1982 Introduction of Singapore mathematics textbooks as they are known today. 1992 Introduction of Problem-Solving Curriculum 1997 Thinking Schools Learning Nation 2001 Introduction of textbooks published by private publishers and approved by Ministry of Education. 2007 New editions of textbooks are published with the introduction of the revised curriculum.

3. Methodology Sample Two textbook series were selected. One was the one published by Ministry of Education in 1982 and revised twice. The edition used in this study is the latest edition (1999). This was the only textbook series used. The other was published by a private publisher in 2001 and revised once. The edition used in this study is the latest edition (2007). This is the textbook series used by majority of schools.

4. Details Textbook Workbook 1999 Series 3A 104 pages 3B 096 pages 3A-1 80 pages 3A-2 72 pages 3B-1 72 pages 3B-2 72 pages 506 pages 2007 Series 3A 136 pages 3B 174pages 3A-1 088 pages 3A-2 104 pages 3B-1 112 pages 3B-2 104 pages 718 pages

5. Emphasis on Visualization See also Ho, S. Y. & Yeap, B. H. (2011). Development of Visualization Skills in Singapore Primary School Mathematics Textbooks. Paper presented at PME-35 Angkara, Turkey. Visuals are used to teach concepts – in this case multiplication.

6. Emphasis on Visualization Visuals are used to teach concepts – distributive property of multiplication – without using formal terms.

7. Emphasis on Visualization Visuals are used in a systematic way to teach terms. The progression from visual to abstract is observed throughout the books.

8. Emphasis on Visualization

9. Emphasis on Visualization There is also an emphasis on the use of concrete materials to lead to visuals. “The main feature of the package is the use of Concrete  Pictorial  Abstract approach.” Primary Mathematics 1999

10. Emphasis on Visualization

12. Emphasis on Visualization Visuals are used extensively in solving of word problems.

13. Emphasis on Visualization The use of visuals such as the model method was in response to students’ poor performance in word problems.

14. Emphasis on Generalization Looking for patterns and making generalization is also emphasized. This emphasizes the relatedness between the 2, 4 and 8 times table. This emphasizes a general idea – the use of doubling to multiply.

15. Emphasis on Generalization Explicit request to engage in higher-order competencies such as to look for a pattern.

16. Emphasis on Generalization There are sections of the later series devoted to higher-order thinking.

17. Emphasis on Number Sense Number sense, as opposed to computation, is given emphasis.

18. Emphasis on Number Sense Mental strategies are taught explicitly.

19. Emphasis on Number Sense Mental strategies are taught explicitly across domains.

20. Emphasis on Communication There are sections in the later series that require students to articulate their thinking in written language.

21. Emphasis on Metacognition Also, the later series require students to identify mistakes.

22. The later series also include some open-ended tasks.

24. Generalization

25. Number Sense

26. Communication

27. Metacognition