Improving Math Performance: Learning From Singapore A Mathematics Professor s Perspective Richard Bisk Profes

2. My Career Trained as a mathematician. Worked entirely at teaching colleges and universities. Many students (25-50%) unprepared for college level math courses. Few (<10%) prepared for calculus

3. My Interests � Two Related Areas College Readiness: Why do students come to my college (and many others) stuck mathematically at the fifth grade level? Mathematical Preparation of Elementary Teachers: In 2007, Massachusetts instituted new mathematics requirements for elementary teachers. www.doe.mass.edu/mtel/MathGuidance.pdf

4. Overview Why the Interest in Singapore Math in the US? Mathematical Preparation of Elementary Teachers. My Experiences with Singapore Math My Perspective on Singapore Math

5. Why the interest in Singapore Math? TIMSS Studies - 1995, 1999, 2003, and 2007. b. National Math Panel Report - 2008 c. Common Core State Standards Initiative (CCSSI) - 2010

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8. Massachusetts - Education Reform Before 1993 Two requirements for a high school degree. One year of American history. Four years of gym. Spending disparities - $3000 to $10000 per student

9. �Grand Bargain� Massive infusion of state dollars. Standards and accountability.

10. What is Still Needed? Frameworks need to be more focused. Testing lacks any emphasis on basic computation, so teachers do not spend enough time on it.

11. National Math Panel Even in elementary school, the U.S. is not among the world leaders; only 7% of U.S. fourth-graders scored at the advanced level in TIMSS, compared to 38% of fourth-graders in Singapore, a world leader in mathematics achievement. (page 4) �� In elementary school textbooks in the United States, easier arithmetic problems are presented far more frequently than harder problems. The opposite is the case in countries with higher mathematics achievement, such as Singapore. (page 26)

12. Common Core Standards The composite standards [of Hong Kong, Korea and Singapore] have a number of features that can inform an international benchmarking process for the development of K�6 mathematics standards in the US. (Second paragraph of introduction- quoted from: Ginsburg, Leinwand and Decker, 2009)

13. Common Core Standards In general, the US textbooks do a much worse job than the Singapore textbooks in clarifying the mathematical concepts that students must learn. Because the mathematics concepts in [U.S.] textbooks are often weak, the presentation becomes more mechanical than is ideal. We looked at both traditional and non-traditional textbooks used in the US and found this conceptual weakness in both. (first page of introduction � Red portion from March, 2010 draft � quoted from Ginsburg et al., 2005)

14. Mathematical Practices - Common Core 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

15. Mathematics Curriculum FrameworkMinistry of Education 2007

16. Mathematical Preparation of Elementary Teachers The Problem: Most U.S. elementary school teachers are weak in mathematics. They lack a deep understanding of the math they teach.

17. If our third grade teachers read at the sixth grade level, there would be cries for action. However, many elementary teachers can�t �do� sixth grade math.

18. How do you teach a mathematical subject when you aren�t proficient in it? You focus on rules, procedures and memorization; or on manipulatives, games and activities that you can�t readily connect to concepts.

19. The habit of memorizing rules and algorithms without understanding is counterproductive. Its negative effects become particularly apparent as students move into middle school. Teachers who don�t understand math well can�t teach for understanding.

20. Why Has This Happened? Few teachers were asked to learn much math in their preparation programs. Often the math courses they take are not relevant to the task of teaching elementary school mathematics.

21. New Regulations for Elementary Teacher Subject Knowledge � 2007 a. Basic principles and concepts important for teaching elementary school mathematics in the following areas. i. Number and operations (the foundation of areas ii-iv) ii. Functions and algebra iii. Geometry and measurement iv. Statistics and probability b. Candidates � must demonstrate not only that they know how to do elementary mathematics, but that they understand and can explain to students, in multiple ways, why it makes sense. c.

22. New RequirementsMassachusetts - 2007 ��.the Massachusetts Tests for Educator Licensure (MTEL) �General Curriculum Test� will include a separately scored section of 40 questions on the mathematics specified in the new regulation.� Commissioner�s Guidelines document articulates �....the scope and depth of mathematics knowledge�both skills and understanding�that are expected of elementary teachers and that will be assessed on the test. �

23. New Requirements Massachusetts - 2007 ��.three to four college-level, subject-matter courses, i.e., 9�12 semester-hours, taught by mathematics faculty, ... These should be taken after any necessary remedial courses and either integrated with or taken prior to math methods courses.�

24. My Singapore Math Experience Accidentally started working with K-12 teachers in 1990. Team taught Professional Development (PD) courses with a middle school teacher. Audience was usually K-8 teachers. Focus was on mathematical content. Most PD at that time focused on pedagogy.

25. Initial Lessons Most primary teachers are dedicated and hard-working. Weak in mathematics. Often confused; sometimes scared. Pass on their math phobia to their students.

26. First SM Experience - 2000 Asked to teach a 10 day grant funded summer content institute based on �Singapore Math.� I had never heard of it, but agreed. Fortunately the books were great.

27. Three middle school teachers assisted with instruction. Five teachers volunteered to teach using the materials. (Grades 5-8) Next two summers � three additional programs. Expanded to include primary teachers. Initially teachers only used materials if they volunteered. But they had to take the course first.

29. Textbook - EMT Parker and Baldridge: Elementary Mathematics for Teachers (EMT) -2003 Designed to be used with five Singapore Primary Mathematics textbooks. Focus on Number and Operations strand.

30. EMT: Why SM Books? From the Introduction: The Primary Mathematics books give an extraordinarily clear presentation of what elementary mathematics is and how it is developed.

31. EMT: Key Features of Primary Books Absence of Clutter and Distraction Coherent Development Short, Precise Definitions C?P?A Approach The Books Serve as Teachers Guides*

32. My Use of EMT and SM PD at schools that plan to use Singapore Math textbooks. PD for elementary teachers who want to improve their understanding of the math they teach. First undergraduate math course for students planning to become elementary teachers.

33. SM in the US Three versions: a. Primary Math � US Edition b. Primary Math � California Standards Edition c. Math In Focus � HMH Adaptation of My Pals are Here

34. What�s different about Singapore Math? What are its key characteristics?My View Depth emphasized over breadth: More time is spent on each topic. Fewer topics are covered in a year. Greater focus on mastery.�

36. Key Characteristics Concrete-Pictorial-Abstract Approach: Abstraction gives math its power. But abstraction must be grounded in understanding. Coherent Development: Topics are introduced with simple examples and then incrementally developed until more difficult problems are addressed.

37. Problem Solving Emphasis: Model drawing diagrams are used to promote understanding of word problems and provide a bridge to algebraic thinking. More Multi-Step Problems: Problems often require the use of several concepts. Mental Math: Techniques encourage understanding of mathematical properties and promote numerical fluency. A high level of expectation is implicit in the curriculum.

38. Stress on Developing Conceptual Understanding: Students and teachers learn to focus on �why� not just �how.� The curriculum teaches for mastery through understanding and practice.

39. Mathematical Examples Note connection between understanding and basic skills in the next slide.

40. Mental Math 3A

41. Addition and Subtraction are Related

42. Making Ten part 7 10 whole part 3

44. Mental Math 7 + 8

45. Emphasis on Place Value

48. Division is the Opposite of Multiplication 24 � 3 = 8 because 8 x 3 = 24

51. Teacher Training Connection Some elementary teachers believe: 12 � � = 6 Few can answer: 9 � 0 = ?

52. Problem Solving and Transition to Algebra The next slide contains a problem from the Massachusetts grade 10 assessment in 2005. It had the largest percentage of incorrect answers of any problem on that assessment.

54. Summary: Learning from Singapore Core Standards reflect influence of Singapore: More focused curriculum Emphasis on conceptual understanding Emphasis on place value Emphasis on problem solving Higher expectations for students

55. Summary Elementary mathematics is not elementary. It is a rich and complex subject. Our universities need to provide future teachers with a deep understanding of the mathematics they will be teaching.