Singapore Math Overview with Common Core Connections Richard Bisk Professor Mathematics Department Worcester State University

Transcription

1 Singapore Math Overview with Common Core Connections Richard Bisk Professor Mathematics Department Worcester State University

2 Warnings about the presenter He talks ahead of his slides. He may have too many slide; so he might skip over a few. They will be posted on the website. He will talk about the Common Core tomorrow too.

3 Singapore Books in the U.S. Three versions, all published by Marshall Cavendish Education: a. Primary Math: US Edition California Standards Edition Common Core Edition c. Math In Focus HMH Adaptation of My Pals are Here

4 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.

5 College Readiness Why do many students come to higher education with significant mathematical weaknesses that limit their career options? Weak foundation that goes back to elementary and middle school. Led to an interest in working with K-8 teachers and their students. Content based PD is my passion. Use books from Singapore because the math is so clear and coherent.

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

7 Grade 4 TIMSS 2011 Grade 8 Singapore 606 South Korea 613 South Korea 605 Singapore 611 Hong Kong 602 Taiwan 609 Taiwan 591 Hong Kong 586 Japan 585 Japan 570 Northern Ireland Belgium 562 Russia Instruction in Singapore is in English 549 Israel Finland 545 Finland 514 England 542 United States 509 Russia 542 England 507 International 500 International 500

8 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)

9 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)

10 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)

11 Mathematics Curriculum Framework Ministry of Education 2007 Beliefs Interest Appreciation Confidence Perseverance Monitoring of one s own thinking Self-regulation of learning Numerical calculation Algebraic manipulation Spatial visualization Data analysis Measurement Use of mathematical tools Estimation Mathematical Problem Solving Concepts Numerical Algebraic Geometrical Statistical Probabilistic Analytical Reasoning, communication & connections Thinking skills & heuristics Application & modelling

12 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.

13 Beliefs Interest Appreciation Confidence Perseverance Monitoring of one s own thinking Self-regulation of learning Numerical calculation Algebraic manipulation Spatial visualization Data analysis Measurement Use of mathematical tools Estimation Mathematical Problem Solving Concepts Numerical Algebraic Geometrical Statistical Probabilistic Analytical Reasoning, communication & connections Thinking skills & heuristics Application & modelling 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.

14 This Presentation Connect the Common Core Standards to examples from the Singapore Books.

15 Reason abstractly and quantitatively. C P A Concrete:? Pictorial: Abstract: 8

16 Abstraction Gives mathematics its power. But abstraction without understanding?? Leads to confusion.

17 Look for and make use of structure MP7: Mathematically proficient students look closely to discern a pattern or structure students will see 7 8 equals the well remembered , in preparation for learning about the distributive property.

18 CCSS.Math.Content.3.OA.B.5 Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = = 56.

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22 Grade 1 Common Core CCSS.Math.Content.1.OA.B.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 8 by finding the number that makes 10 when added to 8. CCSS.Math.Content.1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as making ten ( = = = 14);

23 Grade 2 Common Core CCSS.Math.Content.2.OA.B.2 Fluently add and subtract within 20 using mental strategies. 2 By end of Grade 2, know from memory all sums of two one-digit numbers.

24 Number Bonds part 5 8 whole part 3

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27 Number Bonds

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29 Number Bonds

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31 Progression to Abstract

32 Making Ten part 7 10 whole part 3

33 Ten Frame

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36 Compensation

37 Common Core Grade 3 CCSS.Math.Content.3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b Understand a fraction 1/3 as the quantity formed by 1 part when a whole is partitioned into 3 equal parts; understand a fraction 2/3 as the quantity formed by 2 parts of size 1/3.

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39 This reinforces: Understand subtraction as an unknown-addend problem.

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41 Grade 3 Common Core 3.OA.2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. 3.OA.6. Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8.

42 Number of Objects

43 Number of Shares

44 Common Core Grade 4 Use place value understanding and properties of operations to perform multidigit arithmetic. 4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.

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50 Singapore Grade 2

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52 Common Core Grade 5 5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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54 CCSS.Math.Content.5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1

55 If time

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57 Common Core Grade 6 6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

58 Tape Diagrams Also called: bar diagrams model drawing bar models

59 Apply and extend previous understandings CCSS.Math.Content.7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

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61 Use properties of operations to generate equivalent expressions. CCSS.Math.Content.7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

62 7A 3(2x+4) = 6x+12

63 Common Core - First sentence For over a decade, research studies of mathematics education in high performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country.

64 AMERICAN INSTITUTES FOR RESEARCH Report prepared for the U.S. Department of Education (2005): What the United States Can Learn From Singapore s World-Class Mathematics System. A mathematically logical, uniform national framework that develops topics in-depth at each grade guides Singapore s mathematics system.. The framework covers a relatively small number of topics in-depth and carefully sequenced grade-by-grade,.

65 Summary of Key Connections Focused, coherent, rigorous standards. Emphasis on conceptual understanding and procedural fluency. Early learning of mathematics emphasizes number and operations in base 10. Model drawing as a problem solving technique and precursor to algebra.