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Intriguing Lessons about Teaching and Assessing Math around the World. Steve Leinwand American Institutes for Research SLeinwand@air.org NCTM – April 28, 2012. What a great time to be convening as teachers of mathematics!. Common Core State Standards Initiative
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Intriguing Lessons about Teaching and Assessing Math around the World Steve Leinwand American Institutes for Research SLeinwand@air.org NCTM – April 28, 2012
What a great time to be convening as teachers of mathematics! • Common Core State Standards Initiative • Quality K-8 instructional materials • More access to material via the web than ever • $5 billion with a STEM RttT tie-breaker • A president who believes in science and data • The beginning of the end to Algebra II • A long overdue understanding that it’s instruction that really matters • A recognition that the U.S. doesn’t have all the answers.
And what can we learn from others? • There is more than one way to do things. • Like how a foreign language strengthens ones understanding of English, so too can international comparisons hold up mirrors. • There might be good reasons why other nations outperform the U.S. • In answering “How is it done elsewhere?” we can learn how to change what we do here.
Today’s agenda Glimpses of intriguing differences in: • Curriculum Frameworks and Standards • Instruction • Assessment • Teacher Support
Part 1 Curriculum Frameworks and Standards
Five Content Strands Numbers and operations Measurement Geometry Algebra Data and Probability Five Process Strands Problem-Solving Reasoning and Proof Communication Connections Representations How NCTM (and most states) Organizes the Curriculum
Singapore logically builds-up math topics across grades: numbers I I 8
Singapore, Japanese and Hong Kong Math Standards at: http://hrd.apec.org
Basic rationales for the new Chinese math standards: • We cannot do without mathematics in our daily living, • work and study. • Contents of mathematics learning for school children • ought to be realistic, meaningful and challenging. • Mathematical instructional activities should be based • on children’s cognitive developmental level and build • on past experiences. • Modern information technology has great impact on • the values, objectives, contents and pedagogy of • mathematics education.
A peek at China’s approach: • What is the approximate thickness of 1200 sheets of paper? What is the approximate number of classes that may be formed comprising of 1200 students? What is the approximate length of 1200 footsteps? (grades 1-3) • Estimate the number of words (or characters) contained in one whole page of a newspaper. (grades 4-6)
Initial Lessons • Think holistically, and systemically, not linearly and piecemeal • Coherence and focus • Learning progressions • “Teach less, learn more” • Provide examples
Part 2 Instruction
How about content balance at grade 1? *14 (13%) review and routines lessons
How about content balance at grade 6? *11 (10%) review lessons
U.S. Textbook Problems Emphasize Mechanical Formulas: Gr. 6 Pie Chart Requires Summing to a Total Cost of Raising a Child to Age 18 (for each $100) 23
Singapore textbooks uses structured variation and multi-step Problems: Gr. 6 Pie Chart Problem Incorporating Angles 24
And then there is Singapore’s visual approach to mathematics: The bar model
But what about the actual art of teaching? Here’s a glimpse at the Japanese 6th grade lesson.
The problem- Grade 6 We bought pencils and ballpoint pens and the total number of items was 10 and the price was 460 yen. The price of each pencil was 40 yen and the price of each ballpoint pen was 70 yen. How many pencils and how many ballpoint pens did we buy?
Massachusetts – Grade 3 – 2007 Alan has the number tiles shown below. 4 7 8 1 • Use all of Alan’s number tiles to make the four‑digit number with the smallest value. Use each number tile only one time. Write the number in the boxes below. • What is the value of the digit 7 in the number you made? Explain your answer.
