Iowa Content Network Project Mathematics

1. Iowa Content Network ProjectMathematics Reviewing Research on Instructional Strategies and Programs

2. Background & Overview • Scholarly work within the field that provides a context for the Iowa Mathematics Network (IMN) research reviews, and on which the IMN builds 2. Overview of the IMN project thus far

3. Background and Context Other Research Reviews National Tests National Review Panels Iowa Math Network Project Internatl. Tests Program Ratings Some Cognitive Science

4. Published Research Reviews • Adding It Up (National Research Council) http://www.nap.edu/books/0309069955/html/ • NCTM Standards Research Companion http://my.nctm.org/store/ECat/product.asp?id=12341 • Improving Student Achievement in Mathematics (International Academy of Education) http://www.ibe.unesco.org/International/Publications/EducationalPractices/prachome.htm • Standards-Based School Mathematics Curricula https://www.erlbaum.com/shop/tek9.asp?pg=products&specific=0-8058-4337-X

5. National Tests • National Assessment of Educational Progress (NAEP) http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2000469 http://nces.ed.gov/nationsreportcard/mathematics/trendsnational.asp • SAT http://www.collegeboard.com/press/article/0,3183,26858,00.html

6. International Tests • Third International Mathematics and Science Study (TIMSS) - 1995 12th Grade • TIMSS - 1999 8th Grade Video Study http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2003013 • TIMSS-R - 1999 Repeat with US Consortia http://isc.bc.edu/timss1999b/mathbench_report/t99b_math_report.html

7. Some Cognitive Science • How We Learn: Ask the Cognitive Scientist. American Educator, Winter, 2002. http://www.aft.org/american_educator/winter2002/CogSci.html

8. Program Ratings • American Association for the Advancement of Science (AAAS) - rating of algebra texts http://www.project2061.org/research/textbook/hsalg/charts.htm • US Department of Education - Exemplary and Promising Programs in Mathematics http://www.enc.org/professional/federalresources/exemplary/promising/document.shtm?input=CDS-000496-496_toc,00.shtm

9. National Research Review Panels • What Works Clearinghouse http://w-w-c.org/ • Mathematical Sciences Education Board (MSEB) http://www4.nas.edu/cp.nsf/57b01c7b1b6493c485256555005853cf/5cf09421beb746d185256b7c00568d05?OpenDocument

10. Background Details • Some findings from Cognitive Science • International and National Tests • TIMSS • NAEP • SAT • Research on NCTM-Standards based approach • NSF curricula: US DE, AAAS, NAEP, new book • Research companion to Principles and Standards

11. 4. Existing Reviews & Summaries of Research • Improving Student Achievement in Math • Adding It Up • NCTM Research Companion 5. In-Progress Research Review Projects • What Works Clearinghouse (US DE) • National Research Council • Iowa Math Network Project

12. 1. Cognitive Science “Findings from the field [Cognitive Science] that are strong and clear enough to merit classroom application.” Willingham, Daniel T. How We Learn: Ask the Cognitive Scientist. American Educator, Winter, 2002.

13. Finding 1 “The mind much prefers that new ideas be framed in concrete rather than abstract terms.”

14. Finding 2 Rote Knowledge, Inflexible knowledge, and Deep Structure

15. Rote: Q: What is the equator? A: A managerie lion running around the Earth through Africa.

16. “We rightly want students to understand; we seek to train creative problem solvers, not parrots. Insofar as we can prevent students from absorbing knowledge in a rote form, we should do so. ”

17. Inflexible Knowledge: • Deeper than rote knowledge, but at the same time, clearly the student has not completely mastered the concept. • Understanding is somehow tied to the surface features. • Meaningful, yet narrow. • The student does not yet have flexibility . (Knowledge is flexible when it can be accessed out of the context in which it was learned and applied in new contexts.)

18. Deep Structure Knowledge: • Deeper than inflexible knowledge • Transcends specific examples • Knowledge is flexible -- it can be accessed out of the context in which it was learned and applied in new contexts • Knowledge is no longer organized around surface forms, but rather is organized around deep structure

19. Finding 3 Develop deep structure knowledge: • Solve more problems • Multiple contexts • Focus on meaning • Don’t despair of inflexible knowledge, and don’t confuse it with rote knowledge

20. 2. International and National Tests • TIMSS • NAEP • SAT

21. TIMSS - 12th grade US performs at the bottom of the list of nations A key difference between US high schools and all others in the world: Integrated Curriculum (not Alg 1, Geom, Alg 2, Pre-Calc)

22. TIMSS 8th Grade Video Study • US and 6 countries that outperformed the US in 1999, plus Japan from ‘95 study • March 2003 • Teaching Mathematics in Seven Countries: Results from the TIMSS 1999 Video Study. NCES, 2003

23. US performance is below average (19th out of 38 in 1999) • No single method of mathematics instruction was observed in all of the high-performing countries examined • Hong Kong: most emphasis on procedures • Netherlands: most calculator use • All countries: little use of computers

24. Japan: most connections and relationships • Japan: do more than repeat procedures during private work time • Japan: how to use procedures, not just execute • Netherlands: most use of real-life applications

25. US reduces complexity of problems Lessons taught by US and Australia teachers most often translated connections problems into procedure problems Tendency in U.S. classrooms for teachers to transform intellectually demanding tasks in ways that reduce the cognitive challenge for students

26. US does most review and least new content Review of previously taught lessons plays a larger role in mathematics lessons in the Czech Republic and the United States than in the five other countries where more time is devoted to introducing new content.

27. US least likely to emphasize connections When the researchers examined the ways in which the mathematical problems in the lesson were actually discussed and worked out during the lessons, they found that eighth-grade mathematics lessons in Australia and the United States were the least likely to emphasize mathematical connections or relationships (8 and less than 1 percent, respectively; other countries ranged from 37 to 52 percent)

28. Moral so far: US can learn from other countries that are more successful in mathematics education

29. TIMSS and Singapore • Singapore is top ranked • Singapore curriculum is becoming popular in US • Spring 2003 - Ngee Ann Polytechnic in Singapore announced an agreement to collaborate with the Curriculum Research & Development Group (CRDG) of the University of Hawaii to develop an introductory engineering mathematics course for Ngee Ann students based on a Standards-based curriculum developed at CRDG, Algebra I: A Process Approach.

30. • Ngee Ann selected the program because it uses problem-solving and communication strategies--reading, writing, speaking, critical listening, and multiple representations--features that they believe lead to students' deeper understanding of mathematics.

31. • Though she was initially surprised by the request, Barb Dougherty of CRDG said, "On thinking about it, our Algebra I program is a natural fit with the way math is taught in Singapore. Like us, they use increasingly complex word problems to teach students problem-solving skills, encouraging students to find different ways to solve and express problems, not simply memorize formulas taught by a teacher."

32. Singapore is also seeking to collaborate with “reform” mathematics education curriculum developers at Cambridge University in England. Moral: Learn from other countries, but don’t try to emulate their curricula

33. TIMSS 1999:Michigan Invitational Group • U.S. groups participating in this international comparative study include states, large school districts, and consortia of schools. • The top four U.S. groups are: the Naperville school district in Illinois, the First in the World consortium on the North Shore in the Chicago area, Montgomery County in Maryland, and a 21-school consortium called the Michigan Invitational Group.

34. The top-scoring US groups are using "hands-on learning” and "progressive curriculum strategies.” • Michigan Invitational Group (MIG) also uses "National Science Foundation materials” and has strong implementation. • MIG is significant since it is the only top-scoring U.S. group with a diverse population. A diverse group of students can perform at the top level, right along with the top countries in the world and the top affluent suburban US school districts.

35. Moral: Use NCTM-Standards Based Approach, implemented well, for high achievement with diverse students.

36. “The Nation’s Report Card”National Assessment of Educational Progress (NAEP) Trends in Computation • 17-year-olds. After declining between 1973 and 1982, average scores increased during the 1980s, and more modestly in the 1990s. The average score in 1999 was higher than that in 1973.

37. 13-year-olds. An increase in scores between 1978 and 1982, followed by additional increases in the 1990s, resulted in an average score in 1999 that was higher than that in 1973. • 9-year-olds. After a period of stable performance in the 1970s,average scores increased in the 1980s. Additional modest gains were evident in the 1990s, and the 1999 average score was higher than that in 1973.

38. MORAL: Changing curricula to emphasize computation skills is not warranted. “Reports today saying the curriculum must change to emphasize computational skills are no more valid today than in 1973.” Johnny Lott, NCTM President, NCTM News Bulletin, November 2002

39. SAT Scores • SAT scores highest in 35 years • Continues trend of rising scores • “NCTM has done a tremendous job in its reform efforts. This has really begun to pay off.” -- Wayne Camara, College Board VP of Research and Development (NCTM News Bulletin, October 2003, p. 1)

40. 3. Research on the NCTM Standards-Based Approach • Research on NCTM’s Principles and Standards for School Mathematics • Research on the “NSF Curricula”

41. Research on NCTM’s Principles and Standards A Research Companion to Principles and Standards for School Mathematics Edited by Jeremy Kilpatrick, Gary Martin, and Deborah Schifter NCTM, 2003

42. Does Research Support the NCTM Standards? • Yes • “The Standards are consistent with the best and most recent evidence on teaching and learning mathematics.” • “However, research does not shine equally brightly on all aspects of the Standards.”

43. What Research Cannot Do • Research cannot make value judgments. • Research cannot prove what works or what is best. • Too many variables, conditions, situations • Implementation is essential • Traditional scientific experiments cannot be applied to all educational questions.

44. What Research Can Do • Probe beneath the surface • Extend our knowledge of teaching and learning • Inform our decisions • Show what is possible and what is promising

45. What Do We Know? • Students learn what they have the opportunity to learn.

46. What do we know about traditional programs? • “Presuming that traditional approaches have proven to be successful is ignoring the largest database we have.” • With traditional curricula and pedagogy: • Students knowledge is limited to what the traditional approach emphasizes. • Students knowledge is not robust nor extendable.

47. What do know about alternative “reform” programs? • Emphasizing conceptual development and understanding can promote significant learning without sacrificing skill proficiency. • Solving problems can be used effectively as a context for learning new concepts and skills. • Students in alternative programs implemented with fidelity for reasonable lengths of time have learned more and learned more deeply than in traditional programs.

48. Research on the “NSF Curricula” • US Department of Education Exemplary designation, 1999 • AAAS Ratings of Algebra texts • New book of research • NAEP (MIG) • Individual research studies

49. High School NSF Curricula • Core-Plus Mathematics Project • Interactive Mathematics Program • MATH Connections • Mathematics Modeling Our World (ARISE) • SIMMS Integrated Mathematics • UCSMP Secondary School Curriculum

50. Middle Grades NSF Curricula • Connected Mathematics Project • Mathematics in Context • MathScape • MATH Thematics: The STEM Project