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?id12341
  
• Improving Student Achievement in Mathematics
  (International Academy of Education)
• http//www.ibe.unesco.org/International/Publicatio
  ns/EducationalPractices/prachome.htm
• Standards-Based School Mathematics Curricula
• https//www.erlbaum.com/shop/tek9.asp?pgproducts
  specific0-8058-4337-X

5
National Tests

• National Assessment of Educational Progress
  (NAEP)
• http//nces.ed.gov/pubsearch/pubsinfo.asp?pubid20
  00469
• http//nces.ed.gov/nationsreportcard/mathematics/t
  rendsnational.asp
• SAT
• http//www.collegeboard.com/press/article/0,3183,2
  6858,00.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?pubid20
  03013
• 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/Co
  gSci.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/e
  xemplary/promising/document.shtm?inputCDS-000496-
  496_toc,00.shtm

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National Research Review Panels

• What Works Clearinghouse
• http//w-w-c.org/
• Mathematical Sciences Education Board (MSEB)
• http//www4.nas.edu/cp.nsf/57b01c7b1b6493c48525655
  5005853cf/5cf09421beb746d185256b7c00568d05?OpenDoc
  ument

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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

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• 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

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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.

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Finding 1

• The mind much prefers that new ideas be framed
  in concrete rather than abstract terms.

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Finding 2

• Rote Knowledge, Inflexible knowledge, and Deep
  Structure

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

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• 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.

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• 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.)

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• 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

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Finding 3

• Develop deep structure knowledge
• Solve more problems
• Multiple contexts
• Focus on meaning
• Dont despair of inflexible knowledge, and
  dont confuse it with rote knowledge

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2. International and National Tests

• TIMSS
• NAEP
• SAT

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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

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• 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

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• 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

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• 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.

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• 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)

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

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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.

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• 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 dont try to
  emulate their curricula

33
TIMSS 1999Michigan 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.

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The Nations Report CardNational 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

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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)

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3. Research on the NCTM Standards-Based Approach

• Research on NCTMs Principles and Standards for
  School Mathematics
• Research on the NSF Curricula

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Research on NCTMs 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.

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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.

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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.

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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

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Middle Grades NSF Curricula

• Connected Mathematics Project
• Mathematics in Context
• MathScape
• MATH Thematics The STEM Project

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Elementary Grades NSF Curricula

• Math Trailblazers
• Everyday Mathematics
• Investigations
• Number Power

52
US DE Exemplary Programs 99

• Cognitive Tutor Algebra
• College Preparatory Mathematics
• Connected Mathematics Project
• Core-Plus Mathematics Project
• Interactive Mathematics Program

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American Association for the Advancement of
Science (AAAS) Algebra Text Ratings

• Reviewed traditional and reform texts
• Two categories With Potential, Little Potential

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Algebra Programs With Potential

• Concepts in Algebra
• Core-Plus Mathematics
• Focus on Algebra
• Interactive Mathematics Program
• MATH Connections
• Mathematics Modeling Our World (ARISE)
• UCSMP Algebra

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Book of Research on the NSF Curricula

• Standards-Based School Mathematics Curricula
  What Are They? What Do Students Learn?
• Editors Sharon Senk, Denisse Thompson
• Erlbaum, 2003
• Book editors, grade band reviewers, K-12 reviewer

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Summary

• There is considerable evidence that the
  promises of reform mathematics are real and the
  fears of the anti-reformers unjustified.
  Swafford, p 458
• The studies in this book provide much needed
  evidence that the new programs work. Kilpatrick,
  p 472

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4. Existing Reviews and Summaries of Research

• Improving Achievement in Mathematics
• Adding It Up
• NCTM Research Companion (above)

58
Adding It Up Helping Children Learn Mathematics

• National Research Council
• Jeremy Kilpatrick, Jane Swafford, Bradford
  Findell, editors
• 2001

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Purpose

• Focus on number and operations
• Grades preK-8
• Synthesize research
• Provide research-based recommendations
• Give advice and guidance

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Main Recommendation

• All students can and should be mathematically
  proficient.

61
Mathematical Proficiency

• Conceptual Understanding comprehension of
  mathematical concepts, operations and relations
• Procedural fluency skill in carrying out
  procedures flexibly, accurately, efficiently, and
  appropriately

62

• Strategic competence ability to formulate,
  represent, and solve mathematical problems
• Adaptive reasoning - capacity for logical
  thought, reflection, explanation, and
  justification
• Productive disposition - habitual inclination to
  see mathematics as sensible, useful, and
  worthwhile, coupled with a belief in diligence
  and ones own efficacy

63
Some Findings Related to Need for Improvement

• On the 23 problem-solving tasks given as part of
  the 1996 NAEP in which students had to construct
  an extended response, the incidence of
  satisfactory or better response was less than 10
  on about half of the tasks (p. 138).
• Performance on word problems declines
  dramatically when additional features are
  included, such as more than one step or
  extraneous information (p.139).

64

• 8th graders experience much difficulty with
  problems that ask them to justify and explain
  their solutions (p. 139).

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Some Key Recommendations

• Integrated and balanced development of all five
  strands of mathematical proficiency
• On non-routine problems, students need to slow
  down and ask themselves guiding questions, and
  not prematurely apply operations to numbers in
  the problems.
• Students need to develop conceptual understanding
  of operations, as well as learn standard
  algorithms.

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More Recommendations

• Integrated and balanced development of all five
  strands of mathematical proficiency
• Instruction should not be based on extreme
  positions that students learn, on one hand,
  solely by internalizing what a teacher or book
  says or, on the other hand, solely by inventing
  mathematics on their own.

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• Efforts to improve students mathematics learning
  should be informed by scientific evidence
• Teachers professional development should be high
  quality, sustained, and systematically designed
  and deployed
• Assessment should enable, not just gauge
• Time and resources needed

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Improving Achievement in Mathematics

• International Academy of Education, 2000
• Chapter in the Handbook of Research on Improving
  Student Achievement
• Douglas Grouws and Kristin Cebulla
• Review research on effective teaching in
  mathematics
• Research-based teaching practices

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Research-Based Teaching Strategies and Methods

• Opportunity to learn
• Focus on meaning
• Learning new concepts and skills while solving
  problems
• Opportunities for both invention and practice
• Openness to student solution methods and student
  interaction

70

• Small-group learning
• Whole-class discussion
• Number sense
• Concrete materials
• Students use of calculators
• Note Implementation is essential.

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5. In-Progress Research Review Projects

• What Works Clearinghouse (all)
• National Research Council (NSF others)
• Iowa Math Network Project (all, based on past
  work)

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What Works Clearinghouse

• Established by the US Department of Education
• Review research through contracts to American
  Institutes of Research and the Campbell
  Collaboration
• Identify Scientifically Research Based programs
  and strategies in reading, math, etc.
• For math, 1st is MS, then Elem, then HS
• Alan Schoenfeld is the head of the math section

73
Mathematical Sciences Education Board (MSEB) Panel

• A Review of the Evaluation Data on the
  Effectiveness of NSF-Supported and Commercially
  Generated Mathematics Curriculum Materials
• 13 NSF curricula
• 6 others
• 1st draft of report done, out for review, final
  report in several months.
• Jere Confrey, Chair

74
Iowa Math Network Project Overview

• Established by the Iowa Department of Education
• Review research studies on instructional
  strategies and programs for improving student
  achievement in mathematics
• Ongoing, not comprehensive, rate research design
  not instructional strategies

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Process

• Group of 9 reviewers
• Teams of two, 4 grade bands, Chair
• Initial screening (criteria below)
• Review using standard form
• Rate quality of research design based on standard
  criteria (e.g., comparative groups)

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Initial Screening Criteria

• Peer reviewed
• Student achievement
• Quantitative
• Instructional strategy or program

77
Reviewed So Far

• Instructional strategies (e.g., problem-centered,
  conceptually oriented)
• Programs (e.g., NSF curricula, CGI, RNP)
• About 35 studies in 1st round -- done
• Coded by content strand (perhaps deeper later)
• 2nd round underway

78
Key Themes So Far

• Focus on meaning and understanding
• Multiple representations
• Problem-centered
• NCTM-Standards based approach

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