Iowa Content Network Project Mathematics : Iowa Content Network Project Mathematics Reviewing Research on
Instructional Strategies and Programs
Background & Overview : 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
Background and Context : Background and Context Other Research Reviews National Tests Internatl.
Tests Some Cognitive Science Program Ratings National Review Panels Iowa Math Network Project
Published Research Reviews : 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
National Tests : 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
International Tests : 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
Some Cognitive Science : Some Cognitive Science How We Learn: Ask the Cognitive Scientist. American Educator, Winter, 2002.
http://www.aft.org/american_educator/winter2002/CogSci.html
Program Ratings : 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
National Research Review Panels : 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
Background Details : 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
Slide11 : 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
1. Cognitive Science : 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.
Finding 1 : Finding 1 “The mind much prefers that new ideas be framed in concrete rather than abstract terms.”
Finding 2 : Finding 2 Rote Knowledge, Inflexible knowledge, and Deep Structure
Slide15 : Rote:
Q: What is the equator?
A: A managerie lion running around the Earth through Africa.
Slide16 : “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. ”
Slide17 : 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.)
Slide18 : 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
Finding 3 : 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
2. International and National Tests : 2. International and National Tests TIMSS
NAEP
SAT
TIMSS - 12th grade : 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)
TIMSS 8th Grade Video Study : 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
Slide23 : 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
Slide24 : 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
Slide25 : 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
Slide26 : 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.
Slide27 : 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)
Slide28 : Moral so far:
US can learn from other countries that are more successful in mathematics education
TIMSS and Singapore : 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.
Slide30 : • 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.
Slide31 : • 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."
Slide32 : 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
TIMSS 1999: Michigan Invitational Group : 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.
Slide34 : 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.
Slide35 : Moral:
Use NCTM-Standards Based Approach, implemented well, for high achievement with diverse students.
“The Nation’s Report Card” National Assessment of Educational Progress (NAEP) Trends in Computation : “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.
Slide37 : 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.
Slide38 : 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
SAT Scores : 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)
3. Research on the NCTM Standards-Based Approach : 3. Research on the NCTM Standards-Based Approach Research on NCTM’s Principles and Standards for School Mathematics
Research on the “NSF Curricula”
Research on NCTM’s Principles and Standards : 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
Does Research Support the NCTM Standards? : 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.”
What Research Cannot Do : 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.
What Research Can Do : 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
What Do We Know? : What Do We Know? Students learn what they have the opportunity to learn.
What do we know about traditional programs? : 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.
What do know about alternative “reform” programs? : 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.
Research on the “NSF Curricula” : 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
High School NSF Curricula : 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
Middle Grades NSF Curricula : Middle Grades NSF Curricula Connected Mathematics Project
Mathematics in Context
MathScape
MATH Thematics: The STEM Project
Elementary Grades NSF Curricula : Elementary Grades NSF Curricula Math Trailblazers
Everyday Mathematics
Investigations
Number Power
US DE Exemplary Programs ‘99 : US DE Exemplary Programs ‘99 Cognitive Tutor Algebra
College Preparatory Mathematics
Connected Mathematics Project
Core-Plus Mathematics Project
Interactive Mathematics Program
American Association for the Advancement of Science (AAAS) Algebra Text Ratings : American Association for the Advancement of Science (AAAS) Algebra Text Ratings • Reviewed traditional and reform texts
• Two categories: With Potential, Little Potential
Algebra Programs With Potential : 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
Book of Research on the NSF Curricula : 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
Summary : 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
4. Existing Reviews and Summaries of Research : 4. Existing Reviews and Summaries of Research Improving Achievement in Mathematics
Adding It Up
NCTM Research Companion (above)
Adding It Up: Helping Children Learn Mathematics : Adding It Up: Helping Children Learn Mathematics National Research Council
Jeremy Kilpatrick, Jane Swafford, Bradford Findell, editors
2001
Purpose : Purpose Focus on number and operations
Grades preK-8
Synthesize research
Provide research-based recommendations
Give advice and guidance
Main Recommendation : Main Recommendation All students can and should be mathematically proficient.
Mathematical Proficiency : Mathematical Proficiency Conceptual Understanding – comprehension of mathematical concepts, operations and relations
Procedural fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
Slide62 : 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 one’s own efficacy
Some Findings Related to Need for Improvement : 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).
Slide64 : 8th graders experience much difficulty with problems that ask them to “justify and explain their solutions” (p. 139).
Some Key Recommendations : 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.
More Recommendations : 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.
Slide67 : 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
Improving Achievement in Mathematics : 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
Research-Based Teaching Strategies and Methods : 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
Slide70 : Small-group learning
Whole-class discussion
Number sense
Concrete materials
Students’ use of calculators
Note: Implementation is essential.
5. In-Progress Research Review Projects : 5. In-Progress Research Review Projects What Works Clearinghouse (all)
National Research Council (NSF + others)
Iowa Math Network Project (all, based on past work)
What Works Clearinghouse : 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
Mathematical Sciences Education Board (MSEB) Panel : 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
Iowa Math Network Project Overview : 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
Process : 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)
Initial Screening Criteria : Initial Screening Criteria Peer reviewed
Student achievement
Quantitative
Instructional strategy or program
Reviewed So Far : 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
Key Themes So Far : Key Themes So Far Focus on meaning and understanding
Multiple representations
Problem-centered
NCTM-Standards based approach
Background and Context : Background and Context Other Research Reviews National Tests Internatl.
Tests Some Cognitive Science Program Ratings National Review Panels Iowa Math Network Project