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Monday, November 23, 2009

Research: Traditional vs. Reform

Statement from Laurie Rogers:

In the Fall of 2009, I applied to be and was accepted as a parent member of Spokane's latest high school math curriculum adoption committee. All committee members were given a single book as a resource for decision-making. Concerned about the heavily reform/constructivist/poorly argued nature of that single book, I compiled a list of research suggested to me by generous math/science/research/education professionals across the country.

Below is a list of some of those suggestions, including a small portion of the research, data and commentary I have compiled over 3 years of research into K-12 public education. I offered this complete list, and much of the actual research, on a CD to each committee member.

If you have other research or information to offer to this curriculum adoption committee, please write to me at


Data, Research Papers:

“A Brief History of American K-12 Mathematics Education in the 20th Century” (2003)
Dr. David Klein, California State Northridge
“(NCTM math programs of the 1990s) typically failed to develop fundamental arithmetic and algebra skills. Elementary school programs encouraged students to invent their own arithmetic algorithms, while discouraging the use of the superior standard algorithms for addition, subtraction, multiplication, and division. Calculator use was encouraged to excess, and in some cases calculators were even incorporated into kindergarten lesson plans. Student discovery group work was the preferred mode of learning, sometimes exclusively, and the guidelines for discovery projects were at best inefficient and often aimless. Topics from statistics and data analysis were redundant from one grade level to the next, and were overemphasized. Arithmetic and algebra were radically de-emphasized. Mathematical definitions and proofs for the higher grades were generally deficient, missing entirely, or even incorrect.”

Achievement Effects of Four Early Elementary School Math Curricula Findings from First Graders in 39 Schools (2009)
Roberto Agodini, et al.
“Eight of the fifteen subgroup analyses found statistically significant differences in student math achievement between curricula. The significant curriculum differences ranged from 0.28 to 0.71 standard deviations, and all of the significant differences favored Math Expressions or Saxon over Investigations or SFAW. There were no subgroups for which Investigations or SFAW showed a statistically significant advantage.”

A Close Examination of Jo Boaler’s Railside Report (undated)
Wayne Bishop, Cal. State; Paul Clopton, VAMC; R. James Milgram, Stanford
“This study makes extremely strong claims for discovery style instruction in mathematics, and consequently has the potential to affect instruction and curriculum throughout the country.
… Prof. Boaler has refused to divulge the identities of the schools to qualified researchers. Consequently, it would normally be impossible to independently check her work. However, in this case, the names of the schools were determined and a close examination of the actual outcomes in these schools shows that Prof. Boaler’s claims are grossly exaggerated and do not translate into success for her treatment students.”

A Review of Four High-School Mathematics Programs (Holt; Discovering Algebra; Core-Plus; Glencoe McGraw-Hill) March 2009
Guershon Harel, University of California, San Diego
“As can be seen in the chart below, none of the programs was found mathematically sound on the first two criteria. The (checkmark) in Holt on these criteria in geometry is better characterized as the least mathematically unsound.”

A Study of Core-Plus Students Attending Michigan State University (2006)
Richard O. Hill and Thomas H. Parker
“As the implementation progressed, from 1996 to 1999, Core-Plus students placed into, and enrolled in, increasingly lower level courses; this downward trend is statistically robust .... The percentages of students who (eventually) passed a technical calculus course show a statistically significant ... decline averaging 27 percent a year; this trend is accompanied by an obvious and statistically significant increase in percentages of students who placed into low-level and remedial algebra courses. The grades the Core-Plus students earned in their university mathematics courses are also below average, except for a small group of top students.”

“Brain-Based” Learning: More Fiction than Fact (2006)
Daniel T. Willingham, professor of cognitive psychology, University of Virginia
“… I hope educators will approach claims that instructional techniques and strategies are ‘proven’ because they are based on neuroscience with a healthy dose of skepticism. Cognitive and educational studies are the best sources for educators looking to improve their students’ cognitive and educational outcomes.”

Critical Thinking: Why is it So Hard to Teach? (2007)
Daniel T. Willingham, professor of cognitive psychology, University of Virginia
“As the main article explains, the ability to think critically depends on having adequate content knowledge; you can’t think critically about topics you know little about or solve problems that you don’t know well enough to recognize and execute the type of solutions they call for.”

Direct Instruction Mathematics: A Longitudinal Evaluation of Low-Income Elementary School Students (1984)
Russell Gersten, University of Oregon; Doug Carnine, University of Oregon
“…low-income primary-grade students who received the full 3- or 4-year Direct Instruction mathematics program tended to perform significantly better in all mathematic subtests of the Metropolitan Achievement Test than students who received other approaches, whether experimental or traditional. Direct Instruction Follow Through students achieved at a level much higher than is typical for students with similar demographic characteristics…”
The Elementary School Journal, Vol. 84, No. 4. (Mar., 1984), pp. 395-407.

Direct Instruction Mathematics Programs: An Overview and Research Summary (2004)
Angela M. Przychodzin, et al., Eastern Washington University
“In all, 12 studies published since 1990 were found using DI math programs. The majority (11 out of 12) of these found DI math programs to be effective in improving math skills in a variety of settings with a variety of students.”
Journal of Direct Instruction, v4 n1 p53-84 Win 2004

District 81’s Main and Supplementary Mathematics Materials (April 2009)
These pages represent a list (as of April 2009) of various math curricula used in Spokane Public Schools, along with approved supplementary math materials. This document was 11 pages long.

Don’t Forget Curriculum (October 2009)
Grover “Russ” Whitehurst, Governance Studies, Brown Center Letters on Education, Brookings
“Anyone interested in, ‘doing what works for the kids,’ should pay attention to this table. …Curriculum effects are large compared to most popular policy levers.”

Educating the Evolved Mind: Conceptual Foundations for an Evolutionary Educational Psychology (2007) (Draft)
Geary, D. C. (2007). In J. S. Carlson & J. R. Levin (Eds.), Educating the evolved mind (pp. 1-99, Vol. 2, Psychological perspectives on contemporary educational issues).
“(Schools) are thus often used for purposes that have more to do with the best interests of those attempting to influence this socialization than the best educational interests of children. In fact, the history of education in the United States might be viewed as being more strongly driven by ideology and untested assumptions about children’s learning than by concerns about the efficacy of schooling vis-à-vis the long-term social and employment interests of children …. These ideological debates and the attendant opportunity costs to children’s educational outcomes and later employment opportunities will continue well into the twenty-first century, if current attempts to move the field of education to a more solid scientific footing are not successful ….” (Portions provided to committee, with permission.)

High School Mathematics Curriculum Study, March 2009
Prepared by Linda Plattner, Strategic Teaching
“…none of the reviewed programs were completely satisfactory. Holt was the strongest of the four, meaning the mathematics is not compromised in any of the three topics examined. Discovering was the weakest with all three areas considered inadequate. … The good news is that there are other programs that match well to Washington’s standards.”

How Educational Theories Can Use Neuroscientific Data (2007)
Daniel T. Willingham, Department of Psychology, University of Virginia; and John W. Lloyd, Curry School of Education, University of Virginia
“…most (scholarly treatments of neuroscience in education … argue that neuroscience has been and will continue to be helpful to education …— but they argue that data from neuroscience must be funneled through a behavioral level of analysis … or that neuroscience should be part of a broader approach to research in education, not the sole savior…”

Independent Study of Washington State - K-8 Curriculum Review, November 2008
Prepared by Linda Plattner, Strategic Teaching
“ST reviewed Bridges in Mathematics, Investigations, Math Connects, and Math Expressions for elementary school. Holt Mathematics, Math Connects, Math Thematics, and Prentice Hall Mathematics were reviewed at the middle school level. These are OSPI’s highest-scoring programs. Other programs, such as the Connected Math Project that is widely used in Washington schools, were not reviewed because they did not meet OSPI’s minimum threshold for content.”

K-12 Calculator Usage and College Grades (2004)
W. Stephen Wilson, and Daniel Q. Naiman, , Johns Hopkins University
Educational Studies in Mathematics, 56:119-122, 2004.
“We find that students in the big mathematics service courses at the Johns Hopkins University who were encouraged to use calculators in K-12 have somewhat lower grades than those who weren’t.”

Outcomes Analysis for Core Plus Students At Andover High School: One Year Later
R. James Milgram, Department of Mathematics, Stanford University
“…Andover High School scores are considerably above the state and national means in keeping with Andover’s position as one of the top high schools in the country. However, as was indicated above, both English and reading got stronger against these measures by about 6 percentile points. By comparison, in the final two years of the data, when the effects of the Core Plus mathematics program kicked in, the mathematics scores dropped against these measures by six percentile points.”

Performance Indicators in Math: Implications for Brief Experimental Analysis of Academic Performance (February 2009)
Amanda M. VanDerHeyden, Education Research and Consulting, Inc, Fairhope, AL;
Matthew K. Burns, University of Minnesota, Minneapolis, MN
J Behav Educ (2009) 18:71–91
“Specifically, children who did not master early skills, failed to reach the mastery criterion following intervention for future related skills at much higher rates and earned lower scores on all remaining intervention skills relative to peers who attained the mastery criterion early in the sequence of tasks. … The correlation between fluent computation and faster subsequent learning of related skills is indeed promising, but future studies must examine the degree to which fluent sub-skill computation causes faster learning on more complex related problems. Contemporary research in mathematics seems to indicate a need for explicit teaching of procedural rules to solve both computation and applied problems as well as specific training to apply or generalize that knowledge over time and across varying stimuli (Fuchs and Fuchs 2001; Fuchs et al. 2003; Kameenui and Griffin 1989).

Practice Makes Perfect--But Only If You Practice Beyond the Point of Perfection (2004)
Daniel T. Willingham, cognitive psychology and neuroscience at the University of Virginia
“That students would benefit from practice might be deemed unsurprising. … The unexpected finding from cognitive science is that practice does not make perfect. Practice until you are perfect and you will be perfect only briefly. What’s necessary is sustained practice. By sustained practice I mean regular, ongoing review or use of the target material (e.g., regularly using new calculating skills to solve increasingly more complex math problems, reflecting on recently-learned historical material as one studies a subsequent history unit, taking regular quizzes or tests that draw on material learned earlier in the year). This kind of practice past the point of mastery is necessary to meet any of these three important goals of instruction: acquiring facts and knowledge, learning skills, or becoming an expert.”

Reflections of Evolution and Culture in Children’s Cognition: Implications for Mathematical Development and Instruction (1995)
David C. Geary, University of Missouri at Columbia
American Psychologist, Vol. 50, No. 1, 24-37, 1995
“The basic assumptions that guide constructivist-based instruction appear to be well suited for the acquisition of biologically primary mathematical abilities, such as number and counting. However, constructivist philosophers and researchers fail to distinguish between biologically primary and biologically secondary mathematical abilities and, as a result, treat all of mathematics as if it were a biologically primary domain. That is, given an appropriate social context and materials, children will be motivated and able to construct mathematical knowledge for themselves in all areas. The adoption of these assumptions and the associated instructional techniques appear to reflect wider cultural values and only weakly follow empirical and theoretical work in contemporary developmental and cognitive psychology, much less a consideration of evolutionary issues.”

Reform vs. Traditional Math Curricula: Preliminary report on a survey of the graduating classes of 1997 of Andover High School and Lahser High School, Bloomfield Hills, Michigan, concerning their high school math programs and how well these programs prepared them for college math (1998), and update (1999)
Gregory F. Bachelis, Ph.D., Professor of Mathematics, Wayne State University, Detroit
“The other matter I would like to comment on is the performance of Core-Plus graduates on the placement tests at UMAA, MSU, as well as other colleges. A lot of them complained that they did not do well because of their lack of knowledge of basic algebra, and some said they did not do well even in the courses they were placed into. Now it is all well and good to say that people are just having a bad day when they do poorly on a placement test, but as someone who has taught remedial algebra for more years than I care to remember, let me assure you that there is a big difference between learning basic algebra and then forgetting most or all of it, and never having learned it at all. Core-Plus appears to have created a new category of students who land in remedial math courses - courses that were not designed with such students in mind.”

“Report Cards” for middle and high schools in Spokane Public Schools (2009) /

Washington State High School Math Text Review (March 2009)
W. Stephen Wilson, Johns Hopkins University
“Geometry is important, so the unacceptable nature of geometry in Discovering and Core Plus makes these programs unacceptable. The flaws in these geometry programs are such that they could not easily be compensated for by a teacher, even with the help of supplementation.”

Washington State Mathematics Standards Review and Recommendations (2007)
Linda Plattner, Strategic Teaching
“Simply put, Washington is not focused enough on the important fundamental content topics in mathematics. This is shown in the early grades in which Washington standards do not ensure that students learn the critical algorithms of arithmetic and continues throughout the standards until it ends in secondary school with minimal expectations that are missing most of the algebra, geometry, and trigonometry found in other places.”

What Is Developmentally Appropriate Practice? (Summer 2008)
Daniel T. Willingham, cognitive psychology and neuroscience at the University of Virginia
“Unfortunately, Piaget’s theory is not right. He is credited with brilliant insights and many of his observations hold true—for example, kindergartners do have some egocentrism and 9-year-olds do have some trouble with highly abstract concepts. Nonetheless, recent research indicates that development does not proceed in stages after all.”

What Works Clearinghouse – Investigations in Number, Data, and Space (2009)
“No studies of Investigations in Number, Data, and Space® that fall within the scope of the Elementary School Math review protocol meet What Works Clearinghouse (WWC) evidence standards. The lack of studies meeting WWC evidence standards means that, at this time, the WWC is unable to draw any conclusions based on research about the effectiveness or ineffectiveness of Investigations in Number, Data, and Space®."

What Works Clearinghouse – Scott Foresman-Addison Wesley Elementary Mathematics (2006)
“Scott Foresman–Addison Wesley Elementary Mathematics was found to have no discernible effects on students’ math achievement. Improvement index Average: –2 percentile points; Range: –7 to +3 percentile points”

What Works Clearinghouse – Connected Mathematics Project (2007)
“The CMP curriculum was found to have mixed effects on math achievement. Rating of effectiveness. Improvement Average: –2 percentile points; Range: –12 to +11 percentile points”

Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching (2006)Paul A. Kirschner, Educational Technology Expertise Center, Open University of the Netherlands, Research Centre Learning in Interaction, Utrecht University, The Netherlands; John Sweller, School of Education, University of New South Wales; Richard E. Clark, Rossier School of Education, University of Southern California
Although unguided or minimally guided instructional approaches are very popular and intuitively appealing, the point is made that these approaches ignore both the structures that constitute human cognitive architecture and evidence from empirical studies over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process.”
Educational Psychologist, 41(2), 75–86, 2006


Angry Parents: Failing Schools: What’s Wrong with the Public Schools and What You Can Do About It (2000)
Elaine K. McEwan

Betrayed: How the Education Establishment Has Betrayed America and What You Can Do about it" (2011)
Laurie H. Rogers

Conspiracy of Ignorance: The Failure of American Public Schools (1999)
Martin L. Gross

Crazy Like a Fox: One Principal’s Triumph in the Inner City (2009)Ben Chavis, former principal of American Indian Charter School, California

The Mad, Mad World of Textbook Adoption (2004)
The Thomas B. Fordham Institute

Monographs: Implementation and Child Effects of Teaching Practices in Follow Through Classrooms (1975)
Jane Stallings, Stanford Research Institute

Out-come Based Education: Understanding the Truth About Education Reform (1994)
Ron Sunseri

The Schools We Need and Why We Don’t Have Them (1999)
E.D. Hirsch, Jr.

Visible Learning: A synthesis of over 800 meta-analyses relating to achievement (2008)
John Hattie

What’s At Stake in the K-12 Standards Wars
Edited by Sandra Stotsky

Why Don't Students Like School?: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom (2009)
Daniel T. Willingham, associate professor, University of Virginia


National Mathematics Advisory Panel Final Report (2008)
“During most of the 20th century, the United States possessed peerless mathematical prowess—not just as measured by the depth and number of the mathematical specialists who practiced here but also by the scale and quality of its engineering, science, and financial leadership, and even by the extent of mathematical education in its broad population…
“This Panel, diverse in experience, expertise, and philosophy, agrees broadly that the (current) delivery system in mathematics education—the system that translates mathematical knowledge into value and ability for the next generation—is broken and must be fixed.”

Chapter 2: Report of the Subcommittee on Standards of Evidence
Valerie F. Reyna, Chair; Camilla Persson Benbow; A. Wade Boykin; Grover J. “Russ” Whitehurst, Ex Officio; Tyrrell Flawn
“The Panel’s systematic reviews have yielded hundreds of studies on important topics, but only a small proportion of those studies have met methodological standards. … Many studies rely on self-report, introspection about what has been learned or about learning processes, and open-ended interviewing techniques, despite well-known limitations of such methods ….”

Chapter 3: Report of the Task Group on Conceptual Knowledge and Skills
Francis “Skip” Fennell, Chair; Larry R. Faulkner; Liping Ma; Wilfried Schmid; Sandra Stotsky; Hung-Hsi Wu; Tyrrell Flawn
“Proficiency with whole numbers, fractions, and particular aspects of geometry and measurement are the Critical Foundation of Algebra. Emphasis on these essential concepts and skills must be provided at the elementary- and middle-grade levels. The coherence and sequential nature of mathematics dictate the foundational skills that are necessary for the learning of algebra. By the nature of algebra, the most important foundational skill is proficiency with fractions (including decimals, percent, and negative fractions). The teaching of fractions must be acknowledged as critically important and improved before an increase in student achievement in Algebra can be expected."

Chapter 4: Report of the Task Group on Learning Processes
David C. Geary, Chair; A. Wade Boykin; Susan Embretson; Valerie Reyna; Robert Siegler; Daniel B. Berch, Ex Officio; Jennifer Graban
“Anxiety is an emotional reaction that is related to low math achievement, failure to enroll in advanced mathematics courses, and poor scores on standardized tests of math achievement. Math anxiety creates a focus of limited working memory on managing anxiety reaction rather than on solving the math problem, but it can be reduced by therapeutic interventions. … The mastery of whole number arithmetic is a critical step in children’s mathematical education. The road to mastery involves learning arithmetic facts, algorithms, and concepts. The quick and efficient solving of simple arithmetic problems is achieved when children retrieve answers from long-term memory or retrieve related information that allows them to quickly reconstruct the answer. Retention of these facts requires repeated practice.”

Chapter 6: Report of the Task Group on Instructional Practices
Russell Gersten, Co-Chair; Joan Ferrini-Mundy, Ex Officio, Co-Chair; Camilla Benbow; Douglas H. Clements; Tom Loveless; Vern Williams; Irma Arispe, Ex Officio; Marian Banfield
“The studies presented a mixed and inconclusive picture of the relative impact of these two forms of instruction. High-quality research does not support the contention that instruction should be either entirely “child centered” or “teacher directed.” Research indicates that some forms of particular instructional practices can have a positive impact under specified conditions. All-encompassing recommendations that instruction should be entirely “child centered” or “teacher directed” are not supported by research.”

Chapter 7: Report of the Subcommittee on Instructional Materials
Robert S. Siegler, Chair; Bert Fristedt; Vern Williams; Irma Arispe; Daniel B. Berch; Marian Banfield
“When mathematicians have reviewed already published middle and high school textbooks, however, they have identified a nontrivial number of errors, and a large number of ambiguous and confusing statements and problems. Many of these errors and ambiguities arise on word problems that are intended to elicit use of the mathematical concepts and procedures in real-world contexts. The Subcommittee recommends that publishers obtain reviews from mathematicians prior to publication, so that these errors and ambiguities can be identified and corrected. …Having mathematicians also read textbooks in the formative stages may increase the coherence of the presentation of mathematics between earlier and later grades.”

Chapter 9: Subcommittee on the National Survey of Algebra I Teachers
Tom Loveless, Chair; Francis “Skip” Fennell; Vern Williams; Deborah Loewenberg Ball; Marian Banfield, U.S. Department of Education Staff
“The most frequent type of suggestion among the 578 respondents was a greater focus in primary education placed on mastery of basic mathematical concepts and skills… A substantial number of teachers considered mixed-ability groupings to be a “moderate” (28%) or “serious” (23%) problem… The responses indicate that about 28% of the algebra teachers felt family participation is a serious problem and another 32% believed lack of family participation is a moderate problem…”


The Condition of College Readiness 2009 – ACT
“About 67% of all ACT-tested high school graduates met the English College Readiness Benchmark in 2009. Just under 1 in 4 (23%) met all four College Readiness Benchmarks.
In 2009, 53% of graduates met the Reading Benchmark, while 42% met the Mathematics
Benchmark. Over 1 in 4 (28%) met the College Readiness Benchmark in Science.”

Comparative Indicators of Education in the United States and other G-8 Countries: 2009
“For example, the advanced benchmark (the highest TIMSS benchmark) was reached by 26 percent of Japan’s eighth-graders in mathematics … In the United States, 6 percent of eighth-graders reached the advanced benchmark …
“In Japan, 61 percent of eighth-graders reached the high benchmark in mathematics… In the United States, 31 percent of eighth-graders reached the high benchmark...”

Mathematics 2009 - National Assessment of Educational Progress at Grades 4 and 8National Center for Education Statistics (2009). The Nation’s Report Card: Mathematics 2009 (NCES 2010–451). Institute of Education Sciences, U.S. Department of Education, Washington, D.C.
“Gains in students’ average mathematics scores seen in earlier years did not continue from 2007 to 2009 at grade 4 but did continue at grade 8 … While still higher than the scores in the six assessment years from 1990 to 2005, the overall average score for fourth-graders in 2009 was unchanged from the score in 2007. The upward trend seen in earlier assessments for eighth-graders continued with a 2-point increase from 2007 to 2009.”

Executive summary of 2009 NAEP Mathematics Results (2009)
Nation's Report Card: America's High School Graduates: Results From The 2005 NAEP High School Transcript Study
“How can increasing numbers of students be taking more credits and more rigorous curricula without increased performance on the Nation’s Report Card?”


Project Follow Through: In-depth and Beyond (1996)
Gary Adams, Educational Achievement Systems, Seattle
Only the Direct Instruction model had positive scores on all three types of outcomes (Basic Skills, Cognitive, and Affective). Overall, the Direct Instruction model was highest on all three types of measures. … The Affective Models had the worst affective ranks (6.7 compared to 2.7 for the Basic Skills models).

Sponsor Findings From Project Follow Through
Wesley C. Becker and Siegfried Engelmann, University of Oregon
“The closest rival to the Direct Instruction Model in overall effects was another behaviorally-based program, the University of Kansas Behavior Analysis Model. Child-centered, cognitively focused, and open classroom approaches tended to perform poorly on all measures of academic progress.”

Overview: The Story Behind Project Follow Through
Bonnie Grossen, Editor
“The only model that brought children close to the 50th percentile in all subject areas was the Direct Instruction model. …The most popular models were not only unable to demonstrate many positive effects; most of them produced a large number of negative effects. …
“Yet 10 short years later, the models that achieved the worst results, even negative results, are the ones that are, in fact, becoming legislated policy in many states, under new names. … Every educator in the country should know that in the history of education, no educational model has ever been documented to achieve such positive results with such consistency across so many variable sites as Direct Instruction. It never happened before FT, and it hasn't happened since. … Not enough people know this.”

A Constructive Look at Follow Through Results (1981)
Carl Bereiter, Ontario Institute for Studies in Education, and Midian Kurland, University of Illinois at Urbana-Champaign
“Thus we have, if we wish it, a battle of the philosophies, with the child-centered philosophy coming out the loser on measured achievement, as it has in a number of other experiments … Consistently it is the more direct methods, involving clear specifications of objectives, clear explanations, clear corrections of wrong responses, and a great deal of ‘time on task,’ that are associated with superior achievement test performance. The effects tend to be strongest with disadvantaged children.”

Follow Through: Why Didn't We?
Cathy L. Watkins, California State University, Stanislaus
“The Joint Dissemination Review Panel and the National Diffusion Network were created to validate and disseminate effective educational programs. In 1977, Follow Through sponsors submitted programs to the JDRP. ‘Effectiveness’ was, however, broadly interpreted. For example, according the JDRP, the positive impact of a program need not be directly related to academic achievement. In addition, a program could be judged effective if it had a positive impact on individuals other than students. As a result, programs that had failed to improve academic achievement in Follow Through were rated as ‘exemplary and effective.’ And, once a program was validated, it was packaged and disseminated to schools through the National Diffusion Network…. The JDRP apparently felt that to be "fair" it had to represent the multiplicity of methods in education. Not only did this practice make it virtually impossible for school districts to distinguish between effective and ineffective programs, it defeated the very purpose for which the JDRP and NDN were established.”

Honest follow-through needed on this project (1998)
By Marian Kester Coombs, special to The Washington Times
“After the Harvard article appeared, all the test models were recommended equally for dissemination to the school districts, and by 1982, the least-effective models were receiving higher levels of funding than the most effective ones, in an apparent effort to equalize results. …
“The president of the National Council of Teachers of Mathematics, Gail Burrill, was asked about Project Follow Through in a recent interview and responded, "I have never heard of it" … Mr. Adams shakes his head. "The most puzzling thing is how the very models like whole language and discovery learning that the data showed to be ineffective and even harmful are still being pushed. Parents should be asking, 'Where is the proof these programs work?'”

Our Failure To Follow Through (1994)
Billy Tashman, New York, Newsday
“In fact, the federal oversight panel for Follow Through cut the Direct Instruction program even as it continued other models that were spectacular flops. Eschewing basic skills, the failed programs tried to teach kids how to learn on their own, or tried to raise students' self-esteem (both categories, by the way, in which Direct Instruction students excelled).”

Documents, Letters, Commentary

An Open Letter to United States Secretary of Education Richard Riley (1999)
Dr. David Klein, et al.
“It is not likely that the mainstream views of practicing mathematicians and scientists were shared by those who designed the criteria for selection of "exemplary" and "promising" mathematics curricula. … In an article entitled, "It's Time To Abandon Computational Algorithms," published February 9, 1994, in Education Week on the Web, (Steven Leinwand) wrote: ‘It's time to recognize that, for many students, real mathematical power, on the one hand, and facility with multidigit, pencil-and-paper computational algorithms, on the other, are mutually exclusive. In fact, it's time to acknowledge that continuing to teach these skills to our students is not only unnecessary, but counterproductive and downright dangerous.’
“… Even before the endorsements by the Department of Education were announced, mathematicians and scientists from leading universities had already expressed opposition to several of the programs listed above and had pointed out serious mathematical shortcomings in them.”

Email from Dr. David C. Geary, Curators’ Professor, Thomas Jefferson Professor, Department of Psychological Sciences, University of Missouri (2009)
“The National Mathematics Advisory Panel explicitly reviewed the brain imaging literature on math processing as related to instructional practices and concluded that any instructional claims based on brain sciences is premature.”

Email series from three members of Where’s the Math? Advocacy Group (2009)
“…the reason for so much failure in Algebra I is because many students simply lack most of the necessary skills in order to succeed. When you tell administrators this they say “quit giving me excuses.” It’s kind of like being asked to teach kids to play water polo when they don’t know how to swim. When your water polo team does lousy the administration asks you why these kids are so bad..…. You answer because they don’t know how to swim… Even worse, they won’t let you teach them how to swim…..In fact they are claiming that you can just teach them to swim while they are playing the game….. That is exactly what is happening in math education and the result is that many kids are figuratively “drowning” in this system."

How to Improve National Math Scores - New York Times – (2009)
Bruce Fuller, professor of education and public policy; Lance T. Izumi, Pacific Research Institute; Holly Tsakiris Horrigan, parent; Richard Bisk, math professor; Barry Garelick, U.S. Coalition for World Class Math
“To give students a firm foundation in math, we must start in the elementary grades by providing three things: a substantial improvement in elementary teachers’ knowledge of mathematics; a more focused curriculum that emphasize core concepts and skills; and more challenging textbooks that teach for mastery and not just exposure.”

Letter from Dr. Shannon Overbay, associate mathematics professor, Gonzaga University (not dated)
“At Gonzaga, I have continued to see students who have come from various reform programs struggle with basic skills. My students often complain that they never learned their times tables and say that they should not have been allowed to use calculators in grade school. They do see the damage that has been done. Many programs, such as Investigations (TERC) do not even cover topics such as long division and routine computations with fractions. By the time these students come to college, they are unable to go into technical majors and have to struggle to pass even elementary math classes designed for non-technical majors. By the time the students hit college, the problems and gaps cannot easily be fixed with one or two “refresher” courses. There are often gaps and holes in their mathematics background that would require years of remediation to fix. For most students, that is not a reasonable option. So, instead, they opt for non-technical majors. We are faced with a 20% decline nationally in the number of engineering majors in recent years. It is devastating.”

Letter from Martha McLaren, retired Seattle Public Schools teacher (2009)
“I began to doubt reform math because of what I had seen in my own classroom, and what I later saw throughout the school district. I worked with confused, demoralized students who were frantically grabbing calculators for the simplest computations. Roughly half of middle schoolers and high schoolers did not understand fractions, decimals, or percents, much less negative numbers or pre-algebra skills. I've spoken with numerous overworked and demoralized teachers who were at their wits end trying to help their students become competent in basic math. These teachers almost never spoke out against reform texts because school district administrators gave them no choice but to support reform math -- teachers' jobs were on the line.”

Short Response to Tunis’ Letter to the Editor on Technology in College (2005)
W. Stephen Wilson, Johns Hopkins University
“…I have not yet encountered a mathematics concept that required technology to either teach it or assess it. The concepts and skills we teach are so basic and fundamental that technology is not needed to either elucidate or enhance them….Consequently, all of Tunis’s questions about how to best insert technology into these introductory courses in college are really a non-issue.”

Teaching too-hard math concepts does students no favors (2009)
Joseph Ganem, physics professor, Loyola University, Maryland
We are in the midst of a paradox in math education. As more states strive to improve math curricula and raise standardized test scores, more students show up to college unprepared for college-level math. In Maryland, 49 percent of high school graduates take noncredit remedial math courses in college, before they can take math courses for credit. In many cases, incoming college students cannot do basic arithmetic, even after passing all high school math tests. Recently, it was reported that student math achievement actually grew faster in the years before the No Child Left Behind law.”,0,1068320.story

What Do College Students Know? By this professor’s calculations, math skills have plummeted (2008)
W. Stephen Wilson, Johns Hopkins University
“I am inclined to conclude that the 2006 JHU students are not as well prepared as the corresponding group was in 1989, despite there being significantly more competition to get into JHU today than ever before. This phenomenon is probably shared with many other universities. The year 1989 is, in mathematics education, indelibly tied to the publication by the National Council of Teachers of Mathematics of the report "Curriculum and Evaluation Standards for School Mathematics," which downplayed pencil-and-paper computations and strongly suggested that calculators play an important role in K-12 mathematics education. ...
“Since 1994, the College Board has allowed the use of calculators on the mathematics SAT. … I believe it is precisely this gained “advantage” that causes the SATM to fail universities in the admissions process. My findings spread like wildfire through the mathematics community. … The surprise was the general indifference that administrators at JHU had toward the study. This kind of drop in SAT scores would be a crisis, but the news that high-performing students were less prepared for college math than students 17 years earlier didn’t seem to bother anyone, at least not enough to contemplate taking action.”

What the Data Really Show: Direct Instruction Really Works! (2009)
Dr. Jeff Lindsay
“Direct Instruction is the dirty little secret of the educational establishment. This method, rich in structure and drilling and content, is the opposite of the favored methods of today's high-paid education gurus, and contradicts the popular theories that are taught to new teachers in our universities. Direct Instruction should be no secret at all, for it has been proven in the largest educational study ever (discussed below) and continues to bring remarkable success at low cost when it is implemented.”


din819go said...

Good luck!! The educators truly don't want parental input. You are probably just on the committee because someone said they needed a parent(s). This happened in Nashville when the school district was hell bent on implementing standard school attire. The parents on the committee did the research and had the proof that it would not make any academic or discipline difference in the performance of the students. The educators ignored everything and went ahead and implemented because they wanted it.

Thanks for getting involved...educators tend to be very closed minded. How in the world can anyone outside of their field have any idea on how to improve what they do...

Anonymous said...

I love your list, thanks for posting it. It'll be a resource for the rest of us for a long time!

Alan said...

National math test scores continue to be disappointing. This poor trend persists in spite of new texts, standardized tests with attached implied threats, or laptops in the class. At some point, maybe we should admit that math, as it is taught currently and in the recent past, seems irrelevant to a large percentage of grade school kids.

Why blame a sixth grade student or teacher trapped by meaningless lessons? Teachers are frustrated. Students check out.

The missing element is reality. Instead of insisting that students learn another sixteen formulae, we need to involve them in tangible life projects. And the task must be interesting.

Project-oriented math engages kids. It is fun. They have a reason to learn the math they may have ignored in the standard lecture format of a class room.

Alan Cook

Laurie H. Rogers said...

Thank you for your comment, Alan. However, you are laboring under the misperception that the current math situation is due to "the standard lecture format of a class room."

Many administrators and software/publishing vendors do continue to blame poor achievement on direct instruction and traditional algorithms. However, the nation's K-12 math classrooms have not had much in the way of direct instruction or traditional algorithms for about 20 years.
"Reform" curricula and "discovery" learning usurped their place long ago, and they have removed much real math content from the classroom. Any problems you see in achievement can be laid squarely at the feet of "reform" curricula and "discovery" learning (also known as "constructivism").

You say "project-oriented math" is fun. I say the students are not fooled. I say they find discovery learning to be a real burden, that they are worried and stressed out over a constant slate of "project-oriented math." Kids are engaged nowadays, all right, but they are not learning sufficient real math.

I think it's better, however, to let the students speak for themselves. In an upcoming article, they’ll have an opportunity to do that.
Meanwhile, thanks again for writing. Please check back in a week or so and see what the students have to say.

kprugman said...

I have to agree with you - ordering students to do projects causes stress and students are not fooled. They know their failings.

The reform movement falsely presumes that low income families have no standards, this is unfortunate as this group has probably spent more time growing old in non-productive environments, repeating standards ad infinitum, more than anywhere else in the world.

Been to a Saturday school lately? How would you like to spend it with a hundred students for four hours of a sat morning in a cafeteria mostly for arriving to school late.

In upper tracks, standards are implied, students and teachers already know the rules for achieving. It is the same for failing tracks, only here lower quality curriculum is used and standards (content) are written on the board to appease their administrators.

If teachers were actually engaging students they wouldn't be repeating useless math algorithms like lattice multiplication and touch math - its the same as beating into them that 2+2=5 - this might as well be 1984...

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