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Mathematics -- Specific Math Programs

What Is Your Child's Math Program?

Comparisons of Math Programs

  • Evaluations of Math Programs -- Educational Research Analysts: Click the link for detailed reviews of each program and extensive comparisons. Here are the bottom-line ratings that ERA gives to each program for the two grade levels it evaluated:

    Program3rd Grade
    6th Grade
    Connected Math Worst
    enVision MathBetter 
    Everyday MathematicsWorstVery Poor
    Glencoe Math Poor
    Harcourt HSP MathFair 
    Harcourt Think MathFair 
    Holt Math Fair
    Houghton Mifflin MathFair 
    Macmillan MathematicsPoor 
    McDougal Math Good
    Prentice Math Fair
    SRA Real MathBetter 
    Saxon Math (ORIGINAL)BetterBest

UCSMP "Everyday Mathematics" (a.k.a. "Chicago Math")

    Popularly known as "Chicago math" and published by Wright Group/McGraw-Hill, this program is one of the most pervasive of the original fuzzy, constructivist math programs. It was developed starting in 1985 by a group called the University of Chicago School Mathematics Project (UCSMP). It is legendary for its problems without solutions, incredibly frustrating "games," shallow interest in effective algorithms, heavy use of the demoralizing practice of spiraling and oddball methods such as "lattice multiplication."

  • Everyday Math: Coming to a School Near You! by Barry Garelick, Kitchen Table Math, July 27, 2008. Excerpt: "In the EM promo ... it looks like they've picked up on the criticisms of EM and are now using it in their advertising. To wit: 'There's nothing fuzzy about it.' Excuse me? Nothing fuzzy aboout it? Well, maybe not as fuzzy as TERC, but still... Yes, a casual reading might reveal what look like good problems, but you wouldn't know from looking at the workbook that they don't teach the standard algorithms, that a particular page of problems may represent the last time such types of problems are seen that year, that there are far less computational problems in EM than in the highly disdained 'traditional' textbooks, and the computational problems that are there do not cover a lot of 2-digit or 3-digit multiplication. Not to mention that calculators are allowed fairly often."

  • Barry Garelick comments in Education Week, March 15, 2009,
         "The Deparment of Education's What Works Clearinghouse which evaluates research on the various math programs, reviewed 61 Everyday Math studies. The findings: Of those 61 studies, none met evidence standards, 4 met evidence standards with reservations and 57 did not meet evidence screens. Of the remaining four, the WWC found Everyday Mathematics to have potentially positive effects on math achievement based on one study alone: the 2001 Riordan & Noyce study. Just so everyone is on the same page, Pendred Noyce has a vested interest in Everyday Math in that she has formed associations with several reform math initiatives, at least one dedicated to implementation of Everyday Math: COMAP, for which she serves on the Board of Directors."

  • "Chicago" Math by Mary Damer. A dissection of "evidence" offered in support of Everyday Math, a.k.a. "Chicago Math".

  • Everyday Math: Proof that it works? Hardly by Mark Montgomery, September 29, 2006.
         "Here's what we know about the effectiveness of Everyday Math, based on the research reviewed by the What Works Clearinghouse: Sixty-six studies have been found to focus on the effectiveness of Elementary School Mathematics programs. ... 61 of the 66 studies cited the What Works Clearinghouse focus on Everyday Math, at least in part. Fifty-seven (57) of them were thrown out because they did not meet the evidence screen. None fully meets the evidence standards. Four ... meet the standards 'with reservations.' ... let's actually read what the report has to say about each of the four studies ..."

  • One Step Ahead of the Train Wreck by Barry Garelick, Education News, May 15, 2009. HIGHLY RECOMMENDED for teachers and parents looking for a way to teach math to kids before they have to face the insanities of Everyday Math. The author provides plenty of insight into how Everyday Math fails kids, and gives very helpful and encouraging advice about addressing some of the school-based nonsense through home use of the extremely effective Singapore [Primary Mathemetics] program.
         "The first math tutoring session with my daughter and her friend Laura had ended. I sat in the dining room, slumped in my chair. 'You look sick,' my wife said. 'I am,' I said. My daughter -- subjected to the vagaries of Everyday Mathematics, a math program her school had selected and put in effect when she was in the third grade -- was having difficulty with key concepts and computations. She was now in 6th grade, and with fractional division, percentages and decimals on the agenda, I wanted to make sure she mastered these things. I decided to start tutoring her using the [Primary Mathemetics] textbooks used in Singapore's schools. I was familiar with the books to know they are effective. To make the prospect more palatable, I suggested tutoring her friend at the same time, since Laura's mother had mentioned to me that her daughter was also having problems in math. I figured I would start with the fourth grade unit on fractions which was all about adding and subtracting fractions, which they had already done, and then move rapidly into fifth grade, and start on the rudiments of multiplication. 'This'll be easy,' I thought. 'They've had all this before.'
         "We only made it into two pages of text in the fourth grade book. I came to find out that the concept of equivalent fractions (1/2 = 2/4 = 3/6 and so on) was new to them. This was the beginning of my attempt to teach my daughter what she needed to know about fractions while trying to stay one step ahead of the train wreck of Everyday Math."

  • If Math Were A Color...: A classic on Everyday Math and other modern fuzzy math programs, written by Elmhurst parent Marcia Tsicouris, and printed by the Elmhurst Press.

  • The folks at District 96 have unintentionally performed a public service by creating a set of Quicktime movies to illustrate some of the methods taught in the notorious Everyday Math program. Take a look! In particular, watch with amazement as we see how fourth graders are taught to do 352 times 241 using the Everyday Math method of "lattice multiplication". Then, after pausing for reflection, go on to see how fifth graders are instructed to figure out how 1876 crayons can be put in boxes of 64 each -- not by doing a normal division, but rather by torturing themselves with something that Everyday Math calls "Partial-Quotients with Double Digits". It's hard to see how anyone can get out of this class without a lifelong dependency on calculators.

  • How NOT to Teach Math by Matthew Clavel, City Journal, March 7, 2003. The author describes his experience as a Teach for America volunteer in a Bronx classroom, forced to use the Everyday Mathematics curriculum against his and his fellow teachers' best judgement. Clavel takes issue with the program's over-emphasis on cooperative learning; its placement of "critical thinking" skills before basic knowledge; the haphazard, spiraling, movement between topics; the sudden jumps to advanced topics for which students have not been prepared; misguided homework assignments; and an over-reliance on calculators.

  • Put Two and Two Together By Elizabeth Carson, New York Daily News, October 16, 2006. Excerpts: "Here's a math problem for you: Count the excuses people are trotting out for why schoolkids in New York City and State did poorly in the latest round of math scores. ... If, like me, you're running out of fingers - and patience - there's a reason. Nobody spinning the test scores is zeroing in on the single biggest reason math achievement ... lags and will continue to lag: Our schools use a far-too-fuzzy curriculum that fails to give kids rigorous instruction in the basics. ... In New York City, the program required in the vast majority of schools is called Everyday Mathematics. ... If you ask administrators to explain it, they'll use just enough jargon to make it sound decent.
         "But the truth is, Everyday Math systematically downplays addition, subtraction, multiplication and division, which everyone knows are the foundations for all higher math. Instead of learning those basic four operations like the backs of their hands, students are asked to choose from an array of alternative methods, such as an ancient Egyptian method for multiplication. Long division is especially frowned upon. There are no textbooks; that would just be too traditional. Instead, the idea is that kids ought to sit in groups, while a 'facilitator' - that's the teacher - helps. And, oh, one more thing: Calculators are introduced in kindergarten.
         "Not every single piece of the program is hogwash. But taken in total, the curriculum is soft enough to let down thousands upon thousands of our children. That's why it was rejected - twice - in the careful curriculum analysis process they use in California."

  • Spiraling Through UCSMP Everyday Mathematics (March 2003), by Bas Braams of New York University. The program's spiral nature and the concept of distributed practice is illustrated by the fourth grade coverage of whole number multiplication and division.

  • Dueling Brochures: Everyday Math vs. Saxon Math (original!) by Charles E. Breiling, December 24, 2003. "We'd heard good things about both 'Chicago Math' ... and 'Saxon Math' [original] so we wrote to both, asking for more information." Wow -- read what they discovered!

  • In her book Angry Parents, Failing Schools Elaine McEwan reports on two college professors who examined the research presented in an Everyday Math brochure and concluded "the research was seriously flawed. The snazzy packet was 'smoke and mirrors' and unfortunately a lot of parents and educators were fooled."

  • Evaluation of Everyday Mathematics by David Klein, Professor of Mathematics, California State University, Northridge, July 5, 1999 "I was asked by the California State Board of Education to review materials submitted by Everyday Learning Corporation which are intended to address shortcomings of its K-6 basic adoption submission, Everyday Mathematics. I was also asked to consider the program as a whole. ... My recommendation to the State Board of Education is that the K-6 Everyday Mathematics submission be rejected."

  • The Many Ways of Arithmetic in UCSMP Everyday Mathematics, by Bas Braams (Feb 2003). Does your child's math look like this?

    This article gives an overview of the multiple procedures for addition, subtraction, multiplication, and division in Everyday Mathematics.

  • A Critical Review of the New Constructivist Math Program by Tsewei Wang, Ph.D., professor of chemical engineering at UT Knoxville, March 4, 2001. "[Everyday Mathematics] is very weak and incomplete in its coverage, and it will not prepare high school students to take college math courses upon entering college without first taking a heavy dose of remedial math courses. Implementing it at the lower grade levels will undermine the students' ability to take traditional college preparatory math courses when they enter high school."

  • Review of the Everyday Mathematics Curriculum and its Missing Topics and Skills, by Tsewei Wang, Ph.D., professor of chemical engineering at UT Knoxville, April 9, 2001. A more detailed review of the program. The report also criticizes two major longitudinal studies that have claimed effectiveness of Everyday Mathematics.

  • Weaknesses of Everyday Mathematics K-3, by David Klein, November 2000. The author finds that Everyday Mathematics K-3 should not be adopted for classroom use. Among the major shortcomings are: (1) The failure of Everyday Mathematics to adequately satisfy 12 of the 17 major grade level standards for grade 3 in his home state of California. (2) The failure to develop the standard algorithms of arithmetic and to require memorization of basic addition and multiplication number facts at the grade levels specified in those standards. (3) The excessive and detrimental use of calculators in each of the grades K, 1, 2, and 3 curricula.

  • I'm Failing First Grade by Elena Beyzarov (a doctor of pharmacy and a parent), May 8, 2007. "As I came home from work on Friday afternoon, I just had to yell out to my daughter the one prevailing thought that I had since the minute I woke up that morning. 'Yeah it's the weekend, NO HOMEWORK!!!!!' To add to the effect, I even jumped up and down in my heels. ... You see, my child has been designated by the board of education as one of many 'subjects' who will be undergoing an experimental treatment called 'Everyday Math.'"

  • Presentation to the D308 school board in Oswego, Illinois, September 10, 2007, by a group of parents formally asking for the removal of Everyday Math from their schools.

  • Looking at Everyday Mathematics, a collection of teacher reports from a Pittsburgh Teacher Institute seminar in 2003. NYCHOLD calls our attention to the following PDF reports from that collection:

  • Reading Mastery Is New Requisite For Solving Math, by David J. Hoff (Education Week, Dec 5, 2001). Offers conflicting views on the amount of reading and writing required in reform mathematics programs, drawing on the Everyday Mathematics program for examples.

  • Conflict of interest? McGraw Hill, the publisher of Everyday Math, also owns CTB McGraw Hill which publishes the Terra Nova and other tests used to determine whether teaching has been successful. Several math reformers have commented on the seeming impropriety of the same company selling both a curriculum and the test used to determine whether that curriculum is working.

  • Weighing the Factors - Does [New York]'s Standardized Math Curriculum Measure Up?, by Amy Sara Clark, YouthMatters, Columbia University Journalism Program, 2004.

  • The Effect of Chicago Math on Everyday Students, by Karl Dahlke (2004?). An open letter to the Troy school district, Troy MI.

  • Everyday Math = 'Someday' Problems, by Karen Jones-Budd, posted April 25, 2003, on PBSfx: Parents for Better Schools in Fairfax County, VA. "Some elementary teachers and principals do not deeply understand the ramification of a math education that is poor in content and mastery. They love the warm, discovery-oriented nature of Everyday Math. They also see opportunities for teachers and children to be 'creative' in a group setting. Little do they know that some of the children will not be able to pass by the gatekeeper that is algebra. Or, if these students make it through a less rigorous algebra, then college math stops them dead in their tracks."

  • An Email Exchange about the Quality of Mathematics Education Research and "Everyday Mathematics" (March, 2003). This contains comments by David Klein about mathematics education research in general, with special reference to a study by Riordan and Noyce concerning Everyday Mathematics.

  • Joel Klein's Math Problems, by Bas Braams (op-ed, the New York Sun, Feb 6, 2003). About the choice of Everyday Mathematics as the standard curriculum for NYC elementary schools. "Mr. Klein would do well to reverse himself and listen to the advice about successful curricula that mathematicians and others have provided to him and his staff."

  • To Pittsburgh Public Schools Board of Education, by Wayne Bishop (April 10, 2002) and To Ms Colaizzi and the Pittsburgh Public Schools Board of Education, by Wayne Bishop (Mar 12, 2002). Two letters about reform mathematics programs in the Pittsburgh public schools. The letters provide a very critical look at some of the research cited in support of the Everyday Mathematics curriculum in Pittsburgh.

  • My Experience with Everyday Mathematics, by Karen S. Jones-Budd (Feb 12, 2002). A letter to Superintendent Till of Broward County, FL, describing the author's experience with the need to supplement her childrens' Everyday Math education.

  • Constructivist Mathematics in the Oak Ridge Schools, by Tsewei Wang and J. Douglas Birdwell (updated April 10, 2001). A letter to the public and to local officials opposing the adoption of Everyday Math in the Oak Ridge, TN, schools system. The letter summarizes some of the concerns, nationwide, over the Everyday Mathematics curriculum, and introduces a critical review by one of the authors.

  • A Review of Everyday Math, by Tse-Wei Wang and J. Douglas Birdwell. Transparencies for a presentation to the Head of Curriculum, Oak Ridge Schools, March 26, 2001.

  • Concerned Parents of Reading (MA) to the State Board of Education. A letter of Feb 13, 2000 from Dr. Bob Mandell on behalf of a group of parents concerned about the implementation of the "Chicago Math Program" Everyday Mathematics in their local elementary school. The letter includes an analysis of declining test scores on Stanford-8 and Stanford-9 in the school.

  • Concerned Parents of Reading, MA, Letters. A record of correspondence of the Concerned Parents of Reading with their school administration about concerns over UCSMP's Everyday Mathematics. The page also links to letters to parents and to the press. We highlight the Letter to the Editor of June 25, 1997, which expresses the CPR's disappointment over the lack of cooperation from the district administration.

  • Reading Mastery Is New Requisite For Solving Math, by David J. Hoff (Education Week, Dec 5, 2001). Offers conflicting views on the amount of reading and writing required in reform mathematics programs, drawing on the Everyday Mathematics program for examples.

    Lattice Multiplication

     "Lattice multiplication"
  • New-Math Multiplies by Linda Schrock Taylor. "Yes, New-Math is multiplying, but I am sorry to report that too many children are not learning to multiply with New-Math. ... Multiplication is not all that difficult if one learns the multiplication tables and the logical, precise algorithm for the process. One day I was teaching traditional multiplication when one of the special education students wanted to show me the process she had been taught. Her problem even shocked me, and luckily I had my camera with me. This illustration should help the unaware to understand why so many children in special education, as well as most other children, are coming to believe that math is an alien life form. It is no wonder that, when such foolishness is passed off as an intelligent math procedure, math scores are dropping like stones, while confusion is rising to new heights. It is no wonder that our students grow up: seeing themselves as stupid, hating math, and actually mathematically incompetent!"

  • Posting on an education discussion board:
    "Towards the end of 3rd grade ... I wrote a letter to my son's teacher/principal telling them that unless they could provide me with compelling evidence that using the lattice method of multiplication was helpful (yes, Everyday Math), I expected my son to do all of his multiplication problems using the standard algorithm so that he would get very good at one method, rather than not-so-good at four methods. Shortly thereafter, he came home with a math assignment. The class had been given a worksheet and told to use the lattice method to solve the problems, but Eric's teacher told him he was supposed to use the standard algorithm. I asked him what he thought about that. His response? 'Mom, it took the other kids three times as long to get their work done.' Duh."

  • What Is 5536 Divided By 82?: Compare the standard method versus the "method" used in Everyday Math:

Kendall/Hunt "Math Trailblazers"

    To the embarassment of all of us Chicagoans, here is another fuzzy math program concocted in our backyard. This program was created by something called the Teaching Integrated Mathematics and Science (TIMS) Project at the University of Illinois at Chicago.

  • Wayne Bishop review of Kendall/Hunt Math Trailblazers: This thorough review of this controversial program was prepared by Wayne Bishop when he participated in the state of California's "Content Review Panel" evaluating math programs and curricula under consideration for that state's schools. Bishop's review concludes, "this submission is NOT recommended for adoption."

  • "What is wrong with Kendall/Hunt Math Trailblazers, And why it isn’t good enough for our youngest children": a critical review of this math program, which has been adopted by a number of Chicago suburban school districts. This paper was written by a parent in a Colorado district.

  • A New York Times article ( Fuzzy Answers: The New, Flexible Math Meets Parental Rebellion) includes this wonderfully delicious look at a Chicago school where Math Trailblazers was used:

      The Daniel Boone School, in West Ridge, a tidy working class part of Chicago brightened by magnolia trees and the babushkas of Russian grandmothers, has been a laboratory for the development of TIMS Math Trailblazers, a constructivist program created by the University of Illinois. Math scores have risen since the program was put into effect. The principal, Paul Zavitkovsky, credits the program, but does not rule out increased attention to math, teacher training and collaboration.

      In fifth grade the other day, Mila Kell, a Russian immigrant, taught a crisp lesson in probability, improvising riffs on the probability that the sun would rise in the morning and that she would fly to the moon. The class was enchanted.

      Mrs. Kell said she loved the freedom and creativity of the new math. But on her desk was a secret weapon: a stack of worksheets -- the antithesis of constructivist math -- pages of classic problems in long division, the addition of fractions and reducing the sum of fractions to its simplest terms.

  • Sun-Times columnist Mary Laney wrote this in her column for March 21, 2005: "Recently a group of parents from suburban Wilmette asked me to meet with them. ... Math is taught by 'The Trailblazers Math Program.' ... The parents are angry and frustrated. I can understand why. Those I met with said they couldn't even read the Trailblazers' math book -- and that includes a parent who was a teacher. Trailblazers is in the genre of a new 'new math.' I had experience with "new math" when my eldest son was in sixth grade. He brought his math homework to me and together we worked on the problems. The next day when he returned from school he couldn't wait to see me. 'All the answers were wrong.' ... I have compassion for the Wilmette parents as they struggle to help their children learn a math system that they say is hurting their preparation for high school. ... The problem is not with the teachers, say the parents, the problem is with a school board that has programs that are not working and stays with them."

  • A university instructor wrote this to us: "Math Trailblazers is garbage! My daughter was a victim of Math Trailblazers and despite the research I showed the district, onward they marched. It was and still is pathetic. She went from loving math to thinking she stunk. We picked up and moved and now my 5th grader is doing Saxon 8/7 [original] and loving life."

    In 2011, a Wilmette Mom wrote to us looking back on their family's experience:

    "I just ... would like to make a few comments from my personal experience with Trailblazers. My [two children] attended Wilmette school district and received their math instruction via Trailblazers. It took me a few years to realize that they were not getting any worthwhile math instruction. In fact, by fifth/sixth grade, they knew very little math. At that time, I obtained a math book and homeschooled them. Unfortunately, it was not enough. The precious time in which they should have received 'rote' instruction was hard to make up. They do not know math as well as they could have if they were actually taught to do math. Please do not use Trailblazers because the program does not teach math. In fact, it negatively impacts high school math scores and future career choices that require math in college for the simple reason that children did not learn math in their early academic years and did not have the foundation to build on. Please do not be sold on all the hype that the publishers try to put out. Let's keep in mind that the greatest generation did not have Trailblazers but they knew how to function mathematically! It is something that many of the young people cannot do today. We need to ask ourselves a question as to wheather we want children to have only fun and 'concepts' or wheather we actually want them to know math. I think that the answer is pretty obvious."

Scott Foresman Addison Wesley "MATH"

    Note: Because this program just has the simple name "Math", be careful not to confuse this program with Scott Foresman Addison Wesley "Mathematics" (see next listing) or Scott Foresman Addison Wesley "enVisionMATH" (see listing after that) or or any of the other math programs released under the Scott Foresman or Addison Wesley imprint.

    A number of schools districts in the suburban Chicago area have purchased the Scott Foresman Addison Wesley MATH program. As fuzzy math goes, it is not one of the worst, but it is decidely mediocre.

  • Review: Scott Foresman Addison Wesley MATH. This is our very detailed review of SFAW Math, looking at the dumbed-down methods, deemphasis of algorithms and unnecessary complexity of the series' approach to math, as well as its clutter and visual chaos, political correctness and time-wasting sidebars.

  • John Sikora wrote this review of SFAW and two other math programs (Houghton Mifflin and McGraw Hill). About SFAW, he concluded, "The Scott Forseman-Addison Wesley text has some ... serious problems. The presentation was cluttered by all sorts of cartoon characters and sidebars that would only serve to distract the student."

  • Also go to the programs review page at Mathematically Correct, and search on that page for a keyword such as "Foresman".

Scott Foresman Addison Wesley "Mathematics"

    Note: Because this program just has the simple name "Mathematics", be careful not to confuse this program with Scott Foresman Addison Wesley "Math" (see previous listing) or Scott Foresman Addison Wesley "enVisionMATH" (see next listing) or any of the other math programs released under the Scott Foresman or Addison Wesley imprint.

    This series apparently replaces the SFAW math series with the name "Math". Confused? We asked SF-AW what the differences were, and they told us this:

    The program ["Mathematics"] was a new program; not an update of the ["Math" program]. The top ten differences between the programs are listed below. ...
    1. Teaching for Understanding (Do you know how & Do you understand)
    2. Expanded Research Base and Validation
    3. Structured Instruction (step by step modeling)
    4. Instant check system tied directly to intervention
    5. Online Diagnosis & Intervention
    6. 5 Levels to Investigations
    7. Leveled problem solving
    8. Reading and Writing for Math Lessons
    9. Ongoing Professional Development
    10. More student support in the student edition

    We'll be working to try to find out more about this change.

Scott Foresman Addison Wesley "enVisionMATH"

    Note: Be careful not to confuse this program with other math programs under the Scott Foresman or Addison Wesley imprint.

    "enVisionMATH" is a new series from SFAW, described as "a core elementary math program based on a new research-based instructional model." It appears this will be their new "push" product for math.

  • enVisionMATH scores well in Texas 3rd grade review by Education Research Analysts: In a comparison of eight proposed math programs, enVisionMATH scored in the highest category, along with respected programs Saxon Math [original] and SRA Real Math.

  • One teacher posted (May 2009) these comments on a message board: "My old school district has it. The first quarter was a disaster for the kids as the teachers followed the fuzzy portion of it. Then in the second quarter they dropped the fuzz, kept to the more traditional part of the program and the kids rebounded ... My opinion: [EnVisionMath] tries to reconcile the two approaches, reform and non, which in my opinion are not reconcilable."

TERC: Investigations in Number, Data, and Space

    Investigations is a particularly detestable fuzzy math offering from Pearson/Scott Foresman. Although it has not slithered into Illinois as much as it has in other areas around the country, it may pop up from time to time.

  • Comprehensive collection of reviews and links concerning TERC: Investigations in Number, Data, and Space, from NYC HOLD

  • Investigations Math: Excellent website of a grassroots group in Utah fighting TERC investigations, created by Oak Norton. The website includes
    • a printable flyer (DOC) to help in fighting Investigations math,
    • three radio ads!

  • Beyond TERC Math: Here's an extensive website developed by Linda Moran reporting on the problems of TERC. It contains reports on battles in a number of districts.

  • A Survey of School Districts Profiled in Pearson Scott Foresman's January 2007 Publication, "Investigations in Number, Data, and Space: Evidence for Success", February 24, 2009 (PDF). In January 2007, Pearson Scott Foresman released a report listing school districts as "success stories" for TERC Investigations. In reponse to that, a survey was conducted among the school districts cited. Responses were received from 62 of these districts, with these results:
    • 58% of the districts have discontinued use or are in the process of discontinuing the use of TERC Investigations
    • 27% of the districts currently using TERC Investigations are receiving financial grants for continuing to use it
    • Only two districts said they used TERC Investigations without supplementation

  • Obama, Sidwell Friends, and the Achievement Gap by Barry Garelick, EducationNews, December 1, 2008. "Those closely watching the Obamas and what they are going to do next, have surely noticed that they have elected to send their girls to Sidwell Friends School in DC. ... I'm not particularly interested in that issue so much as I am the fact that Sidwell uses Investigations in Number, Data and Space, one of the NSF-sponsored atrocities that passes as a math course and grossly underprepares students for math. ... If Mr. Obama's girls don't happen to learn math very well, his advisors will assure him it's just fine. I can't help but wonder, however, if Michelle Obama's mother, who will be living with the Obamas, will notice anything strange. Something tells me she won't like that the kids don't know how to add, subtract, multiply or divide. If she's like many parents in this country who are similarly disturbed by such results, she'll supplement their education by teaching them the traditional way and no one will be any the wiser. In fact, Sidwell and other schools will attribute such success to their fine curriculum. In the meantime, however, those children not privy to help from parents, grandmas, tutors, or education centers will continue to remain on the low side of the achievement gap -- that stubborn problem that simply won't go away. For those unfortunate few in the privileged class who do not get such help -- because their parents don't see anything wrong, perhaps their lower scores will help narrow the gap, but don't worry. They will still manage to have their place in the sun. Which brings us back to those who are not so privileged. Those people will continue to be relegated to the day-laborer/non-math capable career paths. All for the want of a solid mathematics foundation."

  • TERC Hands-On Math: A Snapshot View by Bill Quirk. This review discusses how TERC handicaps kids when it omits standard computation methods, omits standard formulas, and omits standard terminology. Also read the full report, TERC Hands-On Math: The Truth is in the Details.

  • Drexel University has a website that welcomes discussion about TERC. The ostensible purpose of the site is to support the use of TERC, but many of the messages posted on the discussion board should raise alarm bells. Here are some excerpts from posted messages:

    • "I am shocked that parents allow this curriculum."
    • "I'm just stunned and thoroughly disappointed."
    • "Our school district has implemented TERC math this year. The parents have flipped out over this. ... The parents of my district ... have gone as far as to retain a lawyer."
    • "A 5th grader in the gifted/talented program at her school came to a carnival. 'How much money did you bring?' 'Thirteen quarters,' she said. 'Well, how much money is that?' A blank look, followed by, 'I don't know - I didn't bring a calculator.' Surprised, I asked her equally bright friend if she knew how much it was. 'We haven't had long division yet,' she responded. The girls in the troop who use a traditional math program knew instantly that the amount was $3.25."
    • "I was really surprised when 4 kids sat down to race up the mountain, and two children who are using the Investigations curriculum in 4th and 5th grades, respectively, could not calculate 3 X 50. One began to draw circles on the paper as a way of solving this problem. When they were helped past this point and reached a division problem (150 divided by 5), they came to a halt and sat staring at the page. It was a disaster..."
    • "I have heard nothing good from any parent or teacher that I have spoken to. The teachers are hesitant to say anything because of politics ..."
    • "We have many parents who are pulling their children out of public school and putting them into charter schools, where Investigations math is not being taught, primarily for that reason."
    • "I believe that Investigations math only confuses a lot of students, and isn't helpful."
    • "To tell children that it is best to rely on their peers for answers, rather than the adult knowledge bearer in the classroom (the teacher) and to suggest to them that their made up algorithms are equal to or superior to matery of the algorithms comprised in the body of mathematical knowledge developed over thousands of years ,is a profound disservice to your students, and pure unadulterated folly."
    • "As an educational evaluator in Manhattan, I have seen more referrals for students concerning math, since these programs were instituted. These students are not learning disabled but rather Curricula Disabled. But the worst is parents don't speak up. They just pay for the tutors, if they can and if they can't they try and justify it. And the districts make the parents look like their crazy if they speak up."

  • A positive result from Investigations, reported by a parent:
    "My grandkid's school bought this baloney 2 years ago. ... Thank God that a Kumon has opened in our area. My daughter will be sending him over the summer. ... At least I now have some credibility in my daughter's eyes. She seemed to think I had fallen off the deep end because I have been so passionately against fuzzy math. Now she knows!!"

  • Review of Investigations in Number, Data, and Space, Mathematically Correct Second Grade Mathematics Review. The review assigns an "F" grade to this program for this grade. The "Overall Evaluation" says, "There is nothing to recommend about this program. The use of this program in our public schools is a strong argument for vouchers."
  • Review of Investigations in Number, Data, and Space, Mathematically Correct Fifth Grade Mathematics Review. The review assigns an "F" grade to this program for this grade. The "Overall Evaluation" says, "This program received the lowest overall rating of the fifth-grade programs in this review. The level of achievement supported falls far short of the expectations in this review. This program cannot be recommended for use in fifth-grade classrooms."

  • Math with Madeline:
    MUST-SEE VIEWING! Fifth grader Madeline shows us vivid examples of the differences between the fuzzy math program that she used in her old school (TERC Investigations) and the mastery math programs (Saxon Math [original] and Singapore [Primary Mathemetics]) she now uses.

    After viewing this, ask yourself, which do you want for your own children?

Connected Mathematics Project (CMP)

    Note: Be careful not to confuse this program with:

  • Comprehensive collection of reviews and links concerning Connected Mathematics Project, from NYC HOLD. This source includes numerous links, not all included here, on parent and teacher comments about Connected Math, coverage of many local battles all over the country, as well as professional critiques of the program and evidence that has been used to support it.

  • Also go to the programs review page at Mathematically Correct, and search on that page for a keyword such as "connected".

  • An Evaluation of CMP by R. James Milgram. This is a wonderfully detailed and thorough analysis of Connected Math, approximately 22 pages in length. If your district is considering CMP, get this!

  • A Comprehensive Assessment of CMP (Connected Math Program) Deficiencies Leading to Supplementation That Meets Key Traditional Educational Needs (MS-Word doc), by Donald Wartonick, Cambridge College, Fall 2005.

  • 6th Grade Connected Math by Arthur Hu, Education News, October 2003. "... 'Connected Mathematics' ... carries on the tradition of nightly homework that is a) hard to figure out, b) takes forever to do once you figure it out, c) after you're done you haven't learned any useful math, d) it goes out of the way to make sure the #1 most important method to know is not taught, or allowed. The whole theme of ed reform seems to be 'work harder and learn less'. ... How can any of you [on our school board] sit there and say with a straight face that you think this stands for excellence in education? Why in the world would anybody deliberately design mathematics that omits the most basic skills and concepts?"

  • Connected Math, Disconnected Parents: the website of a parents group in Plano, Texas, that has drawn national attention over their legal battles to eliminate Connected Math and to restore substantive math instruction

  • Detailed arguments and findings regarding CMP by Prof. Man Yee Betty Tsang, National Superconducting Cyclotron Laboratory, Michigan State University. See that main link for numerous details and reports, but here are a few of special interest:

  • The Government Flunks Math by David Tell, Weekly Standard, December 13, 1999. "... This gasp-inducing error turns out to be merely a surface symptom of the CMP curriculum's paramount, underlying flaw: a nonchalance about -- no, outright hostility towards -- the precision, coherence, and content of mathematics as an academic discipline worthy of study in its own right. Throughout the booklets, CMP students are asked to do a great lot of group 'investigation' into otherwise classic math topics. But those topics are never explicitly defined as such, and the standard algorithms they involve are never introduced. Is whole-number factorization into primes - the fundamental theorem of arithmetic, which CMP only implicitly establishes with 'experiments' proposed for sixth grade - an inviolable principle? The booklets do not say. And they are silent by design. CMP's teacher manuals advise a passive approach to pupils because 'showing them how to do something' only produces an 'impression' of success. Parents are then warned not to fill in the gaps: 'It is important that you do not show your child rules or formulas for working with fractions,' for example. Better that kids just figure it out. Or fail to. Having read this far, you have no doubt reached the not unreasonable conclusion that Connected Mathematics is a pedagogical disaster waiting to happen. You will therefore be distressed to learn that it has already happened; CMP is widely used in public schools across America."

  • Plano Parental Rights Council -- the battle over Connected Math in Plano has blossomed into a full-fledged parents' rebellion over progressivist teaching methods.

  • Plano report on Connected Math: includes numerous reports on the battles in Plano and nationally over Connected Math.

  • Why Guilford Parents Should Oppose CMP Math by William Quirk, Ph.D. in Mathematics: a very in-depth analysis of Connected Math, approximately 10 pages in length

SRA Connecting Math Concepts (CMC)

Core Plus / Contemporary Mathematics in Context

College Preparatory Mathematics (CPM)

  • Review of CPM Mathematics by Wayne Bishop, Department of Mathematics and Computer Sciences, California State University. Excerpts:
         "With regard to mathematics content, this program does not sufficiently address the content standards and applicable evaluation criteria to be recommended for adoption. ... Most of the program is below the specified standards level and there is too much of an assumption that work will be done in teams. Although the publisher claims that all standards are met, several are clearly not met and several more identified herein as met are, in fact, not adequately met. Finally, there is a systemic misconception as to what is meant by logical argument in mathematics. ...
         "Much of Volume 1 actually detracts from developing algebraic competence. Almost all of the mathematical content is at the level of the Grade 7 standards or below, e.g., the equations to be solved all are, but the activities are still very time consuming and sometimes frustrating. The worst of all, however, is not teaching the power of algebra itself. ... This is not algebra and it is not college preparatory math, no matter what it calls itself. Eventually, Volume 2 starts teaching some algebra but it is too little and too late."

  • Click to go to the reviews and articles about CPM on the "programs" page at Mathematically Correct.

Mathematics in Context: A Connected Curriculum (MIC)

    Note: Be careful not to confuse this program with:

    This is a grade 5-8 program based on a Dutch curriculum, revised by the Wisconsin Center for Education Research, published by Encyclopaedia Britannica and sold and distributed by Holt, Rinehart, and Winston. A teacher in District 87, Bloomington, IL, brought this to our attention when she wrote to us to say, "In my opinion, this series has been a dismal failure in teaching math."

    For some truly scary reading, see the publisher's NCTM-drenched "Philosophy."

    We're also impressed by the chutzpah of this statement from the publisher's website regarding field testing of the MIC program:

    Standardized test data were not gathered during the pilot and field testing of the units because it was felt that information from such tests did not reflect the mathematics content of the units or the instructional goals of the project.


  • Review of McDougal Littell's MathThematics Book 2, Mathematically Correct Seventh Grade Mathematics Review. The review assigns a "D+" grade to MathThematics. The "Overall Evaluation" says, "This low rating reflects weakness in content, weakness in presentation, and weakness in student work as discussed immediately above and in each of the content topic reviews. It is not possible to recommend this book to anyone for any purpose."

Interactive Mathematics Program (IMP)

  • Comprehensive collection of reviews and links concerning IMP: Interactive Mathematics Program , from NYC HOLD

  • Comment on IMP by Bastiaan J. Braams, Ph.D., visiting professor of mathematics at Emory University:
    "The Interactive Mathematics Program (IMP) is to the best of my knowledge the worst of all high school mathematics programs. I have found it useful sometimes to show a Grade 9 or Grade 10 IMP text to mathematician colleagues that are a bit skeptical about the Math Wars: it shows them immediately that there is a real issue here. IMP Grade 9 has stories on every page, and one has to turn many pages to find as much as an equals sign in arithmetic, never mind an algebraic expression. It represents the degenerate extreme of NCTM mathematics."

  • Teens Bash New 'chIMP' Math: New IMP word problems send kids in search of numbers by April Capochino, Times Herald-Record [NY], December 03, 2002. "A new math curriculum plus confused students equals angry parents. At least when that new math curriculum is the Interactive Mathematics Program. ... 'The whole program is a travesty,' said parent Traude Ellert, who has made it her personal mission to convince the district to ax IMP. 'It's like a cancer. We are using language arts books to teach math. I'm outraged as a taxpayer. Part of my money was used here.'"

  • Excerpt from Teacher's Manual, Interactive Mathematics:
    Traditionally, mathematics tests have questions with "right" and "wrong" answers. These tests reinforce the misleading image of mathematics as a subject with unique correct answers.


  • Click to go to the list of MathLand articles on the "programs" page at Mathematically Correct.

  • Where's the Math? by Debra J. Saunders, San Francisco Chronicle, October 17, 1999. "UC Berkeley math professor Hung-Hsi Wu couldn't believe the department described MathLand as 'promising.' He'd describe MathLand as 'execrable.' Or how about: 'I can't believe it's math class.' A second-grade MathLand exercise called Fantasy Lunch instructs students to think up their fantasy lunch, draw it on paper, then cut out the 'food' and place their drawings into a bag. A frantic teacher wrote to me two years ago, furious that she had spent 75 minutes on that exercise and there was no math in it. It was 'like therapy,' she said. On more than one occasion, her students asked her, 'Can we do some real math now?'"

  • Illustration of a MathLand "lesson": "Fantasy Lunch" is a second-grade exercise which instructs students to think up their fantasy lunch, draw it on paper, then cut out the "food" and place their drawings into a bag. One spent 75 minutes on that exercise which contained no mathematics. Students would ask "Can we do some real math now?"

Marilyn Burns, Math Solutions

    In-service programs, workbooks and other materials from "Math Solutions Professional Development" and its founder, Marilyn Burns, are promoted in many school districts.

    The same company is also behind something called the Phil Mickelson ExxonMobil Teachers Academies, funded by the famous golf pro. The pitch is that invited elementary school teachers get to attend sessions where they will be taught "best practices" for "encouraging children's interest in math." In reality, it's just another attack on solid math instruction. (One wonders if Mickelson himself would be disturbed at the sight of young golfers using a calculator to add up their scores?)

  • The Fuzzy Math Mindset Behind Phil Mickelson ExxonMobil Math by William G. Quirk, Ph.D. This article dissects the Marilyn Burns approach and has vivid descriptions (with juicy examples) including:
    • How Should Children Learn Elementary Math?
    • What Should Children Learn in Elementary Math?
    • The Marilyn Burns View of How Children Should Learn "Math"
    • Marilyn Burns Rejects Standard Paper-and-Pencil Arithmetic
    • Marilyn Burns "Problem-Solving Activities"
    • Lessons From the Marilyn Burns website

Harcourt Brace: Math Advantage


    The original Saxon Math program, published by the independent publisher Saxon, was a tremendously effective math program that built math understanding and mastery in a slowly evolving sequence. As a result, it was extremely popular with homeschoolers and with learning-centered charter schools and independent schools.

    Sadly, the program was heavily revised after its 2004 purchase by Harcourt, and is now radically different from its original incarnation.

    For these reasons, our discussion of Saxon is split into two sections, covering the original version as well as the current version from Harcourt.

Saxon Math -- ORIGINAL

  • A very interesting study on Saxon [original] is from Anne Arundel County in Maryland, where the 14 schools scoring lowest in math were switched from Everyday Math and Mathland (two fuzzy math programs) to Saxon Math [original]. The results were striking. In all 14 schools, math performance jumped after a year with Saxon [original]:
    For much more information on the tremendous success experienced in Virginia with Saxon Math [original], see the extensive and beautifully designed website of a local parents' group there, PBSfx: Parents for Better Schools

  • Saxon Math [original] at North Beach Elementary, Seattle, January 14, 2008

  • Editorial, Chicago Tribune, April 1, 2002. "... by some measures, several Chicago charters are seriously outperforming neighborhood schools. At the three elementary campuses of Chicago International charter schools, for example, math scores are off the charts compared with the neighborhood schools the kids likely would attend if the charter didn't exist. Officials there suggest it may have to do with the Saxon Math [original] program used at all its schools."

  • Dueling Brochures: Everyday Math vs. Saxon Math [original] by Charles E. Breiling, December 24, 2003. "We'd heard good things about both 'Chicago Math' ... and 'Saxon Math' [original] so we wrote to both, asking for more information."

  • Four Years of California Mathematics Progress, by Wayne Bishop, Ph. D., Department of Mathematics, California State University, September 1, 2002. This excellent short paper documents dramatic improvement when Saxon Math [original] replaced Mathland and other fuzzy math programs in several California districts:
    • "Math scores [in Azuza] there have been surging in recent years and about half the students in grades two through six are now above the national average. This year's are higher. Curriculum helps. Azusa and Sacramento City adopted Saxon Math [original] for the 1999-2000 year, a decision that helped continue the progress already made by abandoning their previous and constructivist curriculum, MathLand."
    • " Another district ... that [has] caught public attention [is] ... Baldwin Park, [a] 'have-not' district ... This district ... adopted the AB-2519 approved Saxon Mathematics [original] program ... [and is an] example of a district that has shown strong success with direct instruction."
    • "Cragmont Elementary of Berkeley Unified ... adopted Saxon Math [original] and a look at the scores indicates that, the mathematics progress was ... striking ..."
    • "Annandale Elementary in LAUSD was singled out ... in an LA Times editorial for ... exceptionally high API increase. It was one of the LAUSD pilots of Saxon Math [original] and progress continued in 2001. This past year, Annandale was told to replace its Saxon [original] curriculum with the district mathematics adoption. ... these scores have [now] stagnated, perhaps due to this curricular change."
    • "Some schools with very [high socioeconomic scores], and a history of comparatively strong performance, are also indicating how far short of potential student achievement had been. One district that has been pointed out to me as exemplary in this regard is Manhattan Beach Unified, another Saxon Math [original] district ... In this district, less than 5% qualify for lunch assistance, more than half the parents are college graduates, most of the teachers hold full credentials, etc. Student performance is approaching astronomical."

  • Well, Shut My Mouth by Linda Schrock Taylor. This is from a Michigan teacher who went to a conference to hear about a new math curriculum and the latest trends in math education. In the process, she had some lively (and entertaining) conversations with the math "experts", drawing upon her decade of successful experience in teaching kids using Saxon Math [original].

  • "Saxon math's [original] approach is reasonably close to what research is telling us about how students learn -- much closer, than are the progressive methods advocated by the National Council of Teachers of Mathematics."
    -- Prof. E. D. Hirsch, The Schools We Need and Why We Don't Have Them, page 131

    Saxon Math [original] at home

  • In addition to being a successful program for use in school, Saxon [original] is also used at home by many parents to provide math instruction for their children when the program at school seems to be failing. It is extremely popular with homeschooling families.

  • Many homeschooling families still use the original Saxon program, buying it used. Try looking on Amazon and eBay.

Saxon Math -- HARCOURT

  • Harcourt buys Saxon: In 2004, Saxon Publishers was acquired by Harcourt, a major national textbook publisher, and folded into its "Harcourt Achieve" group. This has sounded alarm bells among many Saxon fans, who have observed 1) Saxon books are now much more restricted in sales to homeschoolers, 2) recent revisions have introduced a number of fuzzy-math elements, and 3) "Harcourt Achieve" is positioned as the remedial/slow learner division of Harcourt, which is not at all how Saxon afficienados see their beloved math curriculum.

  • Why Now, Saxon? by Linda Schrock Taylor. "I am distressed to read that the order of the topics has been changed in the rewritten books already on the market, despite the red herring claim that the company values the incremental steps of the original Saxon books. I am frustrated to read that instead of instructing, the teacher will serve as 'tutor and coach.' This sounds too much like New-Math to those of us who mourn the loss of America's competitive edge in mathematics..."

  • Questions for Saxon/Harcourt Achieve by Linda Schrock Taylor.

  • A report from a math consultant discusses the sorry state of what is called "Saxon Math" today:

    • I have now worked with [more than a dozen schools that use the current Harcourt version of Saxon Math]. ... In each case, their students collapse at algebra 1 if not earlier. Sure, some of them manage procedurally, but give them a problem that deviates in the slightest from the expected procedure, and they fall down.

      At one school, where the entire class of 8th graders were supposedly ready for Saxon Algebra 1, having finished Saxon from K-7, using Course 1-3 in middle school couldn't solve this:

        The school sold tickets to a play. They sold 300 total tickets. Adult tickets cost $3.50 each and student tickets cost $1.50. They sold $600 worth of tickets. How many adult tickets did they sell?

      Not one could solve it.

      More than half couldn't solve:

        There are 6 more men than women on a bus of 30 people. How many men are there?

      Even after a lesson on these, they couldn't do:

        Lucy spent 3 more dollars shopping than Mary. Together they spent $12.60. How much did each one spend?

      But it's not just word problems. They left Saxon Course 1-3 and the majority of kids in class ... can't solve this:

        -m -10m

      or this:

        -39 = a + (-24)


      Another teacher said "Yesterday, when I was going over the problem (-12ab) + 4ab ... The kids said, 'Can you just work the problem?' They don't want to understand math, they just want the procedure and move on."

      These students will fail at algebra and above. Not because they are dumb, but because they have been mistaught.

      You could claim it is just this school, and this is somehow an outlier. But this school is like the overwhelming majority of the others: well-intentioned but mathematically weak teachers, terrible instruction, terrible curriculum, absolutely no idea what mathematical thinking is, no way of teaching that math is coherent, reasonable, precise. Saxon is a disaster, and it was hobbling these children.

Singapore Math

    "Singapore Math" no longer means just one thing.

    The popular and effective original Singapore program named "Primary Mathematics" is still available and is as good as ever.

    But constructivism has oozed into the education establishment in Singapore as well, and that country has been actively replacing its math materials. The new "Singapore" programs with names such as "Math In Focus" (from Houghton Mifflin Harcourt) and "My Pals are Here" are NOT of the same caliber and clarity of the original "Primary Mathematics" program.

    Singapore math, old and new, are covered in the following sections.

Singapore "Primary Mathematics"

    Since the students in Singapore consistently top the world in math achievement, it makes sense to consider using the same math curriculum they use (and yes, Singapore students are taught in English). The texts and workbooks are comfortably light, and are tastefully attractive and appealing without veering into graphics overload. Each topic is very carefully laid out with well-chosen numeric and word problems, and genuinely helpful illustrations.

    A number of enlightened charter, independent or private schools have adopted Singapore Math as their math program. But relatively few mainstream public schools or districts have done so.

  • University professor of computer science Kevin Karplus has an excellent and richly detailed webpage on K-8 math education, which includes a number of excellent references on Singapore Primary Mathematics.

  • Miracle Math: A successful program from Singapore tests the limits of school reform in the suburbs by Barry Garelick, Education Next, Fall 2006. (Also available as a PDF.) Excerpts:
         "Singapore ... had begun modifying its education policies in the early 1980s to build up its labor force in such a way as to create technical skills unavailable elsewhere in the Third World. The Curriculum Development Institute of Singapore ... had created the math program and the accompanying texts, called Primary Mathematics (which were published in English, Singapore's official administrative language, in 1982), to help boost that technological prowess. The Primary Mathematics series was at the heart of Singapore's national math curriculum as it achieved its successive TIMSS victories. Many professional mathematicians, concerned with the decline of math education in the United States, took a hard look at the Singapore [Primary Mathematics] methods and texts and liked what they saw. ...
         Unlike many American math textbooks, ... which are thick, multicolored, and multicultural, Singapore's [Primary Mathematics] books are thin and contain only mathematics. There are no graphics (other than occasional cartoons pertaining to the lesson at hand), no spreadsheet problems, and no problems asking students to use a calculator to find the mean number of dogs in a U.S. household. With [Singapore Primary Mathematics], students are required to show their mathematical work, not explain in essays how they did the problems or how they felt about them. While a single lesson in a U.S. textbook might span two pages and take one class period to go through, a lesson in a Singapore [Primary Mathematics] textbook might use five to ten pages and take several days to complete. ...
         Singapore's texts also present material in a logical sequence throughout the grades and expect mastery of the material before the move to the next level.      The most important feature of Singapore's [Primary Mathematics] texts is an ingenious problem-solving strategy built into the curriculum. Word problems are for most students the most difficult part of any mathematics course. Singapore's [Primary Mathematics] texts help students tackle them through a technique called 'bar modeling,' in which students draw a diagram to help them solve the problem. Typically, in U.S. texts, students are taught to use a method called 'Guess and Check' -- trying combinations of numbers until the right numbers are found that satisfy the conditions of the problem -- a method that many professional mathematicians consider inefficient (see sidebar). The bar-modeling technique not only provides a powerful method for solving problems, but also serves as a link to algebra. Symbolic representation of problems, the mainstay of algebra, emerges as a logical extension of the bar-modeling technique."

  • Singapore Math: Simple or Complex? by John Hoven and Barry Garelick, Educational Leadership, November 2007. "Using the bar model approach, Singapore [Primary Mathematics] textbooks enable students to solve difficult math problems -- and learn how to think symbolically. ...
        "Bar modeling is a specific variant of the common Draw a Picture mathematics problem-solving strategy. Because Singapore [Primary Mathematics] uses this one variant consistently, students know what kind of picture to draw. That's an advantage if the bar model is versatile enough to apply to many complex problems -- and it is. It is especially useful for problems that involve comparisons, part- whole calculations, ratios, proportions, and rates of change. It communicates graphically and instantly the information that the learner already knows, and it shows the student how to use that information to solve the problem.
        "Singapore's [Primary Mathematics] textbooks are used in more than 600 schools in the United States and also by many homeschoolers. The books were discovered and drew high praise when mathematicians and teachers investigated why Singapore scored so high on international math exams. Homeschoolers and teachers like them for their simple and effective approach. Mathematicians like them for their logical structure, coherent curriculum, and focus on the skills necessary for success in algebra.

  • One Step Ahead of the Train Wreck by Barry Garelick, Education News, May 15, 2009. HIGHLY RECOMMENDED for teachers and parents looking for a way to teach math to kids before they have to face the insanities of Everyday Math. The author provides plenty of insight into how Everyday Math fails kids, and gives very helpful and encouraging advice about addressing some of the school-based nonsense through home use of the extremely effective Singapore [Primary Mathematics] program.

  • New Equation: As Math Skills Slip, U.S. Schools Seek Answers From Asia; Singapore's High Test Scores Win Over Some Educators by Cris Prystay, The Wall Street Journal, December 13, 2004

  • What the United States Can Learn from Singapore's World Class Mathematics System (PDF) by Alan Ginsburg, Steven Leinwand, Terry Anstrom and Elizabeth Pollock. AIR Report, Jan 2005.

  • We All Have A Lot To Learn: Singapore's Students Do Brilliantly In Math And Science Tests by Fareed Zakaria, Newsweek, Jan. 9, 2006

  • News report on Singapore Primary Mathematics, WBBM-TV Chicago Channel 2, May 26, 2000:

    Singapore Primary Mathematics at home

    Singapore Primary Mathematics is used in more and more private and public schools. It is also very popular with homeschoolers, and is quite suitable for use at home for tutoring. Here are some U.S. sources for Singapore Primary Mathematics:

    • SGBox: Singapore's Best Selection carries all of the Singapore textbooks, plus other materials and books. The webpage has an extensive set of links to articles, reviews and suggestions on using Singapore Math.

    • This site concentrates specifically on Singapore Primary Mathematics books, and the website also has links to information and quick tests for determining correct placement in Singapore Primary Mathematics.

    • Sonlight curriculum: this company sells primarily to Christian homeschoolers, but they have good write-ups and discussions that would be of interest to everyone else as well. In their section on Singapore Primary Mathematics, they provided an extended discussion, listing benefits but also some faults of the program, and some interesting comparisons with other programs.

    • Also try searching for Singapore Primary Mathematics on Amazon and eBay.

Singapore -- OTHER Programs

    Your school is considering something labelled as "Singapore Math"? Well, be careful and don't get fooled by fuzzy constructivist math dressed up in borrowed finery.

  • A U.S. distributor of the original and effective "Primary Mathematics" curriculum reports,
      "The HMH (Houghton Mifflin Harcourt) program, Math In Focus, is based upon My Pals are Here (MPH), a series that is currently the most widely used in Singapore. Math In Focus does not resemble MPH Maths in outward appearance, with hardcover textbooks, for example, and has the look of a typical American elementary mathematics series. MIF is an Americanization of MPH Maths, in other words. In any case, MPH Maths is a less rigorous program than Primary Mathematics, reflecting changes Singapore made to the mathematics syllabus over the past several years. This coming year will see yet another round of changes in Singapore and the introduction of some new mathematics programs. Meanwhile, we continue to see steady growth in the U.S. market for both the U.S. Edition and Standards Edition of Primary Mathematics."

Russian Math textbooks

    A series of Russian math textbooks by Enn Nurk and Aksel Telgmaa, and translated by Will Harte is now available from Perpendicular Press. We'll add more info on this highly structured program as we hear more.


    Here are links to several excellent resources for extensive reviews, comparisons and comments on many math programs and textbooks:

    • NYC HOLD Curriculum Reviews:
      Provides information about several fuzzy math programs.

    • Mathematically Correct: Programs
      This page of the MC website has extensive information about a wide variety of "fuzzy" math curricula. You'll also find info about effective math programs as well). Go to that site for extensive information about math programs.

    • Mathematics Program Reviews for Grades 2, 5, and 7: Reviews and comparisons of a number of leading math curricula, from Mathematically Correct.

    • Approved and unapproved math programs in California: This list of approved and unapproved programs is handy as a sort of a who's who among math publishers.

    • Middle School Math Curricula, What Works Clearinghouse (WWC), U. S. Department of Education. This report concludes that most of the mathematics curricula used in American middle schools cannot be proved to be effective. The review considered 44 curricula currently in use and reviewed the record of research on their effectiveness. For only five programs did they feel that there was adequate data on effectiveness. Click through to see what WWC said about research that is claimed to support the program used at your school.

Math Outside of School

    "How can I teach math to my child at home?"

    If your school has stopped teaching math in an effective way, it's up to you to make sure your child learns this vital skill. You cannot rely on your school to make up for a gap that they have caused, or to mend the errors of their way anytime soon.

    Your best course of action of behalf of your own children may be to take up the slack yourself. Here are a few alternatives you may wish to consider:

At-Home Versions of Great Math Programs

    Both of these excellent programs are readily available for at-home use, either for tutoring or homeschooling:

Kumon Math

    Kumon is a very popular math program that combines at-home daily worksheets with weekly visits to a Kumon center. Since parents are highly involved and much of the work is done at home, prices are kept much lower than at most other after-school tutoring programs. The strength of the program is mastery of computational algorithms, serving as a foundation for later understanding.

    As a downside, Kumon work focuses tightly on mastery of a single operation at a time, and then when that is accomplished, work moves on to something else with little looking back. So, there is almost no emphasis on mixed practice, or on maintaining skills that were mastered at one time. There is also almost no coverage of word problems, or putting math skills into practice. It is quite possible for a child to become very adapt and automatic at multi-digit division, say, but have little confidence on when division is to be used. (This is not an argument in favor of fuzzy math! Saxon manages to be extremely effective at maintenance and application, without resorting to endless constructivist games.)

    It seems that about half of Kumon students are trying to catch up in math, and the other half are trying to pull ahead. Many bright kids clearly do very well with Kumon, and the Kumon newsletter features them extensively. However, the newsletter says far less about weaker students. It is of concern whether their success depends on supplementing in the areas that are missing in the Kumon program.

  • Link to Kumon's website

Workbooks, Worksheets

  • There are many sources of good practice workbooks for polishing basic skills at home. Try looking for a teacher's supply store in your area. One publisher with excellent books of math worksheets is Kelley Wingate. Their worksheets are typically straightforward, comprehensive, and many have a single friendly cartoon that adds a bit of cheeriness without being distracting. Click here for some references from Google.

  • There are a number of websites that generate customized math worksheets on the fly. Here is a good one created by Dr. Richard Bechtold.

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