About Connected Mathematics Project (CMP)

Contained here are links to various resources about the Connected Mathematics Project (CMP) curriculum developed at Michigan State University and published by Pearsons Education. CMP was one of the four finalist textbooks selected by the LCHS 7/8 Mathematics Textbook Selection Committee in the 2016-17 school year in the La Cañada Unified School District (LCUSD.) For information about districts around the United States who used CMP, click here.

Basic Information:

  • Connected Mathematics (Wikipedia) – Wikipedia general description of Connected Mathematics program and curriculum content, its core principles, history, purported research findings, and controversy over its adoption. (Note: the article reads like a promotional brochure for the program. A careful reading of its Wikipedia revision history shows most of the contributions and changes to the “Historical Controversy” section come from IP addresses at Michigan State University.)
  • Connected Mathematics Project at Michigan State University – Home base for the group that developed CMP. Contains history about the development of CMP, its goals, research behind the curriculum, and resources for administrators, teachers and parents who use CMP. Did we mention CMP was developed at Michigan State University?
  • Connected Mathematics Project 3 (CMP3) – Publisher’s website at Pearson.com. Contains efficacy and validation studies of CMP2 as well as resources for teachers and parents.

Reviews of Connected Mathematics Project (CMP):

  • NYC HOLD’s Reviews of CMP – The New York City chapter of the Honest Open Logical Debate (HOLD), a grass-roots parent group opposed to implementation of reform-math curricula in their local schools, maintained a list of reviews about CMP content, as well as numerous articles written by frustrated parents and mathematicians about the CMP curriculum. Some of the more salient reviews of CMP are highlighted below.
  • Mathematically Correct’s Review of CMP’s Seventh Grade Curriculum – Mathematically Correct was a grass-roots organization of concerned parents and university math educators started in Southern California in 1995 to combat the then fuzzy math curricula that proliferated throughout California from 1992 to 1998 and decimated the math abilities of an entire generation of public school students. The organization reviewed most of the major reform math curricula of the time, including CMP. About the 1st edition of CMP Mathematically Correct wrote:

There is very little mathematical content in this book. Students leaving this course will have no background in or facility with analytic or pre-algebra skills.

Quality of Presentation: This book is completely dedicated to a constructivist philosophy of learning, with heavy emphasis on discovery exercises and rejection of whole class teacher directed instruction. The introduction to Part 1 says “Connected Mathematics was developed with the belief that calculators should be available and that students should decide when to use them.” In one of the great understatements, the Guide to the Connected Mathematics Curriculum states, “Students may not do as well on standardized tests assessing computational skills as students in classes that spend” time practicing these skills.

Quality of Student Work: Students are busy, but they are not productively busy. Most of their time is directed away from true understanding and useful skills.

Overall Program Evaluation: F

Overall Evaluation: This rating is perhaps deceivingly high, as 7 of the 11 topics rate no higher than 1.2. The rating is as high as it is based largely on two high subscores, proportions and graphing. It is impossible to recommend a book with as little content as this and an inefficient, if philosophically attractive, instructional method.

Click here for Mathematically Correct’s summary of all eleven 7th grade math textbooks reviewed at the time.

  • Education Research Analysts’ Summary Comparison of 6th Grade Math Texts Approved for 2007 Local Texas Adoption – In 2007 the major textbook publishers submitted 6th grade math textbook programs for adoption consideration by the Texas State Board of Education. Educational Research Analysts,  a self-described independent, Christian conservative organization, reviewed the seven textbooks that were approved by the Texas SBOE.  Click here for their top-level page describing the methodology of the textbook review committee. The seven programs reviewed included CMP2, Everyday Mathematics, Saxon Math, McDougal Math, Holt Math, and two Texas Math books from Prentice and Glencoe. The summary comparison chart shows how much practice is provided in adding, subtracting, multiplying, and dividing fractions and decimals; how quickly they teach problem-solving methods; and how well they build personal math skills. Of the seven programs reviewed, Saxon Math rated highest with the Best qualitative rating. CMP2 rated Worst of the seven. About CMP, ERA’s authors cited it as an example of bad pedagogy:
    • Multiplies laborious guessing at how to compute and problem-solve (inefficiency).
    • Takes much time to do this, with less time for practice (minimal automaticity).
    • Promotes calculator-dependence (not personal mental training) in computation.
    • Encourages peer-dependence (not individual skill building) in problem-solving.
    • Assigns complex tasks before mastering simple skills (reversing Bloom’s taxonomy).
  • “Math Problems: Why the U.S. Department of Education’s recommended math programs don’t add up” by David Klein, 2000 – In October 1999, during the height of the Math Wars, the Department of Education released a report designating ten math programs as “exemplary” or “promising”  (click here to read a newspaper account summarizing the report.) CMP was among the five programs designated “exemplary” (the other five programs were designated “promising.”) However, the DoE panel, its composition, methods and its findings were controversial, prompting an open letter to then Secretary of Education Richard Riley by 200 prominent mathematicians across the United States disputing the findings of the DoE committee (click here to read the letter.) Mathematics professor David Klein was one of the 200 co-signers of the letter of protest. The linked article was written by Klein in April 2000 describing the concerns of the 200 co-authors. About CMP, Klein wrote:

“The mathematics programs criticized by the open letter have common features. For example, they tend to overemphasize data analysis and statistics, which typically appear year after year, with redundant presentations. The far more important areas of arithmetic and algebra are radically de-emphasized. Many of the so-called higher-order thinking projects are just aimless activities, and genuine illumination of important mathematical ideas is rare. There is a near obsession with calculators, and basic skills are given short shrift and sometimes even disparaged. Overall, these curricula are watered-down math programs. The same educational philosophy that gave rise to the whole-language approach to reading is part of ED’s agenda for mathematics. Systematic development of skills and concepts is replaced by an unstructured ‘holism.’ In fact, during the mid-’90s, supporters of programs like these referred to their approach as ‘whole math.’ …

Calculator use is also ubiquitous in the ‘exemplary’ middle school program CMP. A unit devoted to discovering algorithms to add, subtract, and multiply fractions (‘Bits and Pieces II’) gives the inappropriate instruction, “Use your calculator whenever you need it.” These topics are poorly developed, and division of fractions is not covered at all. A quiz for seventh-grade CMP students asks them to find the ‘slope’ and ‘y-intercept’ of the equation 10 = x – 2.5, and the teacher’s manual explains that this equation is a special case of the linear equation y = x – 2.5, when y = 10, and concludes that the slope is therefore 1 and the y-intercept is -2.5. This is not only false, but is so mathematically unsound as to undermine the authority of classroom teachers who know better.”

  • An Evaluation of CMP by James Milgram, 1999 – An in-depth evaluation of the 1st edition of CMP by Professor James Milgram of Stanford University. Milgram concludes:

Overall, the program seems to be very incomplete, and I would judge that it is aimed at underachieving students rather than normal or higher achieving students. In itself this is not a problem unless, as is the case, the program is advertised as being designed for all students. In fact, as indicated, there is no reputable research at all which supports this.

The philosophy used throughout the program is that the students should entirely construct their own knowledge and that calculators are to always be available for calculation. This means that:

– Standard algorithms are never introduced, not even for adding, subtracting, multiplying and dividing fractions.
– Precise definitions are never given
 – Repetitive practice for developing skills, such as basic manipulative skills is never given. Consequently, in the seventh and eighth grade booklets on algebra, there is no development of the standard skills needed to solve linear equations, no practice with simplifying polynomials or quotients of polynomials, no discussion of things as basic as the standard exponent rules.
– Throughout the booklets, topics are introduced, usually in a single problem and almost always indirectly — topics which, in traditional texts are basic and will have an entire chapter devoted to them — and then are dropped, never to be mentioned again. (Examples will be given throughout the detailed analysis which follows.)
– In the booklets on probability and data analysis a huge amount of time is spent learning rather esoteric methods for representing data, such as stem and leaf plots, and very little attention is paid to topics like the use and misuse of statistics. Statistics, in and of itself, is not that important in terms of mathematical development. The main reason it is in the curriculum is to provide students with the means to understand common uses of statistics and to be able to understand when statistical arguments are being used correctly.

In the spring of 1999, the PISD School Board voted to adopt the controversial Connected Mathematics Project textbooks for use in all Middle Schools beginning in the Fall of 1999. When these textbooks were reviewed for compliance to the Texas Essential Knowledge and Skills elements by the Texas Education Agency, they failed to address an average of 43.3% of those elements at each individual grade level. The teaching of Connected Math is characterized by group discovery of mathematical concepts with an emphasis on problem solving, communication, reasoning and connections (the National Council of Teachers of Mathematics goals). It also emphasizes student-directed learning (the student learns what he is interested in learning), cooperative instruction (students teach each other), teachers as facilitators (as opposed to direct instruction), use of calculators (students access information instead of acquiring basic facts and skills), and a focus on applied learning.
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One of our main concerns are the complaints of parents who attempt to help their children with their homework. We have been told stories of hours spent at the kitchen table, not so much to get an answer to the problem, but more to figure out what the problem was asking!! In addition, parents tell us that their child will indicate to them that they understand the concept, feel pretty good about doing the homework, and then do poorly on the quiz or test designed to measure the student’s understanding. Sometimes, days are spent in class discovering one conpcept, and then the quiz indicates that the kids just don’t get it! We cannot possibly afford to re-teach all that material and still expect to complete the required curriculum.

“… 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.”