FACT: In 2000, citing serious concerns, California Governor Davis resorted to the unprecedented move to establish Algebra Academies. The academies were to be summer schools for 7th and 8th graders, partly hoping to contain the damage from fuzzy math. Do we really want to repeat this in our schools? (source: "Old Math, Good Math" Los Angeles Times, 1/29/00 page B-7)

The Investigations website makes a weak attempt to provide impact reviews of their curriculum. A valid impact study must be largely free of biases, and clearly capture the program's impact upon students. But, their reviews are meaningless because the same people who developed Investigations also wrote their impact studies. So there was no independent review. However, our research did discover something revealing. The national backlash against Investigations clearly has its developers worried. Why? Because they wrote an entire strategy book specifically to aid school administrators and teachers. It's a complete handbook for handling concerned/difficult parents. Entitled, "Schools and Families: Creating a Math Partnership," it provides canned answers to frequently heard parental concerns and it even suggests unusual activities like sponsoring a "single Parent Night." But by far the most damaging section is the awkward admission that Investigations has been dumbed-down. We quote, "strategies for helping parents see the math in the work their children do." We readily submit that if you, as a parent, cannot tell where's the math, then the math has been dumbed-down by definition. Period!

Meanwhile in an attempt to boost its credibility, the Connected Mathematics website lists two impact reviews, one by Project 2061, and the other by the University of Washington Applied Mathematics Dept. The two groups were sponsored (predictably) by the National Science Foundation. Since both groups failed to maintain true independence, their studies were susceptible to positive bias. However, the University of Washington still identified several serious shortcomings of Connected Math. Furthermore, these identified weaknesses reveal just how far Connected Mathematics has been dumbed-down. We quote from Connected Mathematics' very own curriculum review (Adobe acrobat needed):
(italics & bold added)

• Failure to cover division of fractions: "CMP [Connected Math] and MIC [Mathematics in Context, another fuzzy math program] do not meet these new standards [i.e. the updated NCTM 2000 Standards] in the number strand, one of the most fundamental subjects in Mathematics. For example, division of fractions is not discussed at all even through 8th grade in CMP...." (Page 48) [KidsDoCount Note: The fact that Connected Math does NOT cover division of fractions is shocking!!]
• Failure to keep good students interested: "Moreover, we are skeptical about the possibility of maintaining the interest of high-end students while progressing at the [slow] pace necessitated by the discovery process...." (Page 49)
• Failure to prepare students for later math classes and college: "It is our prediction that students wishing to take calculus before the end of the 12th grade year [or college] are likely not to be on track to do so after completing 8th grade CMP [Connected Math]...." (Page 49)
• Failure to adequately cover fractions and decimals: "Fractions, Decimals, and Percents: CMP [Connected Math] and MIC [another fuzzy math] students do not work fluently with this topic: The calculations are on the whole too simple for these grades, especially those done toward the end of 8th grade.... Students are not working with general fractions to compare them by finding common denominators. By the end of the 8th grade, we feel this is a skill students should have. Instead they use a calculator, which converts the fractions to an approximate decimal form. CMP and MIC were designed to the 1989 NCTM Standards, which had very low standards with regard to fluency and skills involving fractions." (Pages 42-43)
• Failure to expand student's narrow understanding, -missing math generalizations: "CMP [Connected Math] and MIC [another fuzzy math] meet the 2000 NCTM algebra standard, although the mathematical level is much lower than that covered in the Singapore texts [country of Singapore was used as a comparision]. Generalizations and abstractions of concepts discovered and learned, which could have been easily included in the curricula, are mostly absent in the American texts [Connected Math & MIC]. It appears that this may be done deliberately in the authors' attempt to offer easily visualizable problems...." (Pages 49-50)
  "[Connected Math] falls short in follow through with more substantial statements, generalizations, formulas or algorithms. For example, in Growing, Growing, Growing [a Connected Math booklet] exponents are discussed, but the exponential laws are not explicitly written down even after they are discovered. In one exercise students discover that 2⁶ = (2²)³, but they need more practice to reach the generalization that (aⁿ)^m = a^nm ." (Page 11)
• Failure to broadly cover enough material due to excessive time spent in discovery: "A related comment is that discovery-based learning naturally takes more time than the traditional lecture-then-practice format." (Page 51)
  "Also, in order for students to effectively discover the mathematics, more time needs to be devoted to the lessons than in a traditional curriculum. The recommended minimum of 45 minute-long classes seems insufficient." (Page 11)
• Failure to cover/reinforce fundamentals, such as square/cube roots, quadratic formula, fractional exponents, completing squares, and multiplying/dividing polynomials: "There is no discussion of negative and fractional exponents except when students explore exponential functions using graphing calculators. As a result, students miss an oportunity to revisit square roots and cube roots...CMP [Connected Math] misses the opportunity to discuss the quadratic formula or the process of completing the square." (Page 11)
  "However, multiplying polynomials that are higher than the first order [meaning no variables with exponents, like x²] is not covered in the entire [Connected Math] curriculum. This could be because it is difficult to come up with a context for multiplying an area by an area, or it could be the result of a decision [by Connected Math's authors] that the topic is non-essential to a middle school student since it is not explicitly called for by the [weak] NCTM Standards. In either case, it is an omission which requires attention for students who wish to be on an accelerated track in high school. Similarly, the division of a polynomial by another polynomial of lower order is not covered, probably because it would have required conceptual understanding of long division at a level not covered by the [Connected Math] curricula...." (Page 50)
• Failure to provide fundamental math proficiency: "The number strand is arguably the most basic and fundamental mathematics strand and much of the presentation in CMP [Connected Math] is below the level articulated in the 2000 NCTM number standard for grades 6-8. Specifically we find that CMP students are not expected to compute fluently, flexibly and efficiently with fractions, decimals and percents as late as 8th grade. Standard algorithms [step-by-step ways] for computation with fractions...are not used." (Page 10)
  "We feel that CMP's overwhelming emphasis on conceptual development neglects standard computational methods [e.g. adding fractions, learning long division, etc.] and techniques. In our opinion, concepts and computations often positively reinforce one another. ...there is a danger here [in Connected Math] of producing students with conceptual understanding but limited computational skills. CMP admits that "because the curriculum does not emphasize arithmetic computations done by hand, some CMP students may not [will not] do as well on parts of the standardized tests assessing computational skills [e.g. basics like long division, adding/dividing fractions] as students in classes that spend most of their time practicing such skills." This statement implies that we [Connected Math] have still not achieved a balance between teaching fundamental ideas and computational methods." (Page 11)
• Failure to provide appropriate math skills and rigor: "As mathematicians and applied mathematicians, we feel that a major shortcoming of the two American curricula [Connected Math and MIC], ironically, is that they adhered to the 1989 NCTM Curriculum Standards too literally at the expense of the level of the mathematics taught and the mathematical proficiency of the students." (Page 48)
  "The Algebra level in CMP [Connected Math] and MIC appear to be almost two grade levels lower than in the Singapore materials. Division of one polynomial by another or multipling two polynomials of order higher than one is not taught even by the 8th grade in these [Connected Math] American curricula." (Page 43)
  [In the 2000 NCTM Standard for fractions, which Connected Math will try to follow], it appears to suggest that division [of fractions] should be done by repeated subtraction (such as in the cutting ribbon example), which is a flawed algorithm in our opinion and not generalizable to all fractions. Although such a conceptual understanding could be taught as one of the many ways for understanding the meaning of division of fractions, there is a danger here that the curriculum developers may interpret this guidance as the definition of fluency required and stop at that level. To us, doing division [of fractions] by repeatedly cutting off pieces of a ribbon does not remotely demonstrate "fluency." (Page 49)
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