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The Valley Reporter
P.O. Box 119
Waitsfield, VT 05673

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It's the Vermont Math Standards that are the problem


By Marc Lanser

Superintendent Bob McNamara's well-meaning letter addressing the need to strengthen math performance in the district neglects the true underlying cause of the dismal performance of Vermont's students in international assessments of mathematical understanding.

After acknowledging the well-known fact that American students perform at the bottom of the list of developed and developing nations in international math assessments, Mr. McNamara suggests that greater adherence to the Vermont Framework of Standards (2000) and the subsequent Vermont Grade-level Expectations (GLEs) (2004), as recommended in last year's Audit, would begin to remediate this critical deficiency. In fact, this problem has nothing to do with adherence to the Standards or in meeting the GLEs, and everything to do with the Standards and the GLEs themselves.

The Standards and the subsequently clarifying and operative GLEs (which were drafted in response to No Child Left Behind-NCLB) are horrifyingly deficient in their content, rigor and explicitness. In the only published comparative analysis of all states' math standards (written by Klein et al (2005) for the Thomas B. Fordham Foundation based in Washington, D.C.), the Vermont GLEs received a grade of "D" (the other two states that collaborated on writing the GLEs, Rhode Island and New Hampshire, both received "F"). While VT is in good company with its poorly-designed math standards (29 states received "D" or "F"), the failure of Vermont's educational leadership to seize the opportunity presented by NCLB to strengthen its weak Standards can be interpreted as being due to either gross negligence or a cynical attempt to "game" the system by "lowering the bar" for measuring success on NCLB-mandated tests, all to the serious detriment of our students.

In response to the growing "crisis" in U.S. math performance and in distinct contrast to Vermont, Massachusetts and California took seriously their responsibility for their students' math futures and revised their standards to bring them up to world-class level. These two states (and Indiana) received an "A" grade in the above-mentioned comparative analysis of state standards. To those who doubt the objectiveness or the validity of this comparative analysis, all of the states' standards are readily available on the internet. Even a cursory side-by-side comparison of the Vermont math standards with those of California will validate these points.

By way of examples of vagueness and incoherency, the Framework calls for students in grades five to eight to "multiply and divide rational (fractional) numbers." However, the sixth-grade GLE does not mention multiplication and division of fractions but instead expects that the student "accurately solves problems involving single or multiple operations on fractions (proper, improper, and mixed), or decimals; and addition or subtraction of integers; percent of a whole; or problems involving greatest common factor or least common multiple." So, does the "single or multiple operations on fractions" in the GLE refer to multiplication and division, or just addition or subtraction> Does a sixth-grade teacher conclude that multiplication and division of fractions should be taught in the sixth grade, or are those skills to be taught in seventh and eighth grade? And what is the expectation for "addition or subtraction of integers" doing in sixth grade? That belongs in third grade (unless it implies operations with negative numbers, which are not mentioned otherwise). If you believe that this is nitpicking, or is an isolated example, please read, or attempt to read, the Vermont Standards and the corresponding GLEs.

Time or space does not allow for discussion of the genesis of the drafting of the Standards or GLEs for the Vermont Dept. of Education, but suffice it to say that I was unable to find any professional or university/college mathematicians among the contributors. Additionally, the same group of non-mathematics professional educators involved in drafting the Standards, GLEs and the Audit that Mr. McNamara refers to in his letter (more about that below), also recommended certain curricula that were deemed to "align" with these Standards. Two of these curricula, Investigations in Number, Data and Space and Everyday Math, which are used by the majority of elementary schools in Vermont, have been widely disparaged by mathematics professionals across the country as being superficial, devoid of serious mathematical content, and lacking coherent progression of topics. In most, if not all, published rankings of the various math curricula being implemented across the country, Investigations and Everyday Math invariably receive the worst assessments. Investigations in particular has been singled out for its incoherency, superficiality and lack of content. Most districts (including all in California and Massachusetts) that adopted Investigations in the '90s have abandoned it, though ironically enough, local Vermont schools adopted this program in 2003-2004, when testimony to its inadequacies (or at the very least, the extreme controversy) was readily available to anyone who bothered to do the least due diligence on this program.  

The solution to the problem highlighted by Mr. McNamara is therefore not, as he advocates (and as recommended in the referred-to Audit), to ensure that all district schools adhere and perform to the Vermont Standards but to completely rewrite the Standards and the GLEs to align with world-class standards, as exemplified by those of California and Massachusetts. Vermont GLEs were written AFTER those of California and Mass. And, with little expense and far greater results, could have simply been adopted wholesale from those states. Obviously, local political and professional self-serving interests precluded such a solution. Unfortunately, though this solution is still possible, I believe that political and special interest considerations will impede the overhauling of Vermont mathematics standards and curricula. Our children will ultimately pay the price of maintaining this status quo.

Lanser lives in Fayston.

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