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A possible explanation for math failures in Montgomery County Public Schools

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On December 20, 2013, the Superintendent of Montgomery County Public Schools, Dr. Joshua Starr tweeted a link to a Washington Post article calling it an “academic obsession.” The author of the article asserts, in no uncertain terms, “To me, the recent [PISA] test results were no surprise: Of course East Asian kids test well.” It continues, “But the thing about testing is that it creates excellent followers, not leaders. Doing well on tests requires constant test prep. Granted, when it comes to buckling down and cramming for hours on end, Asians kids will beat their U.S. counterparts to a pulp. But give them a task that is not testable or not directly related to school, ask them to do something not for their college application but for themselves, and they’ll draw a blank.”

Yes, fealty to the rote learning deities is not without its inherent debilitating drawback, it creates followers not leaders; mavens of the letter grade, not minds that could move mountains.

Dr. Carol Dweck, whose work has been embraced by MCPS, sheds light on why the learning approach, which produces stellar test performance, is popular. She points out that student goals come in two flavors:

(a) performance goals, and
(b) learning goals.

Getting an A in a class is an example of the former; mastery of the subject matter is an example of the latter. The No Child Left Behind Act of 2001 (NCLB), for example, insists on performance goals: 100% proficiency by the school year 2013-2014. Similarly, MCPS quotas, such as“Algebra 2 by Grade 11 with a “C” or higher,” are de facto performance goals.

The lesson from NCLB is that performance goals tend to elicit teaching to the test. Indeed, as teachers are increasingly asked to teach subjects which require a high level of subject matter competence, for example calculus, teaching to the test is likely to become common place. It creates an illusion of learning and the mirage of good teaching.

Performance goals do not require a comprehensive understanding of the subject matter—by the teacher or the student. Instead, it simply lends itself to prescriptive teaching.

A simple example suffices to illustrate performance goals teaching. Students are taught that the axis of symmetry of the parabola represented by y = ax^2 + bx + c is the line x= -b/2a. No explanation or a derivation of this statement is provided. Consequently, when asked to calculate the axis of symmetry for y=4x^2 + 2x + 6, say, students simply plug in the value of the coefficients, a=4 and b=2 to calculate the axis of symmetry as x= -2/2*4. The ability to solve by prescription is a means of achieving performance goals, without an enduring understanding of concepts or principles.

Consider now, a hypothetical case where a teacher reuses the same assignments, tests, etc., for each and every cohort of students. There is little doubt that some students, if not many, will seek to coast through the recycled material by reproducing the work of their predecessors. In other words, earning a good grade can be reduced to a simple task of reproducing the solutions from the previous year. Indeed, if the teacher created tests were also recycled, students may, in this hypothetical case, do well. However, if the final exam were to be produced by an outside source, the formula for success breaks down.

What if, the grading schema was such that the final exam, under the right circumstances, wouldn’t make much of a difference to the final letter grade? Then, students would have little incentive to study for the final exam. Recent “steep failure rates in countywide tests” could simply be the consequence of this teaching paradigm. The "answers for failed math exams" may lie right before our very eyes.