Review of "A Core Curriculum"

Some comments on "A Core Curriculum"

Page 1: "A need to enlarge the scope of this Newtonian mathematics curriculum began to emerge as mathematics increasingly became a tool in the social sciences."

What exactly do social scientists need from math that is not covered by the standard curriculum? A course in statistics in lieu of pre-calculus or calculus has always been available for students so inclined. Beyond that, the traditional curriculum provides the training to "think mathematically" of which NCTMers are so enamoured. Replacing the "Newtonian" mathematics curriculum with a bunch of vaguely connected statistical concepts dooms students to a lifetime of misunderstanding and misapplying statistics to their daily lives. The unassailable fact is that calculus is still the keystone to understanding all of this allegedly "new" math.

Page 8: Dart Throwing Exercise - "Measure a distance eight feet from the target and place a piece of tape on the floor. Standing behind the tape, the dart thrower throws some number of times at the target."

The purpose of this exercise is basically to do a simulation to discover the percentage of darts that fall within the white area on the target. The mathematical point to take away is that the white area is 78.54% of the square regardless of how many circles are circumscribed in the square. Of course, the number of darts that could reasonably be thrown by the students is not even remotely sufficient to get a reasonable accurate approximation. Even if sufficient accuracy were somehow obtained, statistical fluctuations will ensure that the percentages will never be the same for all the scenarios.

Page 34: "Assessment matters: One approach is to incorporate more student self-assessment. Ask students to write a brief self-assessment after they have completed a written assignment. Writing in a journal is also a good way to get students to reflect on their own performance."

Page 37: "When the instructional emphasis is on concept building through situations reflecting real-world questions and activities, the assessment should be of a similar nature. Open-ended holistically scored questions, interviews, observation of group work, testing with the use of physical models like those used in instruction, and student self-assessment are appropriate approaches."

I will let these monuments of edu-speak stand on their own.

Page 73: "Our axiom is that concepts are more powerful than procedures and more accessible to more students."

Brilliant. Evidence? Experiments? Research? Fuggedaboutit. Assume the very statement you're trying to prove. Then nobody can challenge you. You'd think mathematics educators would be familiar with the meaning of "axiom," but let's go through the motions. "A self-evident or universally recognized truth; A self-evident principle or one that is accepted as true without proof as the basis for argument." Should we really be accepting the statement above as an "axiom"? Come on now.

Page 113: "Old habits inconsistent with the new must be discarded."

Whether or not the old habits were effective and whether or not the new habits are effective.

Page 115: "The half-life of the education of an engineer has been estimated at ten years. In one decade, half of an engineer's training will become obsolete."

This statement is constantly used in support of the plan to replace "Newtonian" mathematics with a statistics-based curriculum. To me, this statement provides support for the diametrically opposite position. If engineers trained with "Newtonian" mathematics can survive the obsolescence of half their knowledge base and continue to function effectively, then this is precisely the training we should give everyone.

Page 117: "Use inductive reasoning to develop ideas where deduction requires too many underpinnings. Consider postulating important chunks of content, then use deductive reasoning from that base of understanding. Conclude coursework with modest deductive systems."

This would destroy the entire logical structure of the deductive system under investigation. As the NCTM should understand, the purpose of introducing deductive systems in high school is not so much to present the material itself but rather to present the concept of a deductive system. Presenting it in the way suggested above would destroy the rationale for doing this and eliminate any educational benefit in doing it at all.

Page 117: "Encourage students to investigate questions of interest to themselves."

Without the teacher controlling this process, most of the questions investigated will be of no value and irrelevant to the content. The uncomfortable (to the ed school powers-that-be) fact is that certain avenues of investigation are fruitful and most others are not; the teacher must provide this direction.