Dumbing Down Mathematics – Part II
In my last article for www.thetentacle.com, I described the goals and strategies used by so-called “reform” educators in their pursuit of mediocrity in American mathematical education.
I mentioned how this is not the result of an evil conspiracy, but of an honest effort to elevate the math achievement of some traditionally disadvantage groups of students – by lowering standards and dumbing down traditional mathematical content and its delivery to such students.
The “math wars” between traditionalists on one hand, and “reformers” on the other, have been with us for many years. Redefining success and obscuring failure are the trademarks of the “reform” movement.
The methods of the reformists include the following:
** Group Learning and Group Tests.
** Overuse and excessive reliance on calculators.
** Undue emphasis on “projects” of dubious value.
In today’s column, I’ll be adding the following four methods to the reformists’ bag of tricks.
Authentic Assessment – One of the greatest evils from the reform perspective is objective testing; it would have to be because these measures can identify failure.
Many arguments are advanced for this perspective. The proposed alternative is frequently called “authentic assessment.” Translating this bit of jargon into English isn't easy. Basically, it refers to a variety of procedures that involve less mathematics, more writing or talking, and very subjective evaluation.
In the worst instances, students suffer if they do not support the intended politically correct perspective in their response. Politics aside, these methods are reliably unreliable. The subjective nature leaves little opportunity for valid information to be obtained. Sometimes one cannot even tell who actually did the work. In the long run, many invalid assessments tend to average out and, again, real differences in achievement go undetected.
Standards – The reform movement claims to be based on standards, although most parents will be surprised by what they find, and what they don't find, in reform standards documents.
It is contrary to the goal of the reform to produce explicit statements about what students know and should be able to do – again, spotting failure would be too easy. Consequently, the reform movement produces standards that are so vague that one cannot tell whether they have been met or not.
Any attempt to write tests for these standards, for example, will be unreliable because the required content is unclear. Reformers hate lists of clearly stated objectives and call them laundry lists. Vague learning expectations, however, are effectively the same as no learning expectations at all. Again, it becomes impossible to differentiate success from failure.
Strands – When attempts are made to subdivide mathematics into content areas, such as algebra and geometry, the subdivisions are often called “strands.” The reform movement uses this technique, while simultaneously avoiding explicit content. Thus, all of the elementary school work with arithmetic falls into one strand which becomes just one of many topic areas students are supposed to address.
Consequence: Students can still succeed while failing in arithmetic. The same thinking reduces algebra to just one component of mathematics in later grades with similar consequences.
Pedagogical Fads – The reform movement places great emphasis on classroom methods, such as those that involve groups, calculators, activities and projects, explorations, art work, and non-mathematical themes. The heavy emphasis on style takes attention away from mathematical content.
As teachers attend to implementing these processes, their evaluations of students become biased toward process and away from content. Mathematical learning will often take a back seat to artistic ability, cooperation, or even political correctness, thus blurring the distinctions between success and failure when it comes to learning mathematics.
With the demise of our ability to differentiate success from failure, the reform movement will claim broad successes. American school systems have the uncanny ability to claim improvements and reforms year after year, while the content is gradually leeched out of the system.
Meanwhile, fewer students will suffer wounds to their self-esteem as their failures go undetected. Such a system will identify fewer failures among poor and minority group students, so reformers will claim a victory for equity.
Unfortunately, success in this approach will have lost its value. The claims of success operate like social promotion as applied to education bureaucrats.
We may gain some "equity" at the cost of achievement, but the more advantaged parents will continue to find ways to make sure that their children learn in spite the best efforts of the reform-minded.
Meanwhile, the net effect of the “reform” will be further deterioration in the mathematical abilities of America's youth. The majority of these students will not find alternative forms of education to make up this deficit.
Sadly, I’m afraid that it is from this majority that we will draw our next generation of teachers.