To solve the challenges confronting our nation so that we can continue to improve our quality of life, we must improve mathematics education, because mathematics is the cornerstone of our civilization. But our schools must provide more challenge for students in all mathematics classes to improve math education. State mandated restrictions and school district imposed curriculum limitations must be lifted to empower teachers to teach more and better math classes as well as for students to have the opportunity to learn as much math as they possibly can.
Listen to students discussing the perceived shortcomings in the quality of their education and the most commonly heard complaint is the lack of challenge especially in seventh and eighth grade math classes. While their parents readily agree, students feel as if their classes too often level down to the lowest common denominator. Students report that teachers spend too much time trying to raise the performance of the lowest common denominator while the more talented students as well as those most in need of instruction languish.
But the key causal factor for the lack of challenge is heterogeneous grouping within each class. Heterogeneous grouping is the inclusion of students of all levels of ability in the same classroom with the same teacher at the same time. No matter how well qualified is the teacher; however, not even a teacher highly trained in differentiated instruction can overcome the problems of heterogeneous grouping. Indeed, it is profoundly difficult to differentiate instruction well enough within a classroom of 20 or so students so that all students benefit equally. This forces the top students to enroll in Advanced Placement or Honors courses so that their skill levels can be stretched while those students at the other end of the continuum seek remedial assistance.
Tracking, on the other hand, is the grouping of students according to their level of ability in the same classroom with the same teacher at the same time. Tracking reflects the reality that students are not all alike. On the contrary, each student is unique and he/she learns in different ways, at different rates and performs best at varying degrees of course content difficulty. Grouping classes according to ability enables teachers to customize instruction so that the entire class not only learns more but also performs at a higher level of achievement. Those students at the polar opposite ends of the ability continuum are not disenfranchised. All students in every grade are able to raise their achievement levels.
But no student should be locked into any track especially one that is lacking in proper mathematics content and challenge for that student. Indeed, all students must be given the opportunity not only to improve their ability in mathematics but also to advance to a higher track level when they have demonstrated such improvement. Tracking is most effective because it enables students to benefit from the rigorous teaching of mathematics.
Why do American students especially those in seventh and eighth grade seem to lag behind those of other nations in mathematics? Perhaps it is because American students may not learn as much mathematics as do their international counterparts. Compared to other nations where mathematics proficiency is rather high such as Japan and Germany, American students do not seem to study the same amount of geometry, algebra and trigonometry in the seventh and eighth grades. Because the students of other nations attend more higher level math classes earlier in their school life, they are also able to study more and achieve greater proficiency in science courses especially physics including Advanced Placement physics. When these factors are combined with the fact that most American school districts have dropped tracking in favor of heterogeneous grouping, the mathematics education gap widens.
The one size fits all approach of heterogeneous grouping penalizes the students particularly at the upper and lower achievement levels while focusing a disproportionate amount of time on the lowest common denominator. As a result, all students suffer and do not learn as much as they possibly can. This leads to the dumbing down of mathematics education. Because learning mathematics is essential for all students, tracking provides perhaps the best way for all students to become highly proficient in mathematics based on the understanding that every student is unique in how he/she learns.