In the 2002 Puerto Rico Department of Education Mathematics Standards, which adhere to a, so called, constructivist philosophy of education, can be found an excercise for kindergarten students entitled:
Activity: Animals in the farm
In this activity we read: The student will complete a bar graph showing the number of animals in the lamina provided.
The activity described is perfectly reasonable for the grade level. However, the coverage of the topic of bar graphs in later grades is symptomatic of a lack of balance. In Appendix 4, Destrezas Prueba Diagnóstica, we find
Third Grade: Interpret bar graphs.
Fourth Grade: Interpret bar graphs.
Sixth Grade: Interpret information in a bar graph.
Eighth Grade: Interpret bar graphs.
Then, as if this were not enough, we find in Appendix 6, an activity on bar graphs for the ninth grade entitled Empleo y Tendencias in which we read the following idiocy:
2 out of 4 points will be given for completing a bar graph with 3 or more errors.
Since there exist arbitrarily large numbers greater than 3 the graph can be infinitely wrong yet still score 50%. It does not take a rocket scientist to understand why students drop out of school. No drill and kill is one of the mantras of constructivists yet here is an example of an essentially trivial topic repeated ad nauseam over at least 9 years. Moreover, syllabi indicate that most students will see this topic again in the university. After remedial mathematics courses, statistics is the most widely taught course in universities. It may be that what is intended is an instance of what some educationists call “spiral learning”. If this is the case it seems that in the step from sixth to eight grades, the student undergoes a descent of the spiral. There is too much emphasis in the PR-DOE Standards on non fundamental material such as elementary statistics and exploratory data analysis. For a student well trained in elementary foundational mathematics, this type of activity is utterly trivial. [More]
Philip Pennance 2002-07-02