Scroll down and tell us what you think about math ed.
The level of mathematics achievement in our public schools is eroding. Educational advancement in the U.S. has traditionally lagged Europe and Asia in the lower grades. Society accepted this and partially rationalized it because we teach all of our children rather than those showing early promise. By grade 9, our students scored well against the rest of the world.
More recently, however, this disadvantage has become general throughout our public schools. Ironically, this lag is co-dependent with a concurrent trend to teach higher-level mathematics in lower grades. How can these two trends coexist? We contend that the answer is "dummying down" of the subject material. Long division is not often taught in the lower grades. Algebra is now being taught in the seventh grade, but with little factoring. The majority of 12-year old students aren't prepared for this type of abstract thinking. Teachers certified for junior high school usually have an elementary-education background and are not trained to teach the material. The early algebra introduction is then followed by geometry in eighth grade. Again, neither the student nor the teacher is properly prepared. The result: an induction-based thought process, without formal proofs, development of analytical thinking, or logic. Then comes an Algebra II course without proper prerequisite material, followed by advanced math and calculus, again lacking the proper foundation. Textbook companies conspire in this, properly stressing PC presentation but lacking rigor.
How important is this problem? Dilution of our math curricula is certainly one of the primary reasons. Secondary mathematics is the primary resource for teaching our students to think objectively, logically, and analytically.
What is the remedy? Include more repetition of low-level math skills in lower grades. Students must be taught math skills both with and without the hand-held calculator. Math with the computer is also helpful, but only as an adjunct to traditional skills. Encourage a thorough introduction to algebra in the eighth grade. Fill the JHS void with skills in business and personal math fundamentals, such as balancing a checkbook, and engage in activities that build visual thinking skills to prepare for the abstractions to follow. Move Algebra I back to the ninth grade for most students, building on the skills introduced the previous year. This moves geometry to 10th grade, where mature minds can grapple with abstract concepts, and Algebra II to eleventh grade. This allows for both ample repetition and inclusion of some of the elements of algebra now considered "optional." Twelfth grade leaves room for trigonometry, probability and statistics, and a reasonably thorough introduction to differential calculus of, perhaps, six weeks. This recommendation is exclusive of advanced "Honors" classes. There is advantage in honors math only if it is truly "advanced". When parental wishes and other political issues temper qualification, it not only loses its purpose, but forces weaker curricula to allow slower students to catch up. Ideally, honors Algebra I in the eighth grade will eventually lead the successful student to advanced placement calculus in the twelfth and on into college. Otherwise, it has little purpose.
Larry & Sylvia Roberts
Larry is engineering manager at Besi Die Handling; Sylvia teaches math in New Hampshire.