Math Pace

There is no speed limit for talented students

The US middle and high school math system consists of Prealgebra, Algebra 1, Geometry, Algebra 2, and Precalculus, followed by AP courses: AP Calculus AB, AP Calculus BC, AP Statistics, AP Computer Science, etc.

The names of Prealgebra, Algebra 1, Geometry, and Algebra 2 do not make much sense, since different states have different names for their math courses, and the spiral learning method requires a lot of repetition.

In contrast, the names of Precalculus, Calculus, and any courses beyond Calculus, make perfect sense. The reason is that Calculus and beyond belong to college, not K-12, and Precalculus includes everything that are needed for Calculus.

After studying the public K-12 math curriculum in Alabama, I think it is reasonable to expect students to follow the so called fast track:

• Grade 6: Prealgebra (everything before algebra; also touches linear equations and quadratic equations)
• Grade 7: Algebra 1 (emphasizes linear equations and linear functions; also touches a little bit of quadratic equations, polynomials, exponential, logarithmic, and rational functions)
• Grade 8: Geometry (emphasizes planar geometry, concentrating on computations but not proofs; also touches a little bit of solid geometry, namely the volumes and surface areas)
• Grade 9: Algebra 2 (emphasizes quadratic equations, quadratic functions, polynomials, exponential, logarithmic, and rational functions; also touches conic sections, trigonometric functions, and the concept of matrix)
• Grade 10: Precalculus (Review and hopefully deepen the understanding of everything students have learned in Algebra 2; also touches a little bit more about analytic geometry, vector analysis, and the concept of matrix)

I am aware that there is no speed limit for talented students. Some school districts allow even faster tracks, Grade 5 (prealgebra), Grade 6 (Algebra 1), Grade 7 (Geometry), Grade 8 (Algebra 2), and Grade 9 (Precalculus). This will allow students to take AP Calculus in Grade 10. It appears that even in our school district students can double-up so that they can finish Algebra 2 and Precalculus in Grade 9, and take AP Calculus in Grade 10. I am not completely convinced that this is the best practice. Based on my teaching experience, many students struggle in Calculus not because they can not understand the basic ideas of differentiation and integration, but because of the lack of knowledge that they should have learned in Algebra 2 and Precalculus. If it is up to me to design a course in precalculus, I would require students to spend a solid year in precalculus, to strengthen their understanding and techniques about all those fundamental functions, and develop their abilities of logical reasoning and writing.

We should try our best to avoid the abysmal situation of A MILE WIDE AND AN INCH DEEP. After all, students will continue their studies in college, and for some, in graduate school.