Having some time off in summer is important to me, to help distill some core beliefs. When I read the Harper’s article that made it’s way around the blogosphere, it triggered me to put in writing some thoughts. A few things to note: (1) The school I teach in is an high school/early college, so instead of doing 11th and 12th grade, students complete Year 1 (Y1) and Year 2 (Y2), corresponding to the two years that they are considered as college students. (2) My school is highly functioning school, with many students that want to do well in math. I do not know whether I believe the thoughts described below would translate to a school with more challenges than my own. So, here goes:
9th grade math needs to be designed so that it is fundamentally important to developing a student’s reasoning skills. It should be so critical to all students that they should neither be tracked into “honors”/”non-honors” sections nor be allowed to “test out of it.” In the course, students must both demonstrate fluency with basic algebraic procedure and (more importantly) become comfortable with abstracting/mathematizing a problem using the language of math.
By the 10th grade, students need to start understanding their own interests, envisioning future career paths, and deciding for themselves whether theoretical math is of interest. Students should be choosing for themselves whether they participate in “honors math.”
For those 10th graders who don’t foresee math (or any of its applications) in their future, the focus on procedure in a traditional Algebra 2 curriculum is inappropriate. It’s far more important to instill within these students a sense of where math is beneficial to our society and a basic understanding of number sense, estimation, extracting information from graphs, and statistics. For this subset of students, working mechanically with rational functions, inverse functions, and complex numbers often decreases any appreciation they have for math and hurts them in the long run. For these students, our goals should be to (1) help them fulfill the basic requirements for whatever future college they wish to attend and (2) instill within them a healthy appreciation of the power of mathematics.
It is important that the decision students make in 10th grade should not prevent them from taking theoretical math in the college. Appreciation and interest in math comes for each person at a different stage in their life. It simply should be left up to students when they take their first steps towards college-level, theoretical math–maybe in 10th grade, maybe Y1, maybe Y2, maybe never.
I envision the following curriculum:
Algebra & Geometry
Students chose which one they wish to take:
i. Algebra & Trigonometry – with a focus toward big ideas and less on procedure
ii. Intensive Algebra & Trigonometry – a more traditional Algebra 2 course in preparation for college-level theoretical math
College Offerings (Y1 and Y2)
Theoretical math sequence:
i. Foundations of Theoretical Math – taken pass/fail, can be skipped by students who have already demonstrated a satisfactory level of algebraic proficiency
ii. Rational, Trigonometric, and Exponential Functions
iii. Limits: Infinity and Beyond
iv. Differential Calculus
v. Integral Calculus
vi. Multivariable Calculus
Survey Courses – no pre-requisites:
i. Statistics of Everyday Life
ii. Quantitative Reasoning & Creative Problem Solving
iii. Computing: Graphics & Games
iv. Explorations in Number Theory
v. Mathematics in Music and Art
…anything that a teacher would get excited to teach!!!!
Applied Math Courses:
i. Statistics (prereq: Functions & Statistics of Everyday Life)