In a recent NCTM President’s Message, Matt Larson’s “Mathematics Learning: A Journey, Not a Sprint” is a reminder that students should be considered for accelerated mathematics coursework (which is defined as skipping a course or two, mainly in middle school) if they must demonstrate “significant depth of understanding of all the content that would be skipped.” This is much broader than a narrow definition of mathematical ability through mere speed and accuracy with numeric computation and/or symbolic manipulation. From the post:
We must emphasize to parents, teachers, counselors, administrators, and students that the goals of learning mathematics are multidimensional and balanced: students must develop a deep conceptual understanding (why), coupled with procedural fluency (how), but in addition they also need the ability to reason and apply mathematics (when), and all while developing a positive mathematics identity and high sense of agency. All four goals are critical components of what it means to be mathematically literate in the 21st century.
In St. Vrain, we have a District goal of increasing student access and successful completion of Algebra 1 in 8th grade, and we also believe in our tagline, “academic excellence by design.” It’s the by design component that is worthy of our attention and efforts, ensuring students are on a pathway that encourages them to access and successfully complete a sequence of challenging mathematics courses throughout high school. For some, this sequence might allow access to college mathematics courses. That’s why our Guidelines for Recommending Advanced Middle School Math Students offer some guidance, yet are purposefully vague. We want to look at a comprehensive body of evidence (achievement data, classroom performance, student interest & goals, etc.) when recommending students for advanced mathematics courses, keeping in mind this is a multi-year decision and course trajectory that must continuously be reevaluated.
Beyond course recommendations, access and equity issues can arise when examining an accelerated mathematics program. Matt Larson offers the following questions from his post for reflection:
- What are the demographics of students in eighth grade algebra? Do they match your district’s overall demographics?
- What are the demographics of students in calculus or AP Statistics?
- How do the demographics change from eighth grade algebra to AP Statistics or calculus enrollment?
- Was the instructional climate not supportive of each and every student?
- Was the instructional focus not on developing depth of understanding?
- Were students accelerated into eighth grade algebra on the basis of computational proficiency, but without the conceptual foundation necessary to be successful in the long run?
One additional question to add: How many students that take algebra in eighth grade also take AP Calculus or AP Statistics (or beyond) in high school?
And two more questions to add for middle school: How do the demographics of students in advanced middle school mathematics courses (in preparation for algebra in eighth grade) match those of your school and our district? How are students identified to access these advanced courses?
As the recommendation and registration season for next year will soon be upon us, how would you and your school (or feeder system) answer these questions? What changes should be or could be made for next year to continue our St. Vrain pride of “academic excellence by design?”