This blog post originally appeared on the blog Math-World Liaison on December 9, 2017.
A recent post on the NCTM discussion forum Those Left Out of the Math Conversation underscores the need for serious dialog between high school and college math departments. The fact that we don’t physically cross paths much does not entirely explain the huge crack so many students fall through on their way to college algebra. Too much dialog is cut off at the wall of pride: “You can’t tell me how (or what) to teach.” Once we get past that, though, it appears we can make some serious headway.
I am pleased with Missouri’s new commitment to do better for its young who are seeking to make their livelihood in a 21st-century career. The Missouri Mathematics Pathways Task Force (MMPT) is addressing much of what Andrew Hacker said in The Math Myth: and Other STEM Delusions without cutting 15-year-old students off at the Algebra 2 gate, as Hacker suggests, by making Algebra 2 “optional.”
The Missouri plan was laid out in a report submitted by the MMPT on June 2015. Their work has recently resulted in breaking down College Algebra into three options for Missouri college students who are not pursuing 4-year engineering degrees:
This plan, that virtually all MO colleges are signing onto, is a great start. However, like most states, there are issues beyond just changing the titles of college math classes and tailoring the content to be more relevant. In many cases, major attitude adjustments will be needed on both sides of the trans-educational divide.
On the high school side, too many Algebra 2 teachers are unaware of the details in the shifts that were supposed to happen with the advent of the Common Core. As a result, we are continuing to turn off large percentages of our students from the path to success at higher levels. On the college side, as is often true of Algebra 2 teachers, math instructors may continue to think of math in a sort of monocular fashion based on the math classes they took. Professional development for adult education is often lacking for those who could benefit from it most: those teaching college freshmen. Most of what I see as a need for high school shifts I have explained in my blog. What I’m seeing at college is a little more fuzzy since I am no longer teaching at that level, and I only have my conversations with those who are there to glean insights. However, the following is a list of issues I believe we should be discussing:
- Colleges who care about their students need to have ongoing professional development for their instructors because their students’ learning needs are changing. Math should not be used as a weed-out class because, for starters, our students are not weeds.
- We tend to define “rigor” differently. Along with the Common Core, high school teachers define “rigorous” work as challenging, analytical, thought provoking, and with high-cognitive demand, and the Shift of Rigor as a balance between conceptual understanding, procedural skill and fluency, and application. I am hearing college instructors define “rigor” as more about memorizing formulas, theorems, and not letting students use calculators or other technology.
- Using color, animations and technology is not juvenile. A large portion of the population does not intuitively think like a typical math instructor. We need to understand how they are thinking and visualizing and bring them on board. I often hear wails of protests about using algebra tiles at the college level. Algebra tiles were never meant to be a permanent crutch, rather a gateway for connections. Young students progress from physical tiles to quick sketches and then, after practice and ability to visualize: symbols. Given the student population and job markets we have, we need to do what it takes to meet the needs.
- We define relevance differently. Our students want to know when, in real life, they will use the math we teach. Telling students they need to learn something because of what’s next quickly sabotages our credibility. Teachers using good inquiry learning do not hear that question very much. If we can’t realistically explain the relevance of what we teach, then we must question why students should have to learn it.
- Math concepts in the 21st-century workforce are shifting focus toward digital, data-driven contexts. Understanding those shifts is key to knowing how to present our content. Reading the Common Core State Standards for math would be a great way to start to see where those shifts have occurred in K-11. Note the suggested topics forth optional 4th year math classes. I highly recommend the progressions documents for a deep understanding of the paths of conceptual development.
For the sake of tomorrow’s socioeconomic health, I would like to invite readers to suggest how we can work together to close the gap. What forum could we use? What would be the medium? If not NCTM, then what?