Friday, April 6, 2012

Thoughts about Alternatives to the "Royal Road" to Calculus

Continued from previous blog: Math Awareness month begins... what I would like to focus on is the third point NCTM made in the quote above: Technology as a tool should [..] influence what mathematics is taught. What mathematics should be taught in the 21st century? Should some of our sacred cows topics take a back seat? My take is that the math topics don't matter as much as long as they are embedded in interesting contexts that engage students in learning; mostly through well crafted projects. This will prepare students to effectively deal with the challenges of 21st century life. Can we collaboratively build towards this vision? cc blog 96

The NCTM president Michael Schaughnessy wrote this message to lead off this month's NCTM Summing Up newsletter:

Some Thoughts on Calculus and a Thank You!
Calculus is often viewed as the entry path to college mathematics. However, a high school calculus course should not be the be-all and end-all of mathematics, nor should it be the only transition path from high school to college mathematics. High school mathematics should prepare students not just for further, specialized study in mathematics but also for the variety of STEM (science, technology, engineering, and mathematics) careers and other professions that will be open to them in the future. Recently NCTM and the Mathematical Association of America (MAA) crafted a new joint position statement on the role of calculus in the transition from high school to postsecondary mathematics. 
Both NCTM and the MAA have found evidence that there are a number of strong mathematics students who successfully finish calculus before or in college and then happily announce that they “never have to take another math course!” As a result, we are losing large numbers of highly qualified mathematics students very early in their college careers. Many of these students are strong candidates for possible STEM careers—some of our best students, in fact. Also, we may be turning a number of potential mathematics students off by pushing them through years of a repetitive and overly narrow, algebra-focused mathematics curriculum, which doesn’t give students sufficient opportunities to broaden their horizons in other areas of mathematics, such as in various geometries, discrete mathematics, statistics, or linear algebra (February 2011 President’s Message, “Endless Algebra,” also discussed this pitfall). Read the entire message.
From "Endless Algebra" (Michael Schaughnessy, 2011):
[...]The Common Core State Standards provide us with an opportunity to rethink the sequence of school mathematics, as well as a challenge to provide exciting new pathways and transitions from high school to college mathematics. We need to offer students alternative pathways as they make their transition from secondary school and into colleges. The mathematics paths that we provide for our students need to prepare them for existing fields that are changing rapidly, as well as for emerging fields—and for fields that don’t yet exist. In my view, the current deadly sequence of ever-repetitive and out-of- touch experiences in algebra—the sequence intended to lead students to a single variable calculus course—will not accomplish this goal. It is time that we replace the eternal algebra transition from high school to college with some viable and exciting 21st century mathematics alternatives.[...] 
For me this change is long overdue. What are your thoughts?
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  1. I'm not seeing how introducing algebraic concepts in 6th grade (specific reference: Standard 6.EE) is going to change the perception of mathematics education as a march to calculus. Or why it's necessary to teach all students about complex numbers (Standard N-CN) or proving trigonometric identities (Standard F-TF) absent calculus as a goal (sorry, but last time I checked, neither were necessary for statistics or discrete mathematics). I really want someone to explain how implementation of the Common Core changes what will be taught in high schools, as opposed to what I think will actually happen, which is simply the repackaging of current curricula in "Common Core" clothing.

    If the argument is that the Common Core will cause curricula to be developed that will prepare students for calculus, advanced statistics, or discrete math, well, great, but don't such curricula already exist? And how does the existence of the Common Core address the issue that the joint NCTM/MAA statement points to - the number of students who "march to calculus" and then never take another math course again?

  2. Yes, this "road" has been finely tuned and well worn. Nothing wrong with that... except that every student that wants to go to college is forced to take the road until they falter and quit from a state of fatigue. We need other paths for students who aren't interested in getting to calculus in high school but would much rather appreciate math for its importance in their lives and become competent everyday math users. That doesn't require mastery of the intricacies of the quadratic equation, only an appreciation for what it is and why its valuable in the study of math. That can be handled in a project based path which requires that knowledge but doesn't ask them to be an expert because they have to take the next step on the RRtC.

  3. Check out this alternative map/path/journey to/through calculus.

    If I was back in middle school, this map would have motivated me to explore this town called Calculus.