Saving College Mathematics

The problem with reality is that it tends to get in the way of where we want to go.

I’m thinking of two recent communications. One, a comment in response to a post here, suggested that the Common Vision will have the same fate as Calculus Reform al a 1990 … in other words, ‘n.s.d.’ (no significant difference), no impact, nowhere. The other, a presentation by a leader of the Common Vision work who suggested that we have reach a critical mass for modernizing college mathematics.

Both speakers are experienced professionals with a strong mathematical background. Both can site ‘data’ to support their conclusion, and both can be wrong. [No surprise to either of them!]

Before continuing, let us consider the three types of college mathematics courses: Developmental; Freshman/sophomore level mathematics; and upper division mathematics. Each of these types has a unique set of forces acting on it to either change or remain the same. The Common Vision report is directly related to the freshman/sophomore mathematics in particular.

Attempts to revolutionize freshman/sophomore mathematics have focused on part of a system. Both the ‘lean and lively’ calculus and college algebra ‘right stuff’ dealt with content, primarily. The AMATYC Standards (Beyond Crossroads) maintained a focus on processes (such as instruction or assessment), though “BC” was hardly calling for revolutionizing college mathematics.

We should consider what has led to a fundamental change in developmental mathematics. The process that is leading to long-term basic change (a good revolution) is driven by three compatible projects which focus first on the content and second on process. [These efforts are the Carnegie Pathways, the Dana Center Mathematics Pathways, and the AMATYC New Life project.] The three projects collaborate in basic ways, even though they could be seen as ‘competing solutions’.

For this purpose, I will ignore the co-requisite movement, which seeks to displace developmental mathematics without impacting freshman/sophomore mathematics in any significant manner. Such an effort has a low probability of long-term survival, though it certainly will create some unintended changes.

The developmental mathematics revolution is working (though it is not yet complete) because the work appeals to mathematicians and because the modern content encourages active learning methods. There is also a continuity with prior professional work, and the engagement of diverse stakeholders in the process.

If we seek to save college mathematics, the core of our work is the freshman/sophomore curriculum. A variety of forces are acting on this work to make ‘revolution’ difficult; even modest reforms seem to be too much of a challenge. However, I think the largest sets of forces in this matrix have their origins in us … the mathematics faculty of colleges.

We worry about ‘transfer’, and we sorry about ‘prerequisite material’. The transfer worry means that we don’t change because our sister institutions might decline the transfer … the prerequisite worry means that we don’t change because it might disrupt a mythical sequence of necessary steps. In many ways, the transfer worry feeds off of the prerequisite worry.

In many states, the transfer worry is managed by a state system. In most of these systems, the decisions are made by ‘us’ (college math faculty). Therefore, the transfer worry is a self-imposed set of forces to resist change. Clearly, the solution is to develop a consensus that change is needed … which means to support colleges who are willing to begin the revolution in mathematics.

Earlier I mentioned the ‘critical mass’ comment. This observation was based on evidence of process changes (mostly, in active learning and some social psychology) primarily in R1 institutions (research universities). Although these changes are welcome and help students, I don’t think the long-term impact will be anywhere near large enough compared to the problems we seek to solve.

College mathematics, especially freshman/sophomore level, is defined by content and structure defined by the needs of a 1965 education for a 1955 occupation (engineers especially). Any long-term solution has to address the known needs of today’s education for 2010 occupations (a more diverse list). Modern teaching methods are not enough.

Saving college mathematics requires that we change the mathematics. Sufficient information exists to develop a new system of courses. Instead of two college algebra or pre-calculus courses followed by three semesters of symbolic calculus … perhaps we can design a system with one pre-calculus course followed by two semesters of calculus which combines symbolic and numeric methods. People more experienced would know how to structure this work, so that both content and process are modernized.

We need to stop the pattern of ‘solving part of the problem’. Solving part of a problem is failing to solve the problem.

It’s time to build a college mathematics system that solves problems and serves our students. We can’t let “reality” prevent us, because often we are that reality.

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Math curriculum in general | Jack Rotman | October 31, 2016 9:42 am

1 Comment

By schremmer, October 31, 2016 @ 4:16 pm

Re.the ‘lean and lively’ calculus […] dealt with content, primarily.

Not at all: consider for instance the Harvard book’s gimmick to put linear and exponential growths side by side. That wasn’t content analysis and/or content architecture the way, e.g., Hestenes thought of it.

For another, much more important example, consider what everybody did with fractions and limits. Essentially left them as is.

So, this is not what I would call recasting contents. So, I stay by what I think I said earlier: if the 19th century research based content analysis is not changed, nothing good will happen.

To give an example, rather than shove ashamedly fractions and limits under the rug, why not make a clean go to decimal and polynomial approximations?

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