Skip to content

Math education

In a discussion between Dave Jones and Jack Ganssle (YouTube) the topic of engineering education came up. This centered on the requirements for calculus despite neither of these experienced electronics engineers recalling having ever used integrals or differentials in their careers. The issue is one of training versus education. Engineering curriculum in colleges is particularly vexed in trying to decide about what skill set their graduates must have – which is easy to measure – and what education they must have – which is difficult to measure. An education prepares a student to go out and find what he needs to know and to be able to acquire necessary skills on his own.

Kevin Knudson describes one effect of this dilemma in The rush to calculus is bad for students and their futures in STEM

Another factor that must be considered is the overall decline in support for enhanced education for gifted students. In an era of shrinking education budgets, school administrators find it tempting to conflate advancement with enrichment. Pushing gifted students ahead at a faster rate via AP courses is seen as a solution for meeting the needs of advanced students.

This approach may be dangerous in any discipline, but it is especially problematic in mathematics, where a strong foundation is key to success in upper division courses. The general strategy in high school is one of uniform advancement – taking advanced coursework in all disciplines under the assumption that gifted students are exceptional in every subject. In the drive to make it to calculus by the senior year, students often rush through algebra and geometry in lockstep with their gifted peers whether they are ready for it or not.

The end result is a group of students who have “succeeded” in high school calculus without really having the proper foundations, a tower built on sand. It is quite possible for students to learn the mechanics of many categories of calculus problems and to answer questions correctly on exams without really understanding the concepts.

Here, the dilemma is labeled as “advancement” versus “enrichment.” For example, if we can program a computer to do it, it is advancement. That is the ability to follow a fixed set of rules to arrive at a ‘correct’ answer to a well stated problem. Enrichment is a matter of understanding the problem and proposed solutions in the realm of a set of values to be able to see good, better, and best.

The climate change brouhaha is an example. The ‘advanced’ are looking at projections of climate models as is to project doom and gloom. The ‘enriched’ are looking for what the models are actually saying to understand limitations, scope, and value.

Another area where a “strong foundation is key to success” becomes evident is in modern theoretical physics. This provides Luboš Motl with ammunition for some of his occasional rants because there are many who ‘just don’t get it’ when it comes to quantum mechanics and string theories in particular. 

Math can be [is] really rather simple. Understanding what you are doing is another thing altogether.