Hands-On or Minds-On?

Abstract mathematics is learned by usage, practice, and memorization. However, for a pragmatic influential political scientist, this idea is unacceptable. His solution?  The same as that of the influential progressive educator of the early 20th century: Just get rid of high school algebra, and instead, create “real-world” courses which teach students “how the Consumer Price Index is computed”, or how mathematics can be used “in art and music — even poetry.” And the idea that “real-world” problems are more effective than abstract symbolic manipulation is being constantly “confirmed” by thousands of (p-hacked) “studies” by progressive reformists, which “have shown” that pure math, such as multiplication table, is bad for students!

A new global report, however, based on how students from 64 countries answered survey questions that accompanied an international test, called the Program for International Student Assessment, or PISA, confirms what advocates of rigor in mathematics education and traditionalists have been saying all along. That applied-math instruction, or the way it is actually taught in classrooms, may not be serving students well. In fact, the report shows that

despite the fact that the PISA exam itself is largely a test of applied math, not equation-solving, the students with more pure math instruction were better able to handle PISA questions.

This report will most likely have little effect on how math is taught in US schools, and “research” results, funded in millions of dollars by the government, will be still pouring out — as they have been since the 1960s — that pure and abstract math instruction is detrimental to student learning … and the performance of students keeps deteriorating (75% of 12th graders failed a national math test in 2015), and the “researchers” convince the government that the solution to students’ failure is more funding and more “research!”

2 thoughts on “Hands-On or Minds-On?”

  1. Very interesting article, professor. The same anti-abstraction movements can also be seen in universities here in Iran. Loads of students and also instructors nowadays tend to think mathematics and in general, scientific theories are useless, outdated stuff which can be abandoned safely. I study engineering at university of Tehran. You would be surpried to know that the majority of my classmates and instructors actually hate mathematics!They assume that new technology and computer sofwares has made math something obsolete. I do not know where this is going but it is a real pitty that many wonderful minds today, spend their whole time fiddling with computer programmes and foucusing too much on them instead of doing some valuable work in science.

    1. Mohamad, It is indeed a pity, and one might say a disaster for our civilization, that abstract thinking is so absurdly devalued! I am particularly sad that Iran, like many other countries, is following the US education model, where practical application is the ultimate goal. American pragmatism is not unlike Roman pragmatism: while they did some engineering marvels, the Romans did not produce a single mathematician. One can argue that the Dark Ages were a direct consequence of the Roman lack of interest in abstraction. So, are we on the verge of another Dark Ages? Who know.

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