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newsletter — February 1, 2014

Advanced mathematics

Homeschooling parents often wrestle with the question: How much math does my highschooler need?

For college-bound students, the usual recommendations are as follows:

• The student must study at minimum algebra 1 and 2, geometry, precalculus/trigonometry.
• For consideration at the more selective colleges, it's recommended that they consider calculus, AP calculus, or statistics.
• If they wish to pursue STEM in college — or want to be considered for the most selective schools or scholarship programs — calculus is a must, and AP courses are strongly recommended.

But while you contemplate this advice, you might want to consider two dissenting points of view.

"The Wrong Answer"

Last summer, Harper's magazine published an article that questioned standard methods of teaching upper-level mathematics — specifically algebra 2 — entitled "The Wrong Answer: The Case Against Algebra II" (requires subscription). The author, Nicholas Baker, skewers one of the most widely used texts in America today:

The textbook's cover is black, with a nice illustration of a looming robotic gecko. The gecko robot has green compound eyes and is held together with shiny chrome screws. It has a gold jaw and splayed gold toenails. Perhaps you like the idea of robotic geckos, and you might expect, reasonably, that there would be something about the mathematics either of geckos or of robots somewhere in this book. There isn't. There is, however, at the beginning of Chapter 8 ("Rational Functions"), an interesting high-speed photograph of a basilisk lizard, also known as a Jesus Christ lizard, that is dashing on tiptoe across the surface of a body of water. A facing caption says:

Rational functions help explain how surface tension allows some animals to tread across a pond's surface. How can you graph rational functions and solve rational equations? You will learn how in this chapter.

But again you discover, to your disappointment, that the lizard image is just a bit of bait-and-switch. There's nothing about surface tension or walking on water in Chapter 8 — and indeed, the caption would puzzle an expert on reptilian locomotion, since basilisk lizards don't actually rely on surface tension to run on water.

This text has been carefully designed to conform with the new Common Core State Standards for math, which are slated to be imposed on all students in all states. But in this same text, Baker cites numerous passages containing mystifying concepts, indecipherable verbiage, and seemingly pointless exercises. This text, he concludes, is "a highly efficient engine for the creation of math rage..."

Baker questions the necessity of force-feeding algebra to all students regardless of their individual aptitudes, inclinations, or career plans. He goes on to quote a number theorist who is a longtime critic of math requirements in schools:

I called Dudley and asked him pointblank whether we should be requiring Algebra II of all high schoolers. "Good heavens, no," he said. "Forcing people to take mathematics is just terrible..."

He also quotes Derek Stolp, a math teacher for 30 years and the author of Mathematics Miseducation:

"Any implication that logical thinking is taught only through mathematics is plainly false," Stolp wrote, "and the argument that it is taught most effectively through mathematics is, at best, questionable." Stolp told me that although he loves teaching algebra, he doesn't believe children should be compelled to master abstract algebraic techniques that they find meaningless.

In the end, Baker concludes that the Common Core enthusiasts want to impose math on all students out of a good impulse: statistics show that students who do well in math are more likely to get into college. The problem, he says, is our circular logic: we made math a requirement for getting into college — so of course students who make it over this hurdle are more likely to end up there.

Another view

In an blog posting last fall, C.J. Westerberg argues that more engaging, interesting applications of mathematics are available to teenage students. These methods will not only leave the students in a better position to understand abstract mathematics; they will enthrall and motivate the students.

Westerberg echoes the dissenting academic voices who say that advanced mathematics should be a gateway, not a gatekeeper, to a successful college education. He cites learning styles as an important consideration when teaching mathematics to teenage students. He suggests "substituting other logic-inducing courses such as coding which may appeal to more hands-on learners who would like to produce something at the end of a day instead of just a grade score."

(Westerberg recommends Conrad Wolfram's TED Talk on math instruction.)

Our two cents

Many educators will admit that textbooks often fall pitifully short of engaging the curious mind of a teenager. Homeschooling parents must be vigilant in math, as they are in other subjects, to provide rich and meaningful content — even in mathematics.

The homeschooling students we know who find meaning in learning abstract mathematical concepts do more than just use textbooks:

• They join local high school robotics teams, like FIRST. The challenge is to find a team that accepts homeschoolers for a First Robotics (FRC) team. There is also the First Tech Challenge (FTC), a slightly less technical and less costly segment of FIRST; homeschoolers can more readily start a team.
• They take part in Science Olympiad. SO teams can be easily started and administered by a homeschooling parent.
• They conduct hands-on projects at home and exhibit their creations at local MAKER Faires or Mini-MAKER Faires.

As an illustration of this last point, consider the young man in our homeschool group who built a jet engine on his own because he was interested in learning more about engines and motors. You can read all about him — and even view photos of his jet engine — here.

The larger point here: We homeschooling parents always have to be looking at our student — and then tailoring our approach to his or her needs and interests. Granted, that approach may incorporate a standard text. But we must also ask ourselves: For my student, what's going to bring this subject to life?