What’s up with pre-calculus?


Pre-calculus is an odd mongrel of a course.

It’s name suggests it’s preparation for calculus.

The course content, commonly involving polynomials, exponential and logarithmic functions, trigonometry and circular functions, suggests the intent of pre-calculus is indeed preparation for calculus.

But there’s something rotten in the state of pre-calculus.

Several people responded recently to a tweet about pre-calculus apparently not working as calculus preparation for about 50% of students who pass it:

Julianna Stockton ‏ (@DrJStockton), April 29, 2012:

“what is the content of PreCalc? Ours (trig) more aptly named “NonCalc” than “Pre…”. Not setting up big ideas of Calculus”

Cody Coy Barlow ‏(@coach_barlow), April 28, 2012:

“math skills are watered down at the elementary school level. When kids can’t do fractions how do we teach calc?”

Jim Wolper ‏ (@DrATP), April 28, 2012:

“Many pre-calc students at my university are given undeserved high grades despite demonstrated unreadiness for Calculus”

ANOVA Learning ‏ (@anova_learning), April 28, 2012:

“more than likely, because they are inadequately prepared for pre-calculus!”

Gregory Cover ‏ (@gcmathfilm), April 28, 2012:

“precalc doesn’t do the job because basic skills are poor coming into the class. I spend half my time teaching pc reviewing”

A colleague checked on several hundred students who were placed by an Accuplacer test into college pre-calculus. Of those students who passed pre-calculus and went into Calculus I, only 50% obtained a grade of C or better.

This is like a coin toss: students place into pre-calculus, pass the course, yet 50% of them do poorly in Calculus I.

Can we say which students do poorly in Calculus I, and can we say why?

Can we figure out how to help them do better?

Is there something about the pre-calculus experience that is not adequately preparing about 50% of students for calculus?

Having discussed this with several other colleagues it seems to me that in pre-calculus classes we are facing a widespread lack of algebra skills, a lack of trigonometry skills, little to no time for preparation for ideas of calculus, a view of mathematics that is entirely procedural ( http://bit.ly/isyw5d ), poor study habits, likely failure to form study groups (http://bit.ly/IvhZ6k ) and a current lack of knowledge on our part as to who are the students that pass pre-calculus but get a D or less in calculus.

Another colleague, Jim Soden, adds:

“I tell my students that if they don’t earn in the mid 70s in Calc I, it doesn’t project well for their success in Calc II. And it doesn’t, by my observation. I am doing them no favors by skirting the issue, and the hard conversations have to be held. But the kids have to take Calc II so they press on. Many of these are committed students who do other things very well. Sometimes they get religion and do better in Calc II, but as a general rule, they struggle. The issue then, is what if anything we can do about the situation or is it, say, an Engineering Dept. decision? ”

Our observations on the parlious state of pre-calculus are not the first (and hopefully not the last):

  • “The failure rate in … precalculus courses can be so bad that as many as 50 percent of students need to take the class a second time. Ms. Thille and her colleagues hope to improve on that record while developing materials of such quality that they’re used by perhaps 100,000 students each year.” http://bit.ly/xPy7bI
  • “… data on UIC students confirmed that passing calculus was a major stumbling block for African-American and Hispanic students in entering into mathematics, science and engineering majors. For many UIC minority students with aspirations for a mathematics or science degree, the obstacle came even earlier, in pre-calculus courses. The staggering percentage of failing minority students exceeded 55% in pre-calculus courses.” http://bit.ly/IvhZ6k
  • “Success and Failures of a Precalculus Reform Project …  College algebra is often taken as a terminal course or as a prerequisite for precalculus or business calculus. Failure rates in both courses are high, and neither course has lasting value for those students who pass, but choose not to take calculus. The size of the institution and the need for transferability of credits between campuses make it difficult for an individual instructor to depart radically from prescribed course content. This limitation led us to conclude that we could improve the courses most effectively by providing innovative approaches to traditional topics.” http://bit.ly/InKXL4


Comments seem currently to have a glitch so I’ve posted the following comment from @suburbanlion as a postscript to the post:

“In high school, I skipped Pre-Calc and went straight into Calculus. I think that doing so was actually beneficial for me in the long term. I had a lot to catch up on about trigonometry and logarithms, but learning them in the context of Calculus seemed to give me a different perspective on them. While most of my classmates would relate the trigonometric functions to right triangles, I would relate them to the unit circle or differential equations. Perhaps the problem with Pre-Calc is that it requires a rudimentary understanding of Calculus to begin with?”

The changing nature of textbook publishing

I was told some  juicy information about academic textbook publishing last week.

A sales representative of a major textbook publisher discussed the medium term plans of the company as it re-thinks its role in publishing.

We discussed the high price of calculus texts for students, a topic close to my heart.

The new calculus book, previously only published in hardcover, will now be available as a paperback for  – wait for it! – a mere $150.

What a bargain!

Why do teachers of undergraduate mathematics, for example,  keep using these highly priced texts?

Answer number one

Because they are too lazy to write their own texts.

What makes them averse to writing their own texts?

By and large it is forming the problem sets and answers.

Which brings us to:

Answer number two

Because the big publishers now have online grading systems that pass the pain of grading home-works and possibly tests, to an online system that records results, does statistics, offers students hints, allows multiple re-takes, allows access to the book online, and gives short video lessons on difficult topics, among other things.

This is a big plus for teachers: homework grading is, for a number of reasons, one of the most irksome parts of the job.

Anything that relieves an instructor of this chore has to be good.

But at $150 a student?

The price is so steep that many students simply do not buy the book, and forgo the homework contribution to their grade.

What’s new in textbook publishing?

The e-book version of some undergraduate texts is now modifiable by teachers.

Suppose you want to insert a video you found on You Tube or elsewhere into the online version of the book.

No problem, you can do it yourself.

Suppose you do not like the author’s explanation of a particular topic.

No problem, you can modify the text with your own version.

Very flexible, and very useful.

However the author and publisher still get paid, and you do not.

What’s on the horizon?

This is the juicy bit.

Publishers – some of the biggest – are re-inventing themselves as facilitators and managers of learning.

What they want you, the teacher, to do is specify your learning goals and learning outcomes, and they will map a path through various resources – text, videos, and software applications – that will help achieve your goal.

The “textbook” per se is on its way out.

In its place will be a multimedia learning environment, managed ny publishers.

Who wins and who loses?

Teachers win in this scenario, in my view, because they get access to a rich array of learning resources.

Students and parents lose, in my view, because this will cost a lot of money and many will not be able to afford it.

My guess is that educational technologists will be in great demand by academic publishers.

I guees, too, that “star” teachers, those who can really make a lesson pop, will be in demand as video performers for publishers.

I am betting on multi-million dollar contracts for outstanding teachers.

These are interesting times!


Readers might like to take a look at the site:

ExpensiveTextbooksSuck. People coming together to defeat expensive textbook prices!