College Algebra is Not Pre-Calculus, and Neither is Pre-calc

“Everybody knows what college algebra is!”  This was said by a math chair from a university in my state, as we worked though our state’s new transfer requirement for mathematics.  Of course, he was wrong … though he has a lot of company.  Today’s main question is this:  Is college algebra a subset of pre-calculus?

The original college algebra course developed in the 19th century at the universities of the day (Harvard, Yale, Bowdain, etc), with a focus on meeting a math requirement for their degree.  Of course, those times were very different … the Yale Catalog listed every student, and every student had the same default schedule.  College algebra was everybody’s math course as a freshman; those ‘desiring’ calculus took it as a Junior.  See http://elischolar.library.yale.edu/cgi/viewcontent.cgi?article=1069&context=yale_catalogue

That tradition carries forward to the present day, in the work of the MAA.  The MAA College Algebra guidelines remain a narrative for a general education class, not a pre-calculus course.  See http://www.maa.org/sites/default/files/pdf/CUPM/crafty/CRAFTY-Coll-Alg-Guidelines.pdf

The use of the name ‘college algebra’ for a calculus prerequisite appears to be a regional variation.  In states use ‘college algebra’ as a prerequisite for pre-calculus; other states use college algebra as the first semester of pre-calculus … or as their one-semester pre-calculus (as in “college algebra and trig”).

Our situation has become illogical and disfunctional.

When publishers market their textbooks, sometimes the key difference between college algebra and pre-calculus is this: pre-calc emphasizes a unit circle for trig functions, while college algebra uses right triangles.  Other than that, the pre-calculus book has more complicated problems, but no substantive differences.  Both courses trace their ancestry back to the 19th century mathematics course later known as ‘college algebra’.  [Search for Jeff Suzuki’s talk on college algebra.]

Neither course is really pre-calculus.

Of course, I don’t mean “students can not take these prior to calculus”; they do, though the benefits are small and accidental.  A pre-calculus course would be designed to prepare students for the work of a calculus course.  We make the fatal mistake of equating the ability to solve complicated symbolic problems with the capacity to reason with those objects.

A good preparation for calculus begins much earlier for many students.  “Developmental” mathematics is being re-formed to focus on understanding and reasoning, with a de-emphasis on artificially complex symbolic work.  A mathematical literacy course is a better preparation for calculus than the traditional algebra course.

More importantly, Algebraic Literacy is where we can begin the serious work of preparation for calculus.  Intermediate algebra is a documented failure as preparation for college mathematics; algebraic literacy is designed deliberately for these purposes.  The Algebraic Literacy course has learning outcomes backward-designed to meet the needs of calculus preparation … to be followed by a well-designed course at the next level which completes that preparation.

Here are some conditions necessary for good calculus preparation, based on the available information:

• diversity of content (algebra, geometry, trig as minimum)
• non-trivial reasoning about mathematical objects
• concrete (context) and abstract situations
• properties of functions, and relationships between types
• reasoning and visualization involving related quantities (2, 3, or 4 at a time)
• procedural expertise and flexibility

I do not intend for this list to be exhaustive.  The intent is to focus on key outcomes so we can determine when we have a real pre-calculus experience that will work for our students.  It is my belief that the great majority (>99%) of our current courses used as a calculus prerequisite are not reasonable preparations for the demands of such a course.

Some of our colleagues are beginning the work of correcting the curriculum; we need to support that work when possible.  If you’d like to explore what the new curriculum would look like, the Algebraic Literacy course provides a good starting point;  I’ll be doing a session at the AMATYC conference (Nov 21, 11:55am) in New Orleans.

We can solve this problem, together.

 Join Dev Math Revival on Facebook:

A Simpler Vision: The New Life Curricular Model

I wanted to post a document I used for some college administrators, which helped them understand a different view of the mathematics curriculum.  This document is a simpler version of the one we have been using for math faculty.

Here is the simpler version:

The full version looks like this:

 
Join Dev Math Revival on Facebook:

STEM Path: Your Time has Come!!

The reform work, at the college level in mathematics, has focused on the needs of non-STEM students.  That work has been effective in creating a large, long-term impact on what students experience … as long as they do not need calculus.  Now, we can turn our attention to the needs of students on the STEM path.  #mathpaths #NewLifeMath #Mathways #Precalc

We need to understand, first, that our current STEM path is a weak design with a track record of poor results.  For example:

• In “The Pitfalls of Pre-calculus” David Bressoud shares some sophisticated research on the benefits of pre-calculus to different types of students; less-prepared students were not harmed by pre-calculus (not helped much either), and well-prepared students were actually harmed by pre-calculus.
• Most publicized research on remediation, which focuses on the transition from developmental to college level (intermediate algebra to college algebra/pre-calculus); the standard result in this research is “no benefit” for a significant portion of the population.
• We lack any body of research showing that our courses work above the developmental level (pre-calculus and calculus in particular).

The STEM path is too important to leave it alone, to accept the current sloppy curriculum as “good enough”.  The research is compelling, and we have other research providing guidance for better solutions.  Take a look at the work in co-variational reasoning, as well as the MAA Calculus Readiness test (those use related concepts).  Take a look at the book “Mathematical Sciences in 2025”.

Some curricular models to improve the STEM path are being developed.  The AMATYC New Life Project outlines content for Algebraic Literacy, which is designed to be an effective preparation for college-level mathematics like pre-calculus; the content is engineered for this purpose (unlike ‘intermediate algebra’).  I’ll be doing a session at the 2015 AMATYC conference on Algebraic Literacy (S149, Saturday Nov 21).

The Dana Center is developing its STEM path, with the Reasoning with Functions courses; that work is informed by the sources cited above, with these courses designed to follow a beginning algebra level course (Math Lit, “FMR”, etc).  In other words, their STEM path places pre-calculus immediately after beginning algebra.  The Dana Center will be doing a symposium at the AMATYC conference next month.

You have opportunities to be a part of this work, to make changes at your institution to help students on the STEM path.  Please consider taking advantage of these opportunities.

 Join Dev Math Revival on Facebook:

Our Students, Respect and Appreciation

So, I received a phone call today that really upset me.  Like most teachers at any level, “my student” is not just a reference … it describes the connection we feel to the people in our classes.  This phone call made me think, and changed how I think about my students.

This student (call her “Tami”) is in my beginning algebra course.  She’s not doing especially well, and has missed a class or two.  When she was not in class today, I did not think that much about it.

Tami left a message on my phone while I was in class.  I did not catch all of what she said, so I called her back and this is what she said:

I’m sorry that I was not in class today.  I wanted to make sure that you would not drop me.  I was in the emergency room this weekend because I got stabbed in the neck.

I thought about that a little bit … here is a person who had a real threat to her safety and continued survival, and she’s calling me about her math class.  How do my flimsy excuses for not taking care of responsibilities stack up against that?

Some people might be thinking “Jack, you’re so naive … did you think that the student might be either lying or ‘enhancing’ the truth?”  Actually, I did think of those possibilities; I’ll know more when I see Tami in class.  In the meantime, I chose to trust my students by default; that is not always warranted, but it sure helps in the efforts to build a positive classroom environment.

Sometimes, we are very quick to presume that students do not come to class because they don’t care.  Certainly, that is the case for some students … though I have more students who attend class in spite of the fact that they don’t care.

I realize that this is not a unique experience; you might have had a similar experience where a student had a ‘survival’ level experience and still showed some commitment to their math class.  However, the experience reminded me that many of our students deserve our respect and appreciation for dealing with the huge challenges in their lives … and still try to work on their math class.  For some, math class becomes their one safe space in a world of threats and chaos.

 Join Dev Math Revival on Facebook: