Prerequisites

Prerequisites are placed on courses for various reasons, from convenience to supporting student success.  Few prerequisites are placed on courses based on validation studies … some prerequisites are used based on professional validity, while others have even less of a scientific basis.

Let’s say that you are working for the department of education in a state such as mine (Michigan), and you have been getting more concerned about the possibility that academic standards are not consistent across regions or levels of education.  You look at mathematics, and notice that college courses use a different organizing system than high schools … and you do not want students to get credit for a college math course that is really a high-school level course.  An easy, and somewhat logical, approach is to enact a rule (or law) that says any college level math course needs to have at least an intermediate algebra prerequisite.

What’s so bad about that arrangement?  If intermediate algebra is at the level of 1oth to 11th grade high school, this seems like a pretty low standard for ‘college’; when challenged, you might add that the really logical rule would be that a college level math course needs to have at least a college-algebra prerequisite … and you’d like to do this, if WE would just make up our minds about what ‘college algebra’ really is.

However, the problems with this approach are too basic to be resolved by this framework.  First, it assumes that all mathematics builds on the stuff in an intermediate algebra course; several basic areas, most notably statistics, do not have any relationship to the concepts and skills of intermediate algebra.  By requiring intermediate algebra as the minimal prerequisite, we mislead students and cause them to take unneccessary courses … both problems are non-trivial.

Second, this approach assumes that a subtle concept like ‘rigor’ can be measured by the prerequisite.  This is not one of the valid uses of prerequisites; rigor is measured by properties of the course in question (the content, concepts, assessment and practices) … which do not necessarily change just because we list “IA” (intermediate algebra) as a prerequisite.  If we want sufficient rigor in college level mathematics classes (and I hope we do), we need to measure those courses — not a prerequisite to those courses.

Third, prerequisites tend to disproportionately affect underrepresented groups.  At my institution, it is not unusual to have 30% of a pre-algebra class be minority; the courses which immediately follow intermediate algebra are often 90% majority.  Sadly, our curriculum is still not a pump … more filtering happens, so any unvalidated prerequisite can lead to wasteful reductions in minority completion.

I’m pleased that my own institution has 5 college-credit math classes that do not have an intermediate algebra prerequisite.  Two of these 5 courses transfer to several institutions in the state.  However, students are still advised to take intermediate algebra “just in case” … they don’t really need it, but they might change their mind later.

If this topic is of interest to you, you will want to follow a position statement being worked on in the Developmental Mathematics Committee (DMC) of AMATYC.  The DMC web site is http://groups.google.com/group/amatyc-dmc?hl=en   The motivation for this position statement is to help institutions and states use appropriate prerequisites, based on validation — not prerequisites to enforce an abstract policy on ‘rigor’.

In the long term, we will replace “IA” with a more reasonable course like the New Life Transitions course — at least for the majority of students who do not need a pre-calculus type course later.  We will also replace beginning algebra with something like Mathematical Literacy for College Students, and this kind of course could really serve all students.  Until this change happens, we can work on better prerequisites relative to IA … and for all courses (including Transitions).

 
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Ban Intermediate Algebra!?

Sometimes, there is a fine line between ‘reasonable interpretation of reality’ and ‘bad idea’.  Should we ban intermediate algebra in colleges?  Would it hurt anybody … help anybody … would anybody notice?

My current ‘reality’ includes teaching an intermediate algebra course that is quite traditional, except for us using an ebook (to save students money, and provide equal access).  This course has the usual combination of topics — functions, absolute value statements, polynomials, factoring (lots), rational expressions, rational equations, rational exponents, radicals, radical equations, quadratic equation methods, and quadratic functions (along with a variety of word problems, which are mostly puzzles).

In case you did not know, I have been teaching for quite a while (something like 39 years).  Originally, intermediate algebra was taken primarily by those who needed pre-calculus … and most of them needed calculus.  For a variety of reasons, the vast majority of my current students are not in this category; for them, intermediate algebra is part of their general education process.  [At my college, intermediate algebra is the MOST commonly used course to meet a gen ed requirement.]

Outside of the small minority of my students who actually need calculus (a group which should be larger), most students are not well served by an intermediate algebra course.  The traditional course does little to enhance their mathematical literacy or reasoning, with its focus on symbolic procedures; the traditional course does not contribute to the GENERAL education of students, since it is fairly specialized (polynomial arithmetic and related symbolic procedures).

For many of my students, intermediate algebra is where their dreams and aspirations wither and die under the negative influence of a curriculum which does not serve their needs.  Even for those who need pre-calculus, the traditional intermediate algebra course does not signficantly increase their mathematical proficiencies.  [The procedures learned are soon forgotten, and not much else was learned in the first place.]

Let’s ban intermediate algebra.  In its place, we should offer a version of the New Life “Transitions” course.  The Transitions course learning outcomes focus on providing mathematical preparation as part of a general education, especially if the student will take science courses (biology, chemistry, etc).

If you do not know about the Transitions course, take a look at the learning outcomes listed at https://dm-live.wikispaces.com/TransitionsCourse.   This course focuses on concepts and connections between concepts, so that students gain more than procedures.  The particular outcomes were chosen to be part of the general education of students needing science courses; some ‘STEM enabling’ outcomes are listed as an option for a course preparing them for pre-calculus.  The “Instant Presentations” page here has a presentation on the Transitions course; see https://www.devmathrevival.net/?page_id=116 

Of the two New Life courses, the first course “Mathematical Literacy for College Students” (MLCS) has generated more interest as an alternative to a traditional beginning algebra course.  I find this interesting, since we could argue that intermediate algebra is a worse match to student needs.  Curiously, the Transitions course is somewhat similar to some materials that are already on the market … which means that implementing Transitions avoids some of the challenges faced by those working on MLCS.

Some of you have been thinking “hey, we are required to use intermediate algebra as the prerequisite for all college-credit math courses”.  Well, I know … our profession needs to work on that problem.  Presently, the Developmental Mathematics Committee (DMC) in AMATYC is working on a position statement related to this problem; see http://groups.google.com/group/amatyc-dmc 

Obviously, I do not really expect us to ‘ban intermediate algebra’ (though I can dream!!).  Perhaps some of us can help our students by using the Transitions course as an alternative for those students who to not need pre-calculus.

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Update about the New Life Project

Quite a bit of activity has taken place, relative to the New Life Project. 

The online community continues to be active.  The wiki site (http://dm-live.wikispaces.com) has a high level of use for this type of thing – consistently 20 to 40 different visitors per day.  This companion blog (https://www.devmathrevival.net) averages about 40 visits per day.  The New Life community has several pilots and implementations underway at this time; if your college is planning or doing one, it would be helpful to let me know (via email, or posting on the wiki site).

Some of us have submitted proposals for the Jacksonville AMATYC conference this November on our New Life work.  The AMATYC program committee is currently reviewing these – whatever the outcome, I appreciate our group’s willingness to share (and the work involved in sharing).

There is now enough activity on implementing New Life courses that textbook companies are developing products to support these courses.  I have had conversations with editors at Pearson, and at Cengage.  They would prefer that I not share details of their plans (since publishing plans are subject to changes for many reasons) … however, the companies are working hard to get materials ready.  Based on what I know, some materials will be ready for class testing this coming year (2012-2013), with regular materials published later (late 2013, early 2014).  I hope this information helps you plan as you consider whether you can implement a New Life model (MLCS and Transitions) at your college.

This activity related to the New Life model has also risen on the radar of companies that provide placement tests (especially Accuplacer and Compass).  Accuplacer now has a process to develop ‘customized placement tests’ in the computer adaptive model, based on a group identifying the content needed and a commitment from a set of colleges to use the customized placement test.  Many of us are using “placing into beginning algebra” as a proxy for “placing into MLCS”, and our pilot projects will provide some information whether this works in practice.  There is less confidence about using a proxy (“placing into intermediate algebra”) for the Transitions course, so this might be an area for us to consider in the near future.  Such a placement test is important because we do not want to assume (or require) that all students need to complete both MLCS and Transitions; we want to provide a mechanism for many students to place directly in to Transitions.  For us to proceed with a customized placement test, we would need to form a work group to coordinate with the company (including the gathering of the commitments from colleges to use the customized test).  We are probably not ready for this step, quite yet … though it might be appropriate to form the work group later this year.

Oh, in case you’ve forgotten the “New Life” course names – the first one (MLCS) is “Mathematical Literacy for College Students”, which provides the mathematics useful to all college students (including some algebra).  The second course is “Transitions”, which provides appropriate mathematics for students continuing in to college algebra, pre-calculus, and other courses at that level; Transitions is intended to be more symbolically-oriented than MLCS (which emphasizes numeric and graphical methods, with some symbolic).  You can go to the wiki site listed above for more information.

 
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What do you need?

The purpose of this blog is (primarily) to help more people make the transition from the traditional developmental mathematics program to a model which serves our students better (either New Life, or Carnegie Pathways).  Most of the posts have dealt with specific or general issues … based on what I am thinking about and conversations I have.

I would like YOUR thoughts on this question:  What do you need?  What would help you make this transition?

Write your comment, with some description of what would help you. 

Perhaps you need some further description of the two models (described briefly on pages in this blog, and elsewhere).  Perhaps you need either some general ideas of how to start the process of changing … or a conversation with somebody who has done it.  Perhaps you need ideas on instructional materials that could be used.  Perhaps it’s professional development that concerns you.  Perhaps you have other areas in mind.

Take a few minutes, and post a comment.  I’ll reply to everybody, and we will work together to get you what you need.  And, your comments might help provide some direction for areas I can address in future posts

“TIA” (thanks in advance)
Jack

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