Curriculum and Collaboration: Data on Pre-Calculus in Michigan

We will be at the MichMAA and MichMATYC meeting this weekend, at Hope College (Holland).  The highlight for me, of course, is my talk on curriculum & collaboration for change … with a focus on pre-calculus courses in Michigan.  That presentation file will be posted here in a couple of days.

The handout is already available, so I am posting that now: references Curricular Change college mathematics MichMAA April 2015

One page of this document is the references … information that might be helpful for those who are concerned about college algebra and pre-calculus courses.  Some of these are ‘standards’ type sources from the MAA; others are viewpoints (like Zal Usiskan’s talk on “cleaning up after the Common Core”) or data (like David Bressoud’s “Pitfalls of Precalculus”).  This page also summarizes what I found when analyzing the pre-calculus courses in Michigan, using 27 public institutions — which shows the tension between the titles “college algebra” and “pre-calculus”.

The other page of the document is a summary of how the prerequisite to calculus I at those 27 institutions transfers to the other 26.  This data is the result of looking at each institution accepted the other courses in transfer; it turns out that many of us (especially community colleges) are not very transparent about how we accept other college’s courses.  In some cases, I could get a tentative transfer result from the Michigan Transfer Network … though I also discovered that this source is fairly likely to contain errors.

Two overall bits of information:

1. In about 25% of the combinations (sending to receiving) I was not able to find any information on the transfer of the prerequisite course for calculus I .  This was found especially for community colleges.
2. Of the combinations where transfer information was available, almost 20% of the transfers “broke” the prerequisite … institution A’s prerequisite did not transfer as institution B’s prerequisite.  This breakage was found for both types of institutions (university and community college).

One pattern in the transfer analysis was especially bothersome — it appears that any modification or difference from the expected titles for prerequisite (“trig” or “pre-calculus”) was associated with a loss of transfer.  Institutions who called it “college algebra with trig” did not do as well as those who called it “trig”, even when the course served exactly the same purpose.  [I can’t speak to the learning outcomes, because very few institutions are transparent about those — universities, in particular, seem to treat learning outcomes as corporate secrets or ‘our secret recipe for math’.]

Jump Start in Math

We just had our Michigan developmental education conference (“MDEC” see http://www.mdec.net/conference/2015/program.html for details).  One of our colleagues at Schoolcraft College did a presentation on their “Jump Start” program for math.

The Jump Start program has two components (each 2 hours long).  The first component is on math study skills; since the person conducting the workshop is a professional in the learning assistance center, she has a good background to provide clear direction to students on being successful in math.  Within this study skills component, she also deals directly with motivational issues — her goal is to provide HOPE for all students.

The second component is the content, where students choose the one that matches their course for the upcoming semester.  Since Jump Start is offered within a few days of the start of the semester, this part of the workshop reviews content needed to be successful in that course.  The college offers a Jump Start option for the first 4 or 5 courses.

You can get some information about their Jump Start program at http://www.schoolcraft.edu/a-z-index/learning-support-services/learning-assistance-center/student-success-seminars-and-workshops/jump-start#.VRKngeFuNyE  with the current schedule at http://www.schoolcraft.edu/docs/default-source/lss—jumpstart/jumpstart-winter.pdf?sfvrsn=0 .

Overall, the Schoolcraft math curriculum is quite traditional; they still offer a basic math class, and do not yet have a mathematical literacy course.  However, I like their Jump Start program; in particular, the 50% (2 hours) invested on study skills (and motivation) is very appropriate for most students.  The professional doing the workshops has a math degree; in fact, she was originally a developmental math student who had to work very hard … and became a math major because “math chose me” (as she says).

The 50% (2 hours) on content would not be sufficient to correct for basic gaps in understanding, and the content done focuses quite a bit on procedures.  However, even this part likely is a good thing for students — the workshop covers a half dozen topics with multiple examples in each, which might help students develop accurate expectations for college math classes, as our pace can be quite an adjustment from high school.

The Jump Start model might be a good alternative for many colleges who can not commit resources to week-long boot camps or similar programs.

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Acceleration as Distraction

One of the tricks used to increase traffic on a web site is to incorporate ‘hot phrases’ in to the pages and articles.  In our field, “acceleration” is a very effective phrase to use.  Sadly, acceleration is not that important … by itself.

Like most colleges, mine has some acceleration models — two-courses in one, boot camps, and self-directed study for example.  Some acceleration work gets very high press coverage, such as the Austin CC ACCelerator program (see http://sites.austincc.edu/newsroom/accs-accelerator-and-developmental-math-course-wins-praise-of-second-lady-and-under-secretary-of-education/ )

Acceleration is better than not accelerating … or is it?

One of my friends tends to use medical analogies in our conversations.  I am envisioning him saying something like this:

A doctor knows that three lab tests being required are without any benefit to the patient (no diagnostic nor any treatment benefit).  What the patient needs is a new treatment, but the insurance will not cover the new treatment.  Is our profession better served by making the three useless tests quicker for the patient … or by working on fixing the basic problem of getting the right treatment?

Our goal should be to fix the problems.  Acceleration is not the basic problem … what needs to be changed is the mathematical treatment provided to students so that there are multiple benefits for students.  In developmental mathematics, our work needs to focus on capabilities that serve all college programs with a focus on quantitative reasoning.  In college level mathematics, our work needs to focus on empowering students for programs or groups of programs.

Acceleration tends to reinforce the current curricular system by masking a symptom (too long to complete).  An emphasis on acceleration distracts us from working on core problems.

I believe that we need fewer courses.  We can start with a course like Mathematical Literacy (or Quantway, or “FMR”), with just-in-time remediation as needed.  The next level can be a course like Algebraic Literacy (or STEM path I), again with just-in-time remediation for students who did not need an entire course before it).  We only need one course to connect that level with calculus I — a deliberate design of a pre-calculus course.

We can do better than acceleration.  With new ideas of content and course design, we can provide important mathematics for our students in an efficient manner.

“Needing acceleration” is direct evidence that the basic curricular structure is inappropriate.  Don’t worry so much about acceleration — fix the basic problem.

 
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When Does Reform Succeed?

I have been thinking lately of a problem considered back when we started the AMATYC New Life project (about 2008).  The problem is not mathematical in nature, which perhaps explains why we have not solved it before.  Now, I am not saying that we found the only solution; I’m not even sure that our solution is sufficient.  I can report that our reform has grown way (way!) past any prior reform of developmental mathematics.

The problem is this:

What properties or methods enable a curriculum reform to succeed over a period of years and across regions?

Prior to our New Life work, many intelligent people had created valid reform ideas or models.  None of them survived time and space; they resulted in temporary changes (in general) and were limited to a few locations (at most).

For those interested in such things, here are my thoughts on strategies the result in successful reforms.

1. Professional organizations need to be deeply involved.

The New Life project was born in the AMATYC Developmental Mathematics committee, which had a large group of faculty willing to work on the project.  In addition, several members of the AMATYC Executive Board both supported and contributed to the work.  The involvement of the national leaders of a group enable that reform effort to connect with similar reform efforts by other groups (see below).

2. Content in the reform math curriculum created by faculty in a collaborative process, based on professional references.

If you look at the material over in the New Life ‘wiki’ (dm-live.wikispaces.com) you will notice that the learning outcomes were drawn from multiple professional sources (MAA, AMATYC, NADE, Numeracy Network, etc).  Both parts of the process were important — collaboration resulted in content that was widely accepted by math faculty, and professional resources helped create content that had external validity.

3. Avoid a focus on one issue.

In general, a reform effort built on one issue is very unlikely to succeed.  That one issue will not appeal to the general math faculty population.   For example, the NCAT redesign work tends to deal (in the curriculum) primarily with technology; as in prior calculator-based reforms, people find that this is a weak motivation for reform.   Addressing multiple issues in the reform means that most faculty will see something they like, which is a critical property for getting the reform adopted.  In the case of New Life, we addressed several content issues, classroom pedagogy, and professional development.

4. Plan for, and support, long-term conversations with faculty.

For some reform efforts, advocates did not sustain conversations with faculty over a period of time.  Only a few faculty will accept any reform when they first hear about it; one could argue that these faculty are actually not good test cases for a reform.  For the New Life project, we sustained conversations online (email, wiki) and at many conferences, for over 4 years now; in addition, we have had people travel to put on local workshops.  In our case, these conversations often result in faculty concluding that teaching our reform course is just more fun than what they have been doing; this is a powerful force for reform.

5. Create or support multiple solutions sharing basic properties.

No matter how good one particular reform model is, some faculty will not be comfortable with it; some institutions or states involve conditions that conflict with a given solution.  Our New Life project is one of three closely related solutions:  Carnegie Foundation Pathways (Statway, Quantway), Dana Center New Mathways, and AMATYC New Life.  The three projects have collaborated, shared resources and talent, and provide faculty & institutions with choices.    The New Life project itself supported multiple solutions — we depend upon commercial textbooks, and each major publisher is creating a solution.

6. Do not depend upon “one good book”.

Prior reforms, at all levels, often involved the creation of one set of materials.  New books face several challenges both in publishing and in getting adoptions.  A single book is just not going to be good enough to result in reform long-term.  The current reform in developmental mathematics involves commercial texts, foundation developed materials, and self-published materials.

I think other areas of college mathematics need basic reform, some perhaps even more needed than developmental.  I want reforms to succeed in ‘college algebra’, pre-calculus, finite math & modeling, calculus, quantitative reasoning, and statistics.  These courses impact hundreds of thousands of students every year; the impact is not uniformly positive.

As  you look at the points above, I am hoping you reach the single biggest conclusion:  Reform is something we do together, with each other, over a period of time.

 
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