Liberal Arts Math … College Algebra … ??

Once upon a time, colleges and universities wanted a math course for students in non-science fields.  The initial math for liberal arts course was designed for this purpose … a little bit of this, a little bit of that, and light on formality.

Once upon a time, colleges and universities wanted a math course for students who might or might not need calculus.  Since the content focused on ‘algebra’ and it was not remedial, the resulting course was called college algebra.

We might be better off if both titles were banned from the collegiate landscape.

In a way, both courses have a ‘this is not the other math’ type of implication.  We should be able to articulate a positive statement (and title) for what the courses are about.  This is not to say that all courses with these titles are ‘bad’ in some way (though some are bad in some ways).  I know of a few liberal arts math courses which are contemporary in design, with a focus on reasoning and some formality.  Some college algebra courses are actually high quality pre-calculus courses.

Back in the day, there actually were many programs that were not scientific.  Even fields like biology were considered non-quantitative, as were social sciences.  This landscape has changed in fundamental ways over the past 30 years; the fields that require no quantitative background are small in number.  Instead of ‘liberal arts’ math, we should use variations on the more modern ‘quantitative reasoning’ title.

College algebra is a mess.  It’s defined by what it is not (not remedial), and the title is used for 3 basic types of courses (general education, pre-calculus, and prep for pre-calculus).  If we need a general education course, we have better alternatives available now than we did 30 years ago (think quantitative reasoning and intro statistics).  Using college algebra for general education ensures that the course will primarily be a barrier to students completing a degree, and likely makes the course very challenging for faculty to teach.  It’s not unusual, of course; a major university close to me uses college algebra as their primary gen ed requirement.

If a college algebra course is meant to be pre-calculus, then we use the better title — pre-calculus.  Calling it ‘college algebra’ when it is meant to get students ready for calculus implies that the primary factor in calculus success is algebra beyond the remedial level.  I hope that this is not the case!

And, if college algebra is meant to be preparation for pre-calculus, there are larger questions.  Is the course non-remedial?  Are we adding a course to the sequence to have more classes to teach and fewer students completing?  If there is a valid reason for having both college algebra and pre-calculus, I have never seen it … and would appreciate seeing such a reason elaborated.

No, I don’t think we need either title anymore.  They once served a purpose, but Liberal Arts Math and College Algebra are obsolete.  The sooner we stop using them, the better we serve our students.

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Is Calculus Instruction Changing (or Curriculum)?

In our applications for living course, we are finishing our work with statistics.  One situation involves students deciding which situation is likely to involve statistical significance:.

Rolling a die 40 times and getting 5 threes             OR

Rolling a die 400 times and getting 25 threes

This is a tricky thing, as students often focus on the sample size only.  Although this problem presents situations where the larger number is connected with significance, there is no general pattern that says ‘larger sample sizes means significance.’

Within our curriculum, developmental mathematics has dominated the news and much of our work for a long time.  There definitely is a larger sample size; is there a difference in statistical significance between developmental math and calculus courses?  In a basic way, yes, there is — developmental math serves a large group of students with multiple academic problems, while calculus serves a group of students with general academic success.  A 60% pass rate in calculus is not good, and is statistically significant given that most students in the calculus courses are expecting a high grade (while developmental math students often expect low grades).

You can try this as I did — search for ‘reform in calculus college’ or similar terms.  Most of the results of this search will be historical artifacts from the 1980’s and early 1990’s.  What’s with that??

I think we have fallen into the large number fallacy — a larger sample size indicates significance (dev math), instead of analyzing each situation separately.  We should be able to expect an 80% pass rate in calculus 1, given the academic skills of students who typically enroll in that course.  My own college gets about 60% pass, and this seems pretty normal.

For programs which require a 4-semester sequence (Calc I – II – III plus diff eq), a 60% pass rate means that a maximum of 13% will ever complete the sequence.  The likely values are far less — some portion of students are lost between courses even after passing.  I suspect that observed values will be between 5 and 10% — which, coincidentally, is the same range as a developmental math sequence.  [These low values are the result of ‘exponential attrition.]

Recently, I did learn of some work of our friends in the MAA on calculus.  It’s not on reform; rather, their focus is to analyze data to identify what we are doing and what is more successful — the Characteristics of Successful Programs in College Calculus (CSPCC) project.  The web page for their work is http://www.maa.org/programs/faculty-and-departments/curriculum-development-resources/characteristics-of-successful-programs-in-college-calculus

David Bressoud is a lead ‘PI’ on this work; he’s written a few articles about their work for the MAA Newsletter, so you may have seen those if you belong to the MAA.  The web site (above) has links to those articles, as well as papers written about their work.

One of the co-PI for the work is Vilma Mesa, who has done quite a bit of work on community college mathematics.  Dr. Mesa did a session at our recent MichMATYC conference on some of the data from community colleges for the CSPCC work, including the contrast between homework and exams in terms of assessment level … and an analysis of prompt types and expected response types (verbal, symbolic, graphic, or multiple).

I encourage you to read the material on the CSPCC web site.

The larger question is this:  Are we doing anything of substance to make basic improvements in calculus?  Or, is our ‘best shot’ using Mathematica and/or MatLab with our students?  I hope that is not the case.

If you are doing some reform in calculus, I hope that you will share your work — the good and not so good.  “Developmental Math” should not be having all the fun!!

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Math for Emerging Technologies — CRAFTY and the Vision

Perhaps we do not think enough about what mathematics is needed in emerging technologies — those fields that are relatively new and generally have good employment prospects for our students.

So, I am getting ready for presentations at the AMATYC conference and at the National Summit on Developmental Mathematics later this month (Anaheim, CA).  My presentations focus on the New Life model, which has been around for about 4 years.  Partially due to the related work of Quantway™ and Statway™, much of the attention in our field has been on the Mathematical Literacy course.  I am actually putting more energy in to the new course which follows Math Lit — Algebraic Literacy.

In the process, I am going back to the source documents that we used to develop our curriculum.  We used professional references to identify learning outcomes for the target courses our students will take.  Among those targets was ‘technology careers’ — what mathematics students need to succeed.

If you have not seen this source, I highly recommend that you study the “Vision: Mathematics for the Emerging Technologies”.  This report is the result of an intensive effort organized by AMATYC in 2000 and 2001, and involved convening dozens of experts outside of mathematics education.  Here is the link: http://c.ymcdn.com/sites/www.amatyc.org/resource/resmgr/publications/visionweb.pdf

Among the identified needs:

• Critical Thinking, Problem Solving, and Communicating Mathematically
• Algebra (ability to apply mathematics topics outside of mathematics, or in a new setting, is vital)
• Geometry
• Trigonometry
• Statistics

The list also included arithmetic (proportional reasoning, measurement), which our Math Lit course takes care of.  The report lists calculus as needed for a few technologies.

The question is … should the development of these needed skills fall entirely on the responsibility of courses in the student’s program?  Or, should ‘developmental’ mathematics provide a foundation in these areas?

If these needs were unique to emerging technologies, we might have some rationale for leaving this work to the occupational programs.  However, each area listed is also important for other reasons — other “STEM” fields need them.  These needs fit very nicely into a course preparing students for a first math analysis course (also known as pre-calculus).

Here are the current goals and learning outcomes for Algebraic Literacy: Algebraic Literacy Course Goals & Outcomes Oct2012 Algebraic Literacy Goals and Outcomes June2013

In case you are wondering, the ‘CRAFTY’ in the title of this post comes from the MAA acronym “Curriculum Reform Across the First Two Years”; the AMATYC grant involved work that supported this effort.

I’ll be talking about this “Vision” report in my Summit presentation on the Algebraic Literacy course, as well as in my New Life session at the AMATYC conference.  I hope you can make it to one of those events.  [I’ll post the presentations here later.]

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Are You There, Mr. Gates? Flip that MOOC right over, guy!

Some of us have been thinking about the influence that foundations (and rich people) are having on education.  What was once an influence of the national science foundation is now the influence of the gates foundation, with a smaller group of people making decisions based on priorities that are not open to public review or political approval.

A recent article described how Mr. Gates suggested to community college trustees that a ‘flipped MOOC’ might be a good solution — especially for developmental mathematics.  [See http://chronicle.com/article/MOOCs-Could-Help-2-Year/142123/].   I suspect that the article is misquoting the ‘doctor-not’ (Mr. Gates); an intelligent person would not use an oxymoron like ‘flipped MOOC’.  (Flipped means ‘lectures’ happen outside of class time; MOOC’s do not have class time.)

However, that minor detail (that is is not possible) will not make any difference.  Because it was Mr. Gates saying it, many of our leaders (college trustees) will be confident that it is true.  I expect to hear from my College’s trustees within a few weeks, as they wonder whether we would like to try a flipped MOOC model at our college to solve our dev math problem.

Coincidentally, I saw a very good presentation on an inverted design for instruction — a better name than ‘flipped’.  This presentation was at my state conference (MichMATYC) — a talk given by Robert Talbert (Grand Valley State University); a reference is http://scholarworks.gvsu.edu/cgi/viewcontent.cgi?article=1183&context=colleagues .  I was impressed by the amount of analysis done by Dr. Talbert to create the inverted calculus classroom; the process is much more complicated than ‘lecture outside of class time’.

To some extent, the ‘flipped MOOC’ phrase illustrates the linguistic process for the evolution of word usage: the initial use of a phrase is specific, becomes accepted, and then is applied in usage to unrelated objects in order to imply something positive (or at least ‘current’).  As educators, we have been damaged by this “phrase drift” many times over the years (mastery learning, back to basics, applications, calculator friendly, collaborative, student centered, and others).  The difference in this period is that our future is being heavily influenced by people who have less understanding of curriculum and instruction … rather than more.

There was a time when ‘trends’ in education were declared by top-level academicians and national policy heads.  These people (generally office holders of some kind) were deeply networked in the collegiate life.  No more; we are spending most of our time either agreeing with or arguing with people ‘on the outside’ — foundations in the completion agenda, philanthropists, and legislators.  It’s not that we should ignore the concerns of outside stakeholders.  The problem is that the outsiders have taken control from us; we react to them.

So, I ask:  Mr. Gates, are you there?   When do we get to have a productive conversation about the problems we are trying to solve?  We could look for problems where we agree on solutions … problems where we agree on the problem but not on solutions … and problems where we see the problem differently.  I know this, Mr. Gates — the process being used so far has put a lot of money is promising practices and technology without much sustained benefit; your return-on-investment is not so good.

When do we have a productive conversation?  Until we have real conversations with the people and groups trying to solve the problems (with the best of intentions) … until we work together, and not in reaction … until we accept both the worthy and not-so-good about the old system … only then do we have any hope of building something that will both solve problems and be capable of surviving in our world.

If you want to ‘solve the developmental mathematics problem’, Mr. Gates, I suggest you start by collecting a team of the 10 best thinkers and practitioners in the field who work with you over a 10-year period.  We want to solve problems; we strive to have students succeed and complete.  Can you recognize the need to have us as partners?

Are you there, Mr. Gates?

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