New Life math … at Parkland College (Illinois)

Change does not necessarily result in progress.  Change with a deliberate plan creates conditions for progress, and this idea is at the core of the New Life work in mathematics.  The math department at Parkland College has taken a professional approach to redesign and reform.

In their work, Parkland has designed a new path for non-STEM students, as have many other colleges.  However, they also examined their STEM-path to identify needs of those students which were not being currently met.

An overview of their work is in this document (which will also appear in the DMC newsletter … Developmental Mathematics Committee of AMATYC):Parkland College DMC article New Life 2012   [Thanks to Erin Wilding-Martin and Brian Mercer for sharing the info.]

Good job, Parkland College!!

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MOOC … Should we welcome them?

In case you do not know the acronym, MOOC stands for Massive Open Online Course.  The “MOOC Movement” has supporters among the foundations contributing funds to special projects, similar to the process that supported the re-design efforts of NCAT (emporium, etc).  Should we, as professionals in mathematics and in developmental mathematics, welcome MOOCs as part of the solution?

The rationale for emphasizing MOOC offerings is fairly simple: If too many students need to take developmental mathematics in college, we could provide a course which does not cost money nor credits.  In some ways, this methodology is similar to the boot-camp or summer bridge courses offered to reduce the need for remediation.  Neither approach has a basis in evidence yet, though the MOOC option is so new that there are no reports yet on actual results. Scientific studies of effectiveness are not available.

One encouraging aspect of MOOCs is that some of them emphasize a broader range of mathematical proficiency than our traditional classes (see http://www.eschoolnews.com/2012/11/15/next-step-for-moocs-helping-with-remedial-math/)    The framework for this particular course is based on the common core state standards.

Can we predict how successful a MOOC will be in helping students succeed in college-level courses?  We have some evidence related to how well developmental math students do in online courses, with divergent results at this time.  [For one study, see http://www.ncolr.org/jiol/issues/pdf/10.3.2.pdf .]  I would expect that any online delivery format would tend to be of average or below average effectiveness with developmental math students.  From this point of view, MOOCs are a positive thing:  even if only 40% succeed, that is 40% who succeeded without spending money or credits.

I think there is a significant issue with motivation, however, with any non-credit non-cost option.  Developmental math students tend to have complicated lives, perhaps even more than the ‘average’ community college student.  When competing needs exist for limited resources (time), priorities will reflect the other two currencies important to students: money and credits.  For a few years, my college offered a free program to help students pass their arithmetic placement test based on a self-study program; we might call that option “POPO” for ‘Petite Open Personal Option’.  The program was logically designed and a total failure — until we incorporated a structure centered around working with faculty.  I would lower my expectations for MOOCs by some significant factor, perhaps down to 20% to 25%.

Since MOOCs are free, a person might conclude that even 20% is a good result.  Could be.  My concern would be the result on students when they try this free option and ‘do not pass’.  Will this impact attitudes and beliefs?  Or, will students attribute this type of failure to behavior or decisions?  Since MOOCs are offered outside of a typical college support system, does anybody take responsibility for providing feedback to students during or after such an experience?

Innovation is a good thing; change is needed in our profession.  MOOCs are sometimes categorized as ‘disruptive technology’, though that aspect does not concern me.  I think MOOCs are a good thing to try, in spite of my predictions concerning success for students.  I would just want some people looking at a number of research questions relative to this method compared to credit courses and other options.

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Math: Applications for Living XIX: Population Decline with Exponential Models

Percent change is all around us.  Sometimes, the percent change is based on the nature of the quantities involved (such as all those finance formulas).  Other times, the data for a situation assumes an exponential property.  Within our Math: Applications for Living course, we are looking at both half-life models and regular exponential models.  The example today applies these models to data about African elephants.

Although the decline of African elephants is not consistently exponential, as it responds to economic and social forces, the general nature is still exponential.  The current estimates used to predict future populations use differing rates of change, depending on assumptions.  The best case scenario is a 3% reduction in population per year; some recent data shows a spike in poaching activities, which would result in reductions well over 3%.

For class, however, we gave a problem like this.

The population of African elephants is declining at a rate just under 4% per year.  Estimate the percent of the current population which would remain in 100 years.

One way we approached this problem is to use the half-life model.  In order to estimate the half-life, we used the banker’s rule of thumb for doubling-time:  70/P.  In this case, 70/4 is 17.5 years; we will round that to 18 years.  The calculation becomes:

0.5^(100/18)

The result is 0.02 (approximately), or 2%; 2% of the current population would remain in 100 years.

We also used the basic exponential model; with a 4% decrease per year, the multiplier is .96.

(0.96)^100

This result is 0.017 (approximately), also rounded to 2%.

Students were uniformly surprised by this result.  They keep hearing about a half-million elephants declining at 4% per year, and this does not sound serious until we calculate the percent left after a longer period of time.

In our class, we do not explore the sociology of this problem, nor the political components (though it might be fun to combine mathematics and politics into one class).  Our focus is on basic mathematical concepts.  The most common theme in the class is percent change.  This application got their attention!

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Algebraic Literacy: A Course to Help Students

At the AMATYC conference in Jacksonville (November 8 to 11), we explored the New Life model was a topic of much discussion and some sessions.  In these conversations, there is growing excitement about our Algebraic Literacy course as an alternative to ‘intermediate algebra’ … an alternative which also meets more students’ needs.

Conceptually, Algebraic Literacy was designed based on looking at the quantitative needs of students in several college courses … needs that exceed our MLCS course.  For example, the Algebraic Literacy learning outcomes deal with the concepts and capabilities needed to succeed in pre-calculus.  The outcomes also reflect much of what was learned by the MAA in its work with our client disciplines (biology, chemistry, and social sciences in particular); the needs identified are consistent with several fundamental concepts of mathematics … rate of change, symbolic and numeric representations, and basic types of relationships (linear, exponential, power, rational, etc).

Okay, so here is a document with the learning outcomes for Algebraic Literacy: Algebraic Literacy Course Goals & Outcomes Oct2012

One thing to keep in mind … Algebraic Literacy is not an intermediate algebra course like we have been used to.  You will see some familiar topics (equations and inequalities); you will also see some less familiar topics for this level (exponential and power equations).  And — you will see a deliberate coordination of symbolic and numeric methods, with some outcomes addressed only in numeric form (for solutions).

To give some idea of the nature of this course, I wrote a sample lesson for one of the function topics (rate of change).  Take a look: Algebraic Literacy Sample Lesson Rate of Change Exponential.

In designing this course to meet the needs of students, we discovered that the result is a course which is more attractive to mathematics faculty.  Rather than dealing primarily with procedures, the Algebraic Literacy course builds on key concepts (mostly from algebra) with an emphasis on both the symbolism and the application.  I hope that you will take a look at the Algebraic Literacy course.

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