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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Answer Standards Fight Mathematics

“Negative exponents are not allowed in answers.”

My intermediate algebra class has not had negative exponents in the material so far.  However, here is what most students remember:

I can not have negatives, so write the reciprocal.  No exceptions.

Given the ‘answer desperation’ of most students, any ‘rule’ about the answer gets added emphasis in learning.  As teachers, many of us try to make it easy for students … so we add our emphasis.  The result is that our standards (often sensible but arbitrary) fight mathematical knowledge.  Students focus on the form of the answer and our rules about that, and have less understanding of the mathematics involved in the situation.

In the case of negative exponents, the rationale for ‘no negative exponents’ is marginal at best.  True, in some cases, positive exponents are simpler; however, for the majority of situations, negative exponents are simpler — they often avoid the need to write a fraction.  The evolution of exponential notation and meaning is based partially on the idea that negative exponents are a simpler way to show division … and fractional exponents are a simpler way to show roots.

For my class, the previous emphasis on ‘no negative exponents’ distracts them from understanding simple division problems.  We do more polynomial arithmetic than is really needed, but these division problems are just dividing a binomial or trinomial by a monomial.  The student answer desperation and the negative exponent prejudice combine to distract them from the basic ideas of division.

A related issue came up in my beginning algebra classes … students wondered if they should finish a fraction problem by changing it to a mixed number.  The context was solving a linear equation with one variable; the form of the answer is a trivial matter compared to the mathematics.  Overall, one of the most common questions I ever hear is “how do we need to write that answer”.  Sometimes, this deals with algebraic concepts and the question is valuable; many times the question is a distraction.  I often tell students that I don’t care what form they give an answer as long as it clearly communicates a correct result.

Perhaps we should take a step back from all of our simplistic statements about ‘form of the answer’.  Many of them are conveniences for grading work, nothing more.

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A Recipe for Success (part of a faculty toolkit)

Earlier this month, I posted an item about a success toolkit for faculty (https://www.devmathrevival.net/?p=1266).  Most faculty know that building student success is not a ‘one and done’ type of effort — feedback, suggestions, and problem solving are needed.  Today, I want to share an update of a tool I like quite a bit — a “Recipe for Success”.

The idea for the Recipe for Success is that students — especially in developmental math courses — do not think enough about HOW they are approaching the course, that they often do not employ meta-cognitive skills.  Meta-cognition is a very complex zone to work in, and getting students started can be a challenge.  For years, I was not sure how to structure this component of success in a math classroom.

Last year, the faculty at Grayson County College (TX) shared a document called ‘Recipe for Success’ — originally developed by Stanley Henderson, who was kind enough to share it with me.  After using it and revisions, the start of the form looks like this:

The form has 4 areas like, with 5 to 7 questions within each.  After checking off a “ROSFA” rating for each, the student does the most important parts — a summary and a plan for improvement.  The bottom looks like this:

I assign points for completing this activity, which I normally schedule about the fourth week of the semester (enough time to have a pattern of working on the course).  Besides judging whether students were honest in answering the questions, I write some brief feedback on most of them (usually circling a couple of questions to think about).

If you want to take a look at the entire document, here is a link (PDF format): Recipe For Success in Math (Rotman Sept2012)

This type of activity can be a critical step in the process of building student success.  The form itself does not cause an improvement — it’s students thinking about learning, and instructor comments, that make the difference. 

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Towards Success in Developmental Mathematics — A Toolkit

Have you been looking for practices that encourage and support student success, especially in developmental mathematics?  I will share a toolkit of practices that seem to be effective with students in beginning algebra (often the most challenging course for us and for students).

Communication is the key.  To start with, write your syllabus (first day handout) with the reader in mind.  My own syllabus is conversational, and full of textboxes and a few graphic elements.  A traditional syllabus discourages reading; I think they also discourage engagement.  We encourage engagement by the design and tone of our syllabus.

It’s all about the learning.  In the syllabus and your attitude, emphasize that the top priority is to learn to the  best of each student’s abilities.  Homework is not just about practice … homework is a learning endeavor.  In my case, I emphasize the ‘learning cycles’ (see https://www.devmathrevival.net/?p=1229) AND reinforce these ideas by comments and actions every day in class.  repetition and action count; saying ‘it’ once does not matter.

Provide a reward for seeking help.  This is really important as a step to change behavior.  Most students, especially those in developmental mathematics, are reluctant to seek help.  At the same time, help is what makes the difference between passing and failing.  My method for this is to give an assignment (8 to 10 points, out of 1000 for the course) for students who seek help within the first two weeks of the semester.  Not only do students get more help, they feel more connected to the college experience.

Dig deep and build; don’t assume ‘they get it’.  Many of my students could combine like terms … as long as the sum was not zero; they could use exponents … as long as the problems were limited.  This is my most recent change; one of my students this semester wrote me an email (in the first week) that this was the first time she understood algebra.  Even some of the ‘high-performing’ students found some gaps.  Specifically in beginning algebra, I am using language concepts (see https://www.devmathrevival.net/?p=1253) and building processes in great detail: we started from “x + x + x = 3x” and “x·x=x²” … we went through zeros in sums [2x + (-2x) – 8 = -8]. 

Assessment as a routine activity, with instructor feedback.  If a student can go 2 or 3 weeks before getting feedback from me, I am assuming that they are ready for college work (and can make their own judgments about learning).  Everyday we have a quiz or a worksheet; I’ve even run a class where we do both (all classes are 2 hours, twice a week).  Obviously, the more assessment activity the more work we have.  My assessments fit in to the “It’s all about the learning” concept; daily assessments are 5 or 6 points, and I ‘drop’ 3 or 4 over the semester so random absences don’t hurt students.

We are a community of learners in this class.  You might call this ‘group work’, or ‘learning together’.  However, it’s not good enough to have 2 people in the class that help a student … we can all help each other.  If I can create an environment where each student is comfortable asking almost anybody in the class … and where every student is willing to help others, this is a powerful tool for motivation and ‘connecting’.  In my case, I model this behavior during class, and build opportunities for students to work with different people; seldom do I arrange the groups.  (Sometimes I will direct them to work with somebody they have not yet worked with.)

My goals for these practices focus on student engagement and learning capabilities; if the practices ‘work’, I will see better learning this semester and the student will be better prepared for other courses — even if they never use the mathematics we study.   Obviously, these practices are just a part of what I do … I hope you find some ideas within them.

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