Wednesday, June 19, 2013

Is MLCS just "fun algebra?"

When I give talks and workshops and as I'm teaching the Canvas MOOC, I use example lessons to help illustrate what MLCS is and how content is taught.  Lessons start with realistic contexts in which the mathematics is pulled from them.  Many times an algebraic topic is developed.  Lessons close with contextual or mathematical connections to the topic that was developed.

I've realized that upon first glance, it looks like we're just taking algebraic skills and trying to make them interesting.  Certainly, we want student engagement.  Developmental math students have been unsuccessful at some point in their math career and because of that, they often shut down when a topic looks familiar.  The mind is powerful; if a student believes they cannot learn a particular topic, that can be a self-fulfilling prophecy.  So that students don't allow their preconceptions to dominate the learning experience, we deliberately try to come at topics in novel ways.  And it works.  I've had students work a long time with a concept, and successfully at that, and then realize, "hey, this is that y = mx + b thing, isn't it!"  One instructor said to me that it's almost sneaky algebra and I wouldn't deny that.  

Pathways courses use realistic and relevant content.  Adult learners are more motivated by content that they can use.  I don't believe something has to be immediately useful to be worth learning.  But if it is, it is much more motivating to students.  Motivation and engagement are necessary for a successful developmental math classroom.

But MLCS is much, much more than interesting, contextualized lessons.  

If MLCS were just fun algebra, we would be covering all the traditional topics in the traditional order.  That's not the case in this course.  We have added new topics and scrapped some traditional ones.  For all topics, the emphasis has changed because the goals for the student have changed.  The approach and development is different so that students can do more than successfully demonstrate a list of skills.  Instead, the emphasis is on understanding and use of skills, not just the skill knowledge itself.  Really, this course is good for students heading on the STEM path as well as the non-STEM one.  With a follow-up intermediate algebra course, STEM-bound students would have all the conceptual and applied knowledge they need from MLCS and any additional symbolic skills from intermediate algebra.  

Beyond the approach to an individual topic, the order of topics has been turned on its ear.  That change isn't meant to be confusing, but instead to create learning.  In all algebra courses, we instructors use a particular order of topics because every book uses it.  Someone at some point chose that order and it stuck.  But it doesn't mean that it creates learning.  For some people with some topics, it does.  But does learning mean the student can perform the skill successfully?  I would say no.  I believe real learning means the student understands the skill, can use the skill, and sees the connections between the skill and others.  The traditional linear order of topics doesn't always allow for the connections which are so important.  

The traditional approach gives the impression that math is made of discrete skills.  Often a problem in an algebra class is a rational equation problem or a graphing problem or a factoring problem.  Real problems are none of these.  They use these ideas and others and integrate them.  A real problem (be it in a mathematical setting or a real life one) will cross over into multiple areas of math at once:  algebra, arithmetic, geometry, etc.  

To help a student learn how to solve these more involved, real problems, the course integrates content.  There are key threads we want students to gain understanding of:  numeracy, proportional reasoning, algebraic reasoning and functions.  True learning takes time.  So each of these threads is not its own unit (as it would be in an algebra book) but instead appears in every unit.  Topics are almost always seen many times, each time going deeper and into different contexts.  That is intentional so that students learn and also take understanding into long-term storage.

To create learning, which is our utmost goal, we have to sequence and pace content very thoughtfully.  For example, slope as a rate of change is a really important idea that has some subtle features.  Most texts teach slope on one day and apply it almost always with 2 points or with an equation of a line.  We start with the idea of rate of change in the first 2 weeks and continue going with that concept into different mathematical settings and formalize it at a specific point, once students have more understanding.  We develop slope throughout each of the 4 units.  It takes a long time.  But in so doing, I can ask a student at the end of the semester if a situation is linear, why or why not, what is the rate of change, what does it mean for this context, etc. and they can answer all of the questions well.

The fact that MLCS uses interesting activities to learn content is the tip of the iceberg of this pathways course.  A micro view gives the impression that the only difference is the use of context.  A macro view shows a much more complex structure designed to elicit learning.  Each lesson, unit, assessment, and project has a role in developing long term understanding.  Much like the homework is deliberate with each problem serving a particular purpose, each component of the course is also deliberately chosen.  The result is a visible progression of learning with each student over a semester and the shift from the developmental level to the point of college readiness.  

And maybe along the way, we'll have some fun too.

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