Thursday, June 27, 2013

Math Lit now available!

Math Lit printed early making it available now.  It might be another week before it can be purchased from vendors.  If you would like to see the full book in the meantime, check with your Pearson rep.

The MyMathLab course is being completed now.  It will go live the first week of August.  In it will be additional supplements in PDF form:

  • Instructor's Resource Manual 
    • Includes quizzes, exams, a final exam, and additional support for focus problems
  • Instructor's Solution Manual
    • Includes detailed solutions to all problems in the text

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.

Sunday, June 9, 2013

Math Lit Book Coming Soon!

Our textbook for the MLCS pathways course, Math Lit, releases the first week of July.  The MyMathLab course that accompanies the book goes live the first week of August.

Here's the final cover:

Tuesday, June 4, 2013

Pathways MOOC Update and Florida Legislation on Remedial Math

Yesterday was the first day of the pathways MOOC that I'm teaching with Heather on Canvas.  Registration is still open if you'd like join.  Follow this link to register.  Here's a picture of the front page of the course:

The course is already active.  I hope to see that activity level continue to grow.  It's fun and informative to talk with other educators and learn from each other. Somewhere we reached a tipping point about developmental math education in the U.S.  It's still a challenge to pilot pathways courses like MLCS in some schools and states but those walls are coming down all the time. It's not that algebra isn't important; it's that it's not the only thing that is important.

Related to pathways, I read an article in the Orlando Sentinel recently about changing legislation on remedial education. It reminded me very much of the changes in Connecticut.  The idea is that we are preventing students from taking college level courses and that with enough support, they can be successful.  Again, if you've taught developmental math and worked with adults who function in terms of reading and math at the 4th grade level, you know that putting them in statistics and just going slower with more tutoring isn't going to make them succeed.  I wish it were so, but it just isn't.  As math teachers, we've all seen students take a course repeatedly and fail it repeatedly.  We know that if they just went back and took the prerequisite course, they would save time and money in the course they're struggling with. You can sit me in a thermodynamics class and go really, really slow and I'm still not likely to pass it because I do not have the foundation skills and knowledge needed for that course.  That is a fundamental truth about some developmental students that has to be addressed and not ignored.  But that's not true for all students.  That is why we need a variety of options for developmental students because one size does not fit all.

One part of the article was encouraging, though:


Pathways courses like MLCS qualify as a  class with an accelerated schedule.  Most students nationwide who place into developmental math, place into beginning algebra.  That allows them to take MLCS.  And the course is one and done.  Meaning it's one semester. And after it, students can take the commonly required college level math courses like statistics and quantitative literacy.

I believe there are workarounds for other students in developmental math.  For students who don't place into beginning algebra, they could be put in bridge programs using products like MyFoundationsLab.  Not to learn the entire math sequence as an emporium model does, but instead to get the knowledge needed to take a course like MLCS.  Bridge programs do not count as courses, but do fall under placement, something the legislators want to improve as well.

For students headed to the STEM track but who still need intermediate algebra, that content could be integrated with college algebra and possibly make both courses better by making one, strong college level course.  Right now, we go so deep into some skills in intermediate algebra that really don't necessitate that for success in college algebra.  We could cut out some of the overly complicated problems for favor of getting the big idea and being able to use it (a philosophy we use in MLCS) and then move into the college algebra topics where the skill is actually used.  Let students learn the content at an appropriate level and then show them why we taught it.  We could also dramatically reduce the overlap between intermediate algebra and college algebra.  This is related to an idea we use in our college's traditional algebra redesign:  cut out overlap and spend more time on each topic, encouraging mastery and understanding.

All is not lost, but some creative thinking is needed to make things work for all developmental math students.