Tuesday, May 1, 2012

21st Century goals mean tough choices about algebra

The role of algebra is a hot-button issue when considering the idea of new developmental math pathways like MLCS.  A common reaction I get is one of wanting all the content we do now in developmental math but done with more relevance and engagement while adding in new topics and skills to address 21st century needs.

The problem with this approach is that it's almost impossible.  Doing everything already in the curriculum but with a new approach and adding content results in large credit hour courses and more time, not less.

New goals mean tough choices.  So what's holding us back? 

Usually it's familiarity and history.  Sometimes it's state guidelines.  But often it's our preconceived notions of what developmental math must look like.

We've always covered certain topics in certain orders in developmental math.  Doing topics in a different order or omitting something can be uncomfortable to instructors.  But what's interesting is what happens when you make these changes.  The classroom is different, the level of engagement is different, and the learning can be greater.  Do we have to graph linear inequalities in a developmental algebra class?  What about absolute value inequalities?  Actually, no.  Look forward to where these topics will be used.  Graphing linear inequalities is used in finite math and business calculus with linear programming.  Ask any teacher of these classes and they will tell you that they have to reteach this type of graphing because students have virtually no recollection of it.  Likewise, absolute value inequalities are use in delta-epsilon proofs in calculus 1.  This is a topic that some calculus teachers omit.  Those who cover it always have to reteach this kind of equation solving because students have no memory of it.  If absolute value functions are used in precalculus, solving is rarely needed.  We graph them and analyze them but solving doesn't usually play into the problems.

We spend a great deal of time on certain topics in algebra, like these, that doesn't pay off in the long run.  Most students don't end up needing the topic and those who do relearn it in the later course through just-in-time instruction. 

But what about what they do need right now?

Right now, the students in developmental math are trying to get the skills necessary to be successful in college and their upcoming math class.  For most, that is not calculus.  Yet, we prepare them all as if that is the goal. 

Across the country, math educators are reaching a common sentiment that calculus is not the end goal for most students, nor should it be for all students.  NCTM and MAA have released a joint position statement acknowledging a change in perspective on this issue:

MAA/NCTM Position

Although calculus can play an important role in secondary school, the ultimate goal of the K–12 mathematics curriculum should not be to get students into and through a course in calculus by twelfth grade but to have established the mathematical foundation that will enable students to pursue whatever course of study interests them when they get to college. The college curriculum should offer students an experience that is new and engaging, broadening their understanding of the world of mathematics while strengthening their mastery of tools that they will need if they choose to pursue a mathematically intensive discipline.

They advocate an engaging college curriculum that is different than K-12 AND one that prepares students for the direction they're headed.  If students are STEM-bound, the traditional algebra route makes a lot of sense.  For most students, their next course is statistics or liberal arts math.  Algebra is not the predominant goal for these outcome courses.  Hence the design of new courses like MLCS that support these needs and goals. 

But MLCS does not feel like an algebra class.  It's very different.  That difference is a good thing.  Just as students have to adjust at first (and they do), instructors do too.  They have to give up old notions that developmental math must include certain topics.  Instead, the goals of this course include critical thinking, reading, problem solving, discussion, and mathematics.  I sometimes wonder where the math is in an algebra class.  Students can mimic their way through without understanding much of anything they're doing.  They're not solving problems, but exercises.  We don't push deeper to challenge understanding but instead work at a skill level.  That isn't good enough anymore.  It's comfortable for us as math teachers, but it doesn't work.  Students aren't prepared for their next course unless it's college algebra.  And many aren't really ready for college level expectations regardless.  The concept of college readiness isn't really addressed in developmental math because our time is spent looking back at high school and plugging knowledge gaps.  Heather often says we're preparing students for something they'll never be asked to do and not giving them they skills they will need.  I'm glad that MLCS is helping change the developmental math landscape, but if anything, it shows me there is more work to be done.  We need to look before and after MLCS and examine our offerings and approaches.  We cannot let history guide all future decisions.

As we wind down on another semester of MLCS, I'm more encouraged by the development of this course.  We are growing our offerings at my college and I expect that will continue each year.  Students like what happens in the classroom and they're getting what they need for their next course (math and otherwise).  Will we still tweak and improve?  Absolutely.  The work is not done.  But I'm encouraged by the progress made in this academic year alone.  3 years ago, 15 math faculty met in Seattle and dreamt of new options and new experiences for students.  Yes, that meant a lot of work and difficult choices, including the role of algebra.  But the outcomes are already proving to be worth it.

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