Friday, June 24, 2011

Two online resources

In February of this year, Pearson hosted a day of webinars on course redesign.  I gave a session on our school's redesign.  Many documents are listed at the left but if you'd like a recording of the presentation (audio and video of PowerPoints included), click here.

The Carnegie Foundation has started a new blog on its Pathways initiatives, Quantway and Statway.  The most recent post describes quantitative literacy and how it differs from mathematicals and statistics.  It's a great read with lots of reference material.

Wednesday, June 15, 2011

Doomed to repeat history?

Those who do not remember the past are condemned to repeat it.

George Santayana

I have received questions about Quantway/Statway and the new MLCS course.  Some want to know, "how is this different than the integrated high school curricula of the 90s?"

Good question.

In the late 80s and early 90s, NCTM released a new set of standards encouraging a different way of teaching and learning mathematics K-12.  Following those standards were years of grant projects, pilots, materials, and eventually textbooks with a new approach:  an integrated approach.  The idea was not to do algebra 1, then geometry, then algebra 2 but instead combine content and integrate it.  A worthy concept but definitely not how we typically teach mathematics.  It has strong supporters and opponents, with good cause.  Because while a curriculum like this can work, it takes a tremendous amount to do so.  It requires good materials, a change in mindset, time to learn how teach in a new way, and abundant professional development.  For more on this subject, please read this article from NCTM's website.

Because these necessary elements do not always occur, integrated models are not always successful.  For a different take on this subject, please read this article about Georgia schools and their experiences with integrated courses.  It is very forthright in both the pros and cons of the approach including why they are dropping this instructional approach.

So what can we learn from this?

Integrated courses have a lot to offer students but execution is key.  This is a new approach to teaching and vastly different from the stack of skills approach most instructors are used to.  It forces us as teachers to integrate our teaching and move between multiple contexts and concepts in one lesson.  Truthfully, not all teachers are comfortable with that nor want to teach that way.  And in my opinion, that's ok. 

Just as students learn differently, instructors teach differently.  It is very difficult to find an approach that suits everyone.  So part of the issue with integrated curricula at high schools was that everyone had to do them.  And they're just not right for everyone.  One person's brain may move in several directions at once, circling constantly to connect ideas.  Another's brain work may work very linearly and sequentially, moving steadily from one idea to the next.  Since we think differently about things, it stands to reason that we should have the opportunity to teach and learn to our strengths. 

Adding to this issue is the concern of what people are using to teach from and how they are teaching it.  Good materials are a must.  But teachers have to know how to use them.  Training and support are just as important.

Integrating these issues (pun intended), here are some reasons courses like Quantway's MLCS can work:

1.  MLCS is one course and does not have to replace the traditional beginning or combined algebra courses.  It augments a program and offers an option for the non-STEM student or the school who wants to offer beginning algebra differently.  But beginning algebra can still live and exist for faculty and students who want it.  It's an option, not a mandate.  Thus, it's more likely to be taught by teachers who like an integrated approach and taken by students who want something different than a traditional algebra course.

2.  The initial scale is small.  Meaning, we're just developing the one course, MLCS, right now.  If it's successful and there is demand, I hope to work on its precursor, a course about numeracy using an integrated approach.  Also, New Life has sketched out a Transitions course to follow MLCS for the student bridging back to college algebra.  There has also been talk of a college level version of MLCS that would be different than the general education math courses that are surveys of areas of math.  Ultimately, all these courses would be options, not replacements, to courses that exist.  And they would be built using a model that would be proven to work.  This "start small and build" approach was not always used by high schools.  Many scrapped their traditional algebra 1-geometry-algebra 2 sequence and instituted Math 1-Math 2- Math 3 sequences.  That can work but if it doesn't, it's hard to change horses midstream.

3.  Materials and a training program are being developed with the goal of addressing issues that will always exist.  I'm a big believer in the idea that "how" is more imporant than "what."  We have components and whole courses in my department's developmental sequence that work extremely well but were flops at other schools.  Why?  Because the execution was different and we tried to learn from mistakes of others.  And I know others have used our mistakes and done better on something than we did.  We're all a part of a large assessment chain.  So, one flaw of the implementation of integrated high school curricula was professional development.  Knowing that, we're designing a training program that will support the materials and course development.  But beyond that, we're developing the materials with the known issues in mind.  One of those issues is that a wide range of instructors will likely teach the course, some who are not familiar with a new type of pedagogy. 

For example, notes to the intructor on teaching the ideas are interspersed throughout the lesson plan and materials.  Instructions on pacing, assessment, grouping, rubrics, and examples of each will be provided.  Additionally, the layout of a lesson attempts to address a common concern:  what's the point of this lesson?  Students will often like integrated lessons but get caught in the detail of the context and miss the forest for the trees.  So we close every lesson by asking students to step back and determine what was learned (mathematical and otherwise) and how it can be used again.  To wrap a unit, we are building specific active tasks that students will do to assess where they're at with all the skills, concepts, and techniques of the unit.  Again, we want students to see the bigger picture and connect what they have learned to date so that they don't get lost in the content.

This is all well and good but ultimately we need to know if it will work.  The Pollyanna in me says yes because I've been through the nonstop assessment process of redesign.  Redesign is not about saying, "we're doing X, now we're done."  It's about implementing something, scrapping what doesn't work, and working until a solution is found.  The pilots this fall around the country will tell us a lot.  Having piloted numerous new projects, I know how exciting and educational the pilot process can be. 

When we redesigned our traditional developmental curriculum, we did so on a large scale right out of the gate.  Meaning, all the pre, beginning, and intermediate algebra classes used the new modular approach with MyMathLab, standard policies and new pacing.  That approach was fine because the changes were largely administrative and structural; teachers could still teach how they liked.  When we redesigned our geometry course, it was just me and two sections of students.  That smaller approach to piloting helped when the content and pedagogy were so vastly different.  Each day, I made modifications and by the end of the semester, we had materials and a method that worked.  And it's continued to work for many more instructors and students.  Partly because of lessons learned during the pilot but also because of the training and instructor resources that were developed after the pilot.  That smaller system approach to piloting will be used as we implement the MLCS course as well.  I'm writing materials and instructor notes now that will be revised as they're piloted, but I'm also keeping notes and doing research for the training program to follow.  One can't work without the other.

So yes, we're in wait and see mode.  But I have a strong suspicion we will see something we like.

Monday, June 13, 2011

The Developmental Math Blogosphere

Jack Rotman was AMATYC's Developemental Math Committee chair prior to becoming a liaison to the Carnegie Pathways project.  He has a blog called Developmental Math Revival.  Check it out and you can see a guest blog article I wrote, Redesign:  Not an Either/Or Situation.