Treisman & Rotman Webinar – June 6 (AMATYC)

Uri Treisman and I have been involved with efforts to systematically reform developmental mathematics, such as New Life, Carnegie Pathways, and the Dana Center New Mathways.  Uri has been very supportive of our AMATYC work, including the New Life project.

On June 6 (4pm Eastern), we will be doing a joint Webinar on Issues in Implementing Reform in Developmental and Gateway Mathematics as part of the AMATYC webinar series.  The goals of this webinar are to present some general concepts to guide our work in reform, and to share some practical means to implement those concepts.

Here is the way the AMATYC webinars work — AMATYC members can register for a webinar (at http://www.amatyc.org/publications/webinars/index.html).  Registration usually begins about two weeks before the event (so you won’t see this one listed in April!).  AMATYC members who register will receive an email with directions (the day before the webinar). 

One thing to point out — people can watch the webinar as a group!  One person needs to be an AMATYC member and register; you can include non-members in the viewing process.  (The directions you receive will even tell you how to make the group process work better.)

I hope you can join us for this webinar.

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Math on the Other Side

A recent post here dealt with the metaphor of developmental mathematics as a bridge, designed to help students reach the other side.  The ‘other side’ is not just mathematics (would we really want that?), with a diverse collection of courses … some of which are called ‘gateway courses’, while others are ‘just’ college courses.  So, the question today is “What about the math on the other side”?

Is the math ‘on the other side’ the good stuff (important mathematics)?  Do courses ‘on the other side’ place a high priority on student success?  If we reform developmental mathematics in to a program which makes a difference in the mathematical learning of students, will their ‘college math courses’ have the same vitality?

These are questions which I can not answer; I am not immersed in the world of college-credit math classes (just parts of it).  However, I do know that our profession is rather silent on this component of our curriculum … we are talking a great deal about developmental mathematics, and I hear quite a bit about STEM and calculus.  Not so much about college algebra … pre-calculus … liberal arts math … or math for elementary education majors.

The easy target in this list is college algebra.  Pre-calculus … at least we know what the goal is (calculus), and students taking pre-calculus can be assumed to have that goal (even if incorrectly assumed).  However, we have absolutely no agreement on what ‘college algebra’ is.  For some of us, college algebra is what we happen to call our pre-calculus course; for this group, I would say “Hey, be honest … call if pre-calculus!”   For others, college algebra is actually a prerequisite to pre-calculus; on this … “how much time is needed getting ready for calculus?”  [Perhaps we place additional steps in between to make sure that only the best survive; I hope not.]  For still others, college algebra is a course outside of the pre-calculus sequence, perhaps used as a preparation for symbolic-based science courses; this is a good reason to have a course … though I question whether ‘algebra’ is the majority of what the students need.  Some use ‘college algebra’ as a general education course; I suggest to you that a course could be either college algebra OR general education … but not both.  One of the problems with the ‘college algebra’ label is that the traditional developmental math courses generally have ‘algebra’ in the titles; is ‘college algebra’ more of that developmental stuff?

Perhaps my worries here are just due to my extensive ignorance of some aspects of our curriculum.  Perhaps, outside of the college algebra mess … perhaps we have generally sound mathematics and important ideas in our curriculum.   Perhaps my problem is that I look at textbooks.  If most of my colleagues who specialize in these courses tell me that ‘things are okay’ on the other side, I would certainly be relieved.  However, with all of the current focus on developmental mathematics, it is possible that we are ignoring something equally important.

In our bridge metaphor, are we working on improving the bridge … just so that students can be delivered to a great wasteland of college mathematics on ‘the other side’?

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Sticky Math

In the world of web design, there is a concept called ‘sticky web pages’ or ‘sticky content’ … the concept being that a design can encourage people to click on links and/or return to the page.  [A brief explanation at http://en.wikipedia.org/wiki/Sticky_content, and some tips at http://techtips.salon.com/sticky-pages-10404.html.]

If you are changing your developmental math program … are you creating ‘sticky math’?  Are students motivated by the design to spend more time than required?  Are students inspired to take more math than is required?

I can hear the cynics among us thinking ‘That is just not reasonable — students just will not do more math than required’.  Well, this is not a question of past evidence … this is a question of the over-arching goals of a math curriculum.  Are we providing the absolute shortest (and presumed negative or neutral) experience with mathematics … or do we seek to provide appropriate mathematics in an attractive manner that inspires students to be more mathematical?

I have been thinking about this concept for quite a while.  Historically, developmental mathematics has been an overly long series of courses to prepare students for the ‘good stuff’ (calculus, in that paradigm).  Some of the current redesign efforts have a deliberate goal of getting students out of mathematics as quickly as possible — often via a set of modules, of which most students need a proper subset.   This “quick out” approach is an understandable reaction to the old courses, and has appeal to people outside of mathematics (like administrators and policy makers).  Most “modularized developmental mathematics redesigns” are based on a quick out for students.

We can do better than a “quick out” methodology.  A common theme of the emerging models for developmental mathematics — New Life, Carnegie Pathways, and Dana Center Mathways — is students are capable of learning sound mathematical concepts presenting in an engaging fashion, which will result in some students being inspired.  Some students will be inspired to work harder on one course or just parts of it; other students will be inspired to consider taking additional mathematics.

Reasoning about quantities, core ideas about proportionality, key ideas of algebraic reasoning, and concepts of functions are components of ‘sticky math’.  Even some traditional polynomial algebra can be ‘sticky’, though not when presented as a series of procedural skills disconnected from broad ideas.  However … the most fundamental ingredient for ‘sticky math’ is the faculty students work with.   Technology has strengths and a role to play; by itself, technology is not enough.

However you redesign or reform your developmental mathematics courses, I encourage you to create sticky math experiences for all of your students.  Provide the ‘good stuff” (important mathematics) with faculty deeply engaged with the learning environment.  Inspire your students!

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The Math Bridge

Imagine, if you will, two small towns near a bridge over a large river. One town (Prima Factoid), priding itself on details and being thorough, shared a belief that ‘being ready’ meant having all of the basic skills taught in their local high school.  They spoke of alignment, of mastery, of students’ taking responsibility for their learning.  The neighboring town (Stepped Up), being populated by realists, shared a belief that every body was ready enough … or they were not eligible.  They spoke of evidence, reports, and things not working.

These towns share the bridge that is developmental education, a major part of this structure being called developmental mathematics.  Prima Factoid constructed levels and additional ramps to the bridge; Stepped Up put everybody in vehicles all going the same speed (fast) with some extra handbooks and ‘life line’ calls.  The two towns had a friendly football rivalry, but this hid a deep mistrust between citizens of the two towns.

So here is my motivation:  Complete College America released a report Remediation: Higher Education’s Bridge to Nowhere    (see http://www.completecollege.org/docs/CCA-Remediation-summary.pdf).  I am disappointed in this report … within their goal of fostering a completion agenda, they label remediation as a failure beyond recovery; they suggest that we place all students in college-level courses (as in Stepped Up). 

However, many of us actually live in Prima Factus, and we need to recognize how mismatched this approach is to the needs of college students.  By living via a basic skills mentality, with an honest desire to help students, we present unnecessary barriers and extra courses in front of students without much evidence of this being effective for the majority of students.

For the developmental education bridge to actually work, we need to be much more deliberate and thoughtful in its design.  To think that all students are ready for college courses with support ignores the deep educational needs of a large portion of our students; to think that all students need to pass courses covering basic skills from arithmetic and polynomial algebra is to provide a weak foundation for college work.

We need balance; we need a clear vision … a vision that recognizes that there are many students who just need some extra support to be successful in college courses without taking developmental courses, while there are many other students with academic needs that should be met in a few courses (like 1 or 2 math courses). 

Reports that totally condemn what we are doing do not help us move forward, just as reports that totally defend the current basic-skill oriented models.  We have fundamental work to do so we truly help our students … ALL of our students.

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