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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Building a New Developmental Math Curriculum

You may have been wondering whether anybody is ‘making this  real’ when people talk about basic change in developmental mathematics.  Here at Lansing Community College (MI), we have been working on building pathways for students.  Beginning in 2013, we are offering a new course — Math105, Mathematical Literacy based on the MLCS course (New Life).  Math105 will be a prerequisite for 3 of our existing general education math courses.

Connected with this, we planning on a second introductory statistics course which can use this Math105 as a prerequisite.  As a result, students will be able to move from Math105 to one of 4 destination courses — all meeting a degree requirement.  Our beginning algebra course (Math107) will continue to meet the prerequisite for these 4 destination courses, as well as intermediate algebra. 

Here is an image of our math pathways, effective 2013:

NOTES: The prerequisite to Math105 and Math107 is the same (‘pre-algebra’).  We also have another pathway for ‘Tech Math’ (Math114 and 115), which is stands apart from this image (in general); we make exceptions for some students who change programs after starting Tech Math.

So, here is the main point of this post:  Most of us have math courses that are outside of the beginning algebra to college algebra route, such as business math (Math117 at LCC) or quantitative reasoning (Math119 at LCC) … you can implement a course like MLCS (mathematical literacy for college students) to use as a prerequisite for these other courses.  Some of us are still using arithmetic or pre-algebra as the prerequisite for such courses, and you may find that those prerequisites do not meet the needs very well … and MLCS could be an excellent match. 

We at LCC are enthusiastic about building better math pathways for our students, and we hope you will join us in this work.

 
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Mathways Webinar – Video available (April 17 webinar)

The Dana Center (University of Texas – Austin) hosted an excellent webinar on April 17.  If you would like to see the video of the webinar, use this link:

https://danacenter.webex.com/danacenter/lsr.php?AT=pb&SP=EC&rID=5109287&rKey=d960ab9030d6c9f9

One part of the webinar shows this image of the curriculum structure:

I can see some encouraging similarities between this visual and the New Life model; our work in New Life will be very consistent with the work of the Dana Center.

 
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