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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Math – Applications for Living IX

In our Math119 course, we are studying models — linear (repeated adding) and exponential (repeated multiplying).  Although some of the details we are including are not very practical, some are practical … and helpful in understanding everyday numbers like ‘inflation’.

Here is a situation we looked at:

If prices increase at a monthly rate of 1.5%, by what percentage do they increase in a year?

Much of our work in class has been on translating from a “percent change” statement to a “multiplying statement”.  Most students saw that this 1.5% increase meant that the multiplier was 1.015.  To answer this question, we just evaluated

We did have a little struggle about using the resulting value (1.1956 …); with a little nudging, we agreed that the annual increase was 19.6%.  Even though we have done quite a few finance applications, this result was a little surprising … students thought we would multiply 0.015 by 12 (18%).

While we were working on models, we also introduced using a calculator procedure to find answers to ‘difficult’ questions [meaning that we used a numeric approach to solving exponential equations].  Take a look at this problem:

Fifty mg of a drug are administered at 2pm, and 20% of the drug is eliminated each hour.  When will it reach 10 mg in the body (the minimum effective level)?

We’ve got that percent change going on; students are generally getting that — this is a multiplier of 0.80.  [This problem is much tougher when I give them drug levels for consecutive 1 hour intervals … like after 3 hours and after 4 hours.].  We set up this equation

To solve this problem, we used a graphing calculator ‘intersect’ process … placing this function on ‘y1’ and the output we needed (10) on ‘y2’.   Our solution (about 7.2 hours)  is useful in understanding the frequency for some prescriptions (3 times per day in this case).  In class, we also approach this same problem as a ‘half-life’ situation; conceptually, that is more complex … and specialized, so we do not emphasize the half-life method.  [Half-life is mostly there to help students if they take a science course which uses half-life concepts.]

We also point out that the intersect process used here is very flexible; it may be one of the most practical things they get out of the course.

 
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