Because the Data Says So!!

A very brief story:  During the portion of a statistics course dealing with inference, the professor presents data on predictors of success in graduate school.  The variables included test scores (GRE, GMAT, or similar), undergraduate transcript data, economic background, and lifestyle (diet, exercise, etc).  The analysis of this data was conducted to see which variables correlated the highest with eventual success in graduate school.  The undergraduates listened with some interest, and expected the professor to announce that it was the grade in an undergraduate statistics course the correlated the best; the class was sad to hear the identity of the winner — eating cooked carrots.  Eating cooked carrots (as opposed to raw, or not eating any) had the strongest correlation to graduate student success.  The statistics professor then stated the obvious conclusion:  We should only accept students who eat cooked carrots, and we should all start eating cooked carrots; only after a uncomfortable minute did the professor challenge us to examine the validity of transitioning from data to a policy decision. 

Last week, the Washington Post published an article on the “Algebra II movement” for all high school students.  (See http://www.washingtonpost.com/business/economy/requiring-algebra-ii-in-high-school-gains-momentum-nationwide/2011/04/01/AF7FBWXC_story.html?)  

Within the movement, the policy makers cite data showing that success in Algebra II is the strongest predictor of success in higher education and the workplace.  Based on this pattern in the data, the ‘obvious’ conclusion is that we need to require all students to complete Algebra II in high school.  As part of the mathematics community, should we accept this support for mathematics even though it is clearly based on faulty reasoning?  Does it matter to college math professors & instructors?

We should definitely care about this … “algebra II” is a self-reinforcing mythology that affects mathematics in the first two years of college.  To some extent, our entrance requirements, our placement tests, and our graduation requirements are all predicated on the “algebra II standard”. Policy makers tend to assume that students who have ‘had algebra II’ should not (as a group) need to repeat it in college — there is an expectation that remediation needs will decline over the next few years. The Common Core Standards (http://www.corestandards.org/the-standards/mathematics) are consistent with the algebra II movement, and many states are adopting these standards with the promise of lessened needs for remediation.

Developmental mathematics is one of the few professions in which the practitioners would like to be in a world where their services were not needed; I know I would be happy beyond description if most students arrived at our doors with sufficient mathematics to enter directly into college mathematics. However, past experience indicates that this outcome for the Common Core & Algebra II are far less than certain.

Of course, we as college math faculty can not (and should not) seek to undermine any standard or policy for school mathematics. However, when possible, we should share our expertise and judgment with policy makers so that they might have a more realistic expectation for the results of a proposed change in school mathematics.
We, along with our professional associations, should seek to remain engaged partners with efforts to improve the mathematics preparation in our schools and colleges.

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Lessons from a Struggling Student

Teresa came to my office this week, in something of a desperation move.  She has been struggling all semester in my beginning algebra class, and did not know what to do.  Teresa  is very thorough about doing homework; as a person returning to being a student after 15 years in the workforce, she knew how to follow through on her responsibility.  

Teresa knew the course was going to be hard work, but it is part of her plan to get an associates degree in 18 months.  When her performance was not at the passing level on the first test, she took immediate action; she hired a tutor, and bought an extra book to study.  After the second test and still lower scores, she changed tutors and bought more books.  Her motivation is outstanding; her commitment to the course is unequaled, and she seeks help at every opportunity.  Routinely, Teresa would understand a topic but be unable to retain her knowledge through time.  Teresa’s frustration was evident; she did not need to tell me that discouragement had caused her to shed quite a few tears.

How could I help such a student?  What was wrong with her strategies? 

Essentially, the problem with Teresa’s strategies is that they were oriented towards external sources, especially experts.  People were answering her questions, and telling her what she needed to know.  Teresa needed to move from a helpless perspective to an active role, one based on confidence in her own learning skills in understanding mathematics.  In addition, Teresa needed to stop expecting frustration and failure … even though failure has been her constant companion for ten weeks in this course.  Learning when expecting failure is nearly impossible.

Do we, as a profession, approach our work like Teresa?  Are we looking for somebody else (‘experts’) to tell us the answer?  Maybe if we just offer modules, mastery learning and extra help we will be successful.  Do we expect to continue to get results like we have had before?  Are we applying our impressive learning abilities to understand the root problems?  Perhaps we can find the ideal text format and content organization … and solve the problem by using contexts that students see as relevant to their lives.   Who owns the problem that is developmental mathematics?

I am completing my 38th year as a professional in developmental mathematics, and there have been ‘movements’ and ‘trends’ before.  For the first time, there is actually an opportunity for us to build something new in developmental mathematics.   Resist the temptation to accept solutions from the outside.  We are mathematicians with keen insights into helping students understand mathematics, and we have access to information on designing a program to respond to the diverse mathematical needs of our students. 

Come to the revival of developmental mathematics … and learn what that means for you and your students.  Come to the revival of developmental mathematics … and imagine our courses dealing with some essential mathematical ideas in a manner that enables students to apply those ideas across other disciplines.  Come to the revival of developmental mathematics … and reach for the goal of a program that enables students to reach their goals, and perhaps inspires them for higher goals.  Come to the revival of our profession!!

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Is Developmental Mathematics an Issue for Racial Equity?

If you are very sensitized to issues of race, this might be an uncomfortable post.  I’ll try very hard to not offend anybody (the comfort level is a different issue than offense).

Some work in Achieving the Dream is framed in terms of focusing on certain groups; see http://www.tjcnewspaper.com/tjc-fulfilling-its-mission-to-achieve-a-dream-1.2133583 for example.  In this article, it is reported that Tyler Junior College is focusing the work especially on “African-American and Hispanic men” … though it seems like both references should say ‘American’.  I won’t get in to the ‘American’  label in this post.

Do you agree with a view of low pass rates in developmental mathematics being a racial equity issue? 

At my own college, the chair of my department did some research on students in our lowest class (pre-algebra); the conclusion was that a course like pre-algebra can serve as a all-too effective racial screening device … the difference in pass rates was fairly extreme.  I don’t want to post them here, but I will tell you that my own research on this over the past 35 years is very consistent with the view that relatively few minority students (especially men) tend to survive the most basic developmental math courses.   

“Why” is the issue?  A student is quoted in the article about Tyler JC as saying this is somewhat related to lifestyle and culture.  I suspect that there are other systemic factors that are at least as important, including the possibility that our standard procedures are less appropriate for students from some cultural or language backgrounds.  I believe that there are factors within the instructional context of our classes that have differential impacts on different groups of students.

A few years ago, I attended a short-course on retention for under-served students led by Craig Nelon (http://www.bio.indiana.edu/faculty/directory/profile.php?person=nelson1) and Bob Grossman (Kalamazoo College, MI); you can see some of this information online at http://www.csmd.edu/istem/events_presentations_nelsongrossman.html.  I encourage you to look for professional development, and resist the temptation to accept low minority pass rates in our courses.

Equity is a basic goal of developmental mathematics, in my view.  We can not ‘solve society’s problems’ by ourselves, but we can be part of the solution.

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Complete College America — focus on ‘remediation’

A recent webinar (March 11) addressed some central concerns of the Complete College America (CCA) alliance, a collaboration of 24 states. 

In this webinar (see http://www.completecollege.org/docs/Completion%20Fundamentals%20Webinar.pdf) remediation was a central issue.  Early in the presentation, the statement is made that “Remediation, as it currently exists, does not make a difference” based on analysis of data for students in gatekeeper courses who had passed remedial math versus those who placed in remedial but did not take remedial math. 

Although this point is valid based on the data, I was encouraged by the fact that the results for math were better than the results for reading or writing:  78% passed the gatekeeper after completing remedial math, versus 68% who placed into remedial math but did not take it. 

Later in the presentation, some novel solutions are described.   Since the presentation was done by several people, I found that the result was a good mix of ideas.  The session on “Transformative Technology” lists “A flavor of the possible” (a very nice phrase), which serves as a reasonable summary of many of the current efforts. 

I was a little disappointed that this CCA webinar did not mention either the New Life project nor the Carnegie Pathways.  We seem to be flying under the radar for many policy makers; this will shift as our implementations begin.