Policies that Encourage … Policies that Inhibit … Social Mobility and Equity

Recently, I heard that Ohio is the latest state to officially declare that Intermediate Algebra is the minimum prerequisite to college credit bearing math courses.  The results of such policies are seldom positive for students (and these policies do not help us in mathematics education), and they reflect archaic notions about college mathematics.

I suggest that this ‘intermediate algebra’ policy is a regressive practice which disproportionately impacts students from under-represented groups and those from social groups with lower levels of resources.  Stated another way: These policies prevent community colleges from properly serving specifically those groups for whom community colleges are the institutions of choice.  These groups, collectively seen as “low power social groups”, are critical to both the community college mission and our country’s future.

Most data that I have seen suggests two separate factors that make this policy (and its consequences) so bad:

1. Low power groups (underrepresented, or low resources) are placed into developmental math at disproportionate rates and at the lower levels of math at disproportionate rates.
2. Low power groups tend to have even lower rates of success in developmental mathematics (compared to majority/high power groups).

An “intermediate algebra is a gatekeeper” policy reinforces existing inequities in our society, as the students with the fewest options are placed in lower levels of math with more courses to complete but with a lower probability of doing so.

The emerging models (New Life, Carnegie Pathways, Dana Center Mathways) have a basic strategy of creating appropriate mathematics courses for all of our students with a deliberate reduction in the length of the math sequence; instead of 3 or 4 math courses, the new models plan on 2 as a typical sequence.  The “intermediate algebra is gatekeeper” policy conflicts with quicker access to college work, and will limit college completion initiatives; such a policy creates a 72-credit associate degree (counting the required math prerequisites), which means that students using financial aid will ‘run out’ of resources. 

Policy makers are likely to be creating these rules without information on their impact for our students and for the success of our programs.  The AMATYC Developmental Mathematics Committee (https://groups.google.com/forum/?fromgroups#!forum/amatyc-dmc) has a small team currently working on a position statement which might help inform those involved with such policies in the future.

 
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Hope, Vision, and Developmental Mathematics: Moving towards a Mathematical Literacy Approach

This year has seen a number of reports and articles with very strong negative statements about developmental or remedial mathematics.  As an example, Complete College America issued a report calling remediation a ‘bridge to nowhere’ (see http://www.completecollege.org/docs/CCA-Remediation-final.pdf).  A quick online search will produce many citations of this report; other reports and articles have been published. 

Is there hope for developmental mathematics?  Do we have a role to play in the upward mobility within American society?

If we conceptualize developmental mathematics as basic skills or as ensuring that all students have ‘the math they should have had in high school’, then the answer is probably no to both questions.  These approaches describe a remedial mathematics program.  Since many people see ‘developmental’ as a polite descriptor for remedial, perhaps we should begin to advocate a shift towards mathematical literacy as a framework for our work in colleges.

Policy makers look at the results of our programs and conclude that the investments are not appropriate.  Legislatures see the credits used for remedial or developmental mathematics as an inappropriate redundant expense — they have already paid for students to do this work in the K-12 system.   Researchers find that completion of remedial or developmental mathematics courses is not strongly connected with success in college.  States consider banning developmental or remedial mathematics (or all developmental courses).

I suggest that we can, in fact, drop our traditional developmental and remedial math programs as they are currently designed.  These programs are historical artifacts, dating from an era when colleges and universities held different standards for entering students:  College students had to have been good high school students, therefore students who could not show current knowledge of school mathematics had to complete ‘remedial’ courses.

I suggest that we focus on mathematical literacy as a framework for getting students ready for college work.  A mathematical literacy framework means that we do not fixate on the high school math curriculum; rather, we directly deal with the mathematics needed in college.  Instead of 200 ‘basic skills’ in a remedial program, a mathematical literacy program would have a small set of important mathematical concepts and tools — proportionality, growth and decay, representations, numerical methods, basic symbolic methods.

A mathematical literacy program has the promise of a closer integration of mathematical preparation with other college work.  Most college courses do not deal with dozens of discrete skills with few connections to each other; most college courses focus on a smaller number of big ideas, with a focus on understanding and application.  Students who experience a mathematical literacy preparation will have a shorter bridge to cross in order to reach the demands of other courses.  A mathematical literacy program offers the promise that students will be inspired to learn more mathematics, instead of looking for the earliest exit ramp.

The emerging models of developmental mathematics are steps in this direction, although they sometimes allow the traditional developmental math program to continue.  Our long-term goals should include providing a more powerful experience for all students, not just those in select programs.  Whether it takes 5 years or 10 years, let us work towards the goal of replacing an antiquated remedial math model with a functional mathematical literacy model.

Especially in community colleges, enabling upward social mobility is part of our core purpose.  Far too often, our current model prevents students from achieving this upward mobility due to too-low pass rates and too-low completions of a sequence.  We can … and must … do better.  The vision of a mathematical literacy approach offers hope for us and the students who depend upon us.
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Teachers as Resource … Teachers as Problem

Once in a while (more often than you would know from posts here), I read something about education that shows how poorly some people outside of teaching understand what we do, and how we develop.  Today, I read a post on an effort (New Jersey) to remove  ‘bad teachers’ … based in part on standardized test scores.  I have posted about the value-added models that use standardized test scores; if you want to see a critique of value-added models from a mathematician’s viewpoint, see http://www.ams.org/notices/201105/rtx110500667p.pdf .

The article is at Test scores add value to teacher review, which is a blog post.  (I realize that one should be skeptical about the voracity of anything posted on a blog … you never know :).)  We could get distracted by the value-added component, and miss the more central error in such efforts:

Most good teachers were bad teachers at one time.

Personally, I began teaching (like most of us) with good training but bad real preparation.  How can a teacher be prepared to be a good teacher in the first two or three years?  I believe that some people have such an unusual background that they are actually good teachers from the first day; I believe that this is not a reasonable expectation for the group of all new teachers, regardless of the particulars in their training.  Yes, we can improve preparation of teachers at all levels — even college teaching.  Yes, we should have high expectations of teachers … with commensurate high rewards.

At the college level, our ‘standardized measure’ of outcomes is the set of grades we assign to students.  If we analyze these at the level of a specific college, the grade measurements are likely to be valid and reliable enough that some meaningful analysis is possible, always supplemented by insight and wisdom.  At the level of an individual instructor, grades are not so good; depending on the institution, there may not be any standardization at all in this measure.

To me, an obvious approach to the developmental mathematics problem is this:

Faculty are the most powerful resource available.

Instead of saying ‘bad teacher’, we should say “That does not look so good; what did you see happening?”  Instead of saying ‘bad teacher’, we should say “Are there conditions which negatively impacted your students that we could, together, improve?”  Instead of saying ‘bad teacher’, we should say “Can we identify what barriers exist in the learning for specific groups of students … and what development is needed for us to help all students succeed?”

Some of us might think that we do not need to worry about ‘removing bad teachers’ coming to higher education.  Especially in community colleges, we certainly do need to be concerned … whether it is at your institution yet, many colleges have become aware that they have opportunities to prevent new faculty from continuing by critiquing their teaching in the first two years.  Some states are implementing performance-based funding, where colleges get points … and $$ money $$ … for students ‘completing’ developmental mathematics as shown by grades; colleges in these states will have a vested interest in removing ‘bad teachers’ who fail too many students.  [I would like to believe that, in most cases, this removal will not be based just on the grades.]

In the emerging models (New Life, Pathways, Mathways), faculty are seen as the most powerful resource.  Professional development is intended to be be continuous and purposeful; expertise is gained both by the deliberate professional development and by the involvement in network of faculty.  In my view, a ‘bad teacher’ is a temporary condition … and one most of us have in our history.  Like mathematics for our students, becoming a good teacher is basically working hard with appropriate strategies.

Teachers are the most powerful resource; faculty are at the core of all solutions to the developmental mathematics problem.

 
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Our Success — What does it look like?

Perhaps you have been involved with a process which includes classic design principles.  One of the basic design principles basically says “Imagine what success looks like … what it feels like … what it smells like.”  Ideally, this process is done by a group in a relaxed environment; no particular outcome is expected (besides a description).  After this description of what success is (based on perceptual characteristics), the process is designed to lead up to that outcome.

For us in developmental mathematics, what would our description be?  How would we describe success based on what our senses could directly perceive?  Would we even be able to describe success without the use of tests or assessments?

My concern is that we have described our work so much by learning outcomes and by tests (placement tests in particular) that we have very little thoughtful design in our work.  I worry that ‘success’ in developmental mathematics is mostly measured by correct responses to a predictable set of questions.

If developmental mathematics is about ‘getting ready’ for success, then our success imagination should reflect this concept.  Getting ready is not a description that can be used for design — we need to make ‘is ready’ concrete.  Descriptions like “articulate in quantitative issues”, “flexible with basic symbolic procedures”, and “responds positively to novel problem situations” are a start.  What descriptions would you add?

In the emerging models for developmental mathematics (New Life, Pathways, Mathways), some thought has been given to answering this basic question of what success would look like.  However, design is not a universal process; we can not just copy what some smart people have done.  Designing for success is a local process … what does success look like for your students?

I suggest to you that sustainable change in developmental mathematics will only be possible if we apply a deliberate design that considers a larger picture than categories and sets of learning outcomes.  The emerging models provide a necessary component, but not a sufficient one.

I invite you to initiate a ‘design for success’ process at your college.

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