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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Modules for the Developmental Mathematics Not Needed

Modularized mathematics is a common curricular strategy in our era, with a common justification and design strategy being the identification of what math students need.  Separately, I have posted about the use of modules (and I will have more to say on them); today, this is about the use of ‘identifying the math they need’. 

Here is a short story, a parable, with your indulgence:

Felicia and Ashley have been managing a service-oriented hardware store in their town for five years, and they finally have enough capital accumulated to remodel their store.  In their planning process, they realize that it is important to make sure that they effectively meet the needs of their customers.  With the help of a PR company, Felicia and Ashley design a web survey form that the customers can use to identify the items and categories of need.  Naturally, the items and categories are based on what the store has already been selling.  Many customers complete the survey, with a surprising consistency in the general results.  Based on the results of the survey, a remodeled store opens with the merchandise reflecting the survey … items needed by many are in-stock and visible in an attractive display; items needed by a few are done as a special order.
After two months, it becomes clear that the new store is far less profitable than the old.  A new survey is done to determine the problem, including areas for general comments. The results of this survey show that there were two causes of the problem.  First, it turns out that the ‘items needed by a few’ were significant as a group … many items “less needed” accumulated over many customers creates a large change; the special order process did not meet the needs.  Second, and mentioned on every comment, is the fact that there were four areas of emerging need in hardware that were not listed on the original survey; since they were not even listed, customers could not report this need.  These emerging needs reflect both the newest do-it-yourself projects and the maintenance of the newest homes.

When we design modules or courses based on a content survey, we are beginning with the assumption that “what is needed” is within the existing content.  This survey approach is commonly used for module designs, as well as research on the mathematics needed in various occupations.  If we run a hardware store, there is an implied responsibility to understand ‘hardware-ology’ deeply to understand the needs of the patron even before they know what they need.

We run a mathematics learning enterprise.  We carry a responsibility to deeply understand the mathematical needs of our students.  Our situation is, in fact, far worse than the hardware store in the parable; the hardware store was successful before the change to ‘needed’ items.  Mathematics programs …developmental or college credit … are definitely not successful currently.  If a particular math program was already successful, there would not be much motivation to ‘modularize’ or to identify math needs; the fact that a program is modularized is a direct statement of non-success.

I suggest that you consider the more basic question:

Is it possible that our mathematics programs are not meeting the mathematical needs of our students and that this is a major factor in the program not successful?

Existing developmental math content is based on an archaic set of school mathematics content; it does not reflect the changes in schools since 1965.  Existing introductory college mathematics is based on a curriculum extended from that archaic foundation.  As you know, extrapolating from a model to a new set of domain is a risky process; not only do we assume the validity of the original model (not justified in math), we assume that the extrapolation is valid.  We have significant curricular studies that conclude that the extrapolation is not well founded; see the work of MAA ‘CRAFTY’ (http://www.maa.org/cupm/crafty/.

Here is what we need instead of ‘need based on current content’:

We need to identify the basic mathematical knowledge needed for our students to be prepared well for the mathematical needs of their college academic work as well as societal needs.

A friend of mine is a somewhat famous economics educator in community colleges.  Current economics work is very advanced mathematically; however, introductory economics (micro, macro) are taught qualitatively with very small doses of quantitative work.  The reason?  It’s not that economics educators don’t want or need quantitative methods at the introductory level … the reason is that their students are woefully prepared for quantitative work, even after algebra courses.  We ‘cover’ slope, but not rate of change in general (for math courses most students take); what we do cover is done in a way that inhibits transfer of learning to a new setting (economics).  I’ve had this same conversation with science faculty, with the same result; I expect that much of the same story would be found in some social sciences.

The use of modules in curricular design raises issues about learning mathematics.  The use of ‘what students need’, when based on existing content, reinforces an archaic model of mathematics.  It is our responsibility to understand our students’ mathematical needs at a deep level, to the depth that we can identify content that is outside of the current curricula.  If we can not judge this need, nobody else will.

The New Life model was based on exactly this type of work; we identified the needs based on a professional understanding of the quantitative demands of current students, especially those in community colleges.  Some of this work is now imbedded in the Carnegie Pathways, and has a similar development in the Dana Center’s “New Mathways Project”.  The curricular design in these efforts seeks to begin meeting students quantitative needs, starting on the first day of their first math course (developmental or not).

 
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Editing Math: Writing as a Guide to Better Mathematics Learning

I was talking to a colleague who teaches writing about the placement test, wondering if the test they happen to use gives them results that seem valid for getting students in to the best course.  As we were talking, I wondered … could we learn from the writing placement tests and writing courses about how to help our students?

The writing placement test we were talking about is one of the very common instruments used to place students at community colleges.  The test contains a series of writing samples (one at a time); students need to identify sentences with errors, and then also answer a question or two about the writing.  When I asked my colleague about how well this worked, he said that it primarily just tested editing skills as opposed to writing skills.

Would math learning be improved if we held ‘editing’ in higher esteem?  Would students become more able to think in mathematical terms if they routinely examined their mathematical writing?  Should our math placement tests involve the process of students editing mathematical work to identify either strategic or tactical errors?

Like many of us, I routinely tell my students to check their work for errors.  Competing with this ‘proofreading’ direction is the type of ‘check’ suggested in most textbooks (put it back in).  The concept of editing applies to mathematical work, which we practice when we develop handouts and other materials for our students.

In developmental mathematics, a portion of our population are not yet ‘college level’ in their writing; students are challenged to write clear sentences and paragraphs … and challenged to write clear mathematical steps and solutions.  Writing is the most direct measure of the knowledge held by the student, which is a tool for the student to look for gaps and confusions.   Perhaps editing this work is a step along the path towards more developed metacognitive skills.

I would like to try this concept in my classes: Editing mathematics as a learning tool.

Separate from the classroom use, I wonder — should math placement tests involve different processes other than “get the answer”?  Would we get better measures of readiness if students needed to examine a few steps of mathematical work to identify errors? 

 
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Reform Efforts in Developmental and Gateway Math Courses

Are you looking for a ‘one-stop’ summary of reform efforts?  Perhaps you have been told you need to do a redesign, and wonder if there is a better alternative.  Maybe you have been teaching in a redesigned curriculum with intense use of technology, and are looking for something that works  better for your students.  The purpose of this post is to provide a quick summary of some national efforts and a few state-based efforts.  [Some of this was shared at the end of the June 6, 2012, webinar on reform in developmental and gateway math courses.]

New Life Project  (AMATYC Developmental Mathematics Committee) — project information at http://dm-live.wikispaces.com

The New Life Project developed a general curricular model to replace the traditional developmental mathematics courses, based on applying the work of prior professional work (such as MAA, NADE, Numeracy Network, and others) with a goal of fundamental change not only in the curriculum but in the profession.  The work is fundamentally based on the more progressive ideas in the AMATYC Standards ( Beyond Crossroads, http://beyondcrossroads.amatyc.org/).  Colleges and faculty implementing the New Life work adapt the general model to their specific local needs and resources; no grant money is involved with the project.  The New Life model can be used for targeted groups, or for all students.

Dana Center New Mathways Project — information at http://www.utdanacenter.org/mathways/

The New Mathways Project is an evolution of the Statway™ and Quantway™ work, which was a shared development by the Carnegie Foundation (see below) and the Dana Center (University of Texas – Austin).  The Dana Center used additional faculty and college input to elaborate a model for 3 basic paths — Statistics, Quantitative Literacy, and STEM, each sharing a new Student Success course.  The New Mathways Project includes development of all instructional materials, which is about to begin.  The project web site has a very useful implementation guide which will help any reform effort.

Carnegie Foundation Pathways (Statway™, Quantway™) — information at http://www.carnegiefoundation.org/pathways-connection

The Pathways Project was begun in 2009, which parallels the work of the New Life Project; the initial math learning outcomes for the pathways came from the New Life work, and several people were involved with both efforts.  Currently, the Pathways are “closed systems” — access to the curricular materials and homework system is limited to colleges which are members of the “Networked Improvement Community” (NIC); members of the NIC work together to implement a generally uniform curriculum.  The Pathways implementations are limited to targeted groups of students — those who need a statistics course or those who need a quantitative reasoning course.  The development of the Pathways was grant funded; colleges joining at this stage will be paying modest fees to support the work of the NIC.

AMATYC Right Stuff for college algebra — information at http://www.therightstuff.amatyc.org/

The Right Stuff project developed alternative lessons for a college algebra course used for general education, with NSF funding.  A strength of this effort is the concrete modules that instructors can implement; the project also has a web page of other resources for college algebra (see http://www.therightstuff.amatyc.org/resources/).  At this time, there is no known effort at the national level to broadly change the college algebra courses … though MAA has issued a number of reports and calls for change.

State effort — FOCUS (Texas State University ) — information at http://www.math.txstate.edu/devmath/FOCUS.html

State effort – CAP (California Acceleration project) — information at http://cap.3csn.org/

State effort — RPM (Rethinking Precollege Mathematics, Washington) — information at http://rethinking-precollege-math.wikispaces.com/

If you are aware of other efforts (national in particular, or especially in college algebra  & gateway courses), please let me know!

 
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