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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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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Teams for the June 6 Webinar

Separately, I’ve posted information about the June 6, 2012 webinar (“Treisman and Rotman”).

I encourage you to participate in this webinar as a team.  Perhaps you have a conference room with a large monitor, or a classroom with a digital projector.  Being there as a team can be part of your local process of change building toward reform.

In addition, more people can participate this way.  Registration for the webinar is limited to AMATYC members … others are welcome to participate as a team.

Also, if you can not participate at all on June 6, note that the recording of the webinar will be posted later in June.  When it is available, I will put the information here.

Webinar Registration is open — Treisman & Rotman, June 6 (AMATYC)

Registration is now open for AMATYC’s next webinar: Issues in Implementing Reform in Developmental and Gateway Mathematics.  Details appear below; registration is currently open to AMATYC members and there is no cost to register for the webinar.

Webinar Details:

Presenters: Uri Treisman and Jack Rotman

Date: Wednesday, June 6, 2012

Time: 4:00pm EDT / 3:00pm CDT / 2:00pm MDT / 1:00pm PDT

Description: Uri Treisman and Jack Rotman will discuss issues that should be considered in implementing reform efforts in early college mathematics starting with a comprehensive theoretical framework to guide the work and narrowing down to key principles for the work on-the-ground.

Sponsoring Committee: Developmental Mathematics

To Register, Click Here

Registration is limited to AMATYC members; however, the webinar will be recorded and posted for general viewing later.  I’ll post a notice when that recording is ready.

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