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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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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Apples, Hats, and Word Problems

In almost all math courses, an emphasis is placed on word problems … applications … real-world  … translation.  Is there a valid reason to include this work?  Or, should the mathematics in a course be restricted to that which is needed to deal with the contextual situations that students encounter?  Do these verbally-presented situations have a valid purpose in our math courses?

Here is the reason I am thinking about these issues — one of my ‘Facebook friends” (also a friend in ‘rl’ = ‘real life’) posted a link to a captioned picture at an online site.  The caption reads:

Everytime I see a math word problem, it looks like this:  If I have 10 ice cubes and you have 11 apples … How many pancakes will fit on the roof?
Answer: Purple because aliens don’t wear hats.

This ‘spoof’ takes its energy from the fact that we tend to have problems that are either obviously worthless (pancakes on the roof) or unreasonable (hats).  You are most likely responding the same way I did … “The problems in MY course are good and realistic problems!”  The criticism here is not what experts might see … the criticism is in what students (novices) see in this work.

First, here is a link to a short report I wrote a few years ago:  Ignore the Story  This report does not deal with how effective ‘word problems’ are — it deals more with qualitative studies.

Second, let us admit a basic fact:  The problems we can include in a course will not convince the majority of the students that those problems provide a justification for the mathematics covered.    Yes, I realize that some faculty will not agree, and hold the position that properly chosen contexts and applications will convince students.  We have a tendency to underestimate the complexity of going into a context to apply mathematics and coming back out of the context; this is hard work, and many students will seek any avenue possible to avoid dealing with the deeper relationships — sometimes working harder to avoid the process than it would be to complete it.  In other words, students will tend to map application processes to the procedures required at the shallowest level that ‘works’.

This minimalist tendency is not unique to word problems; nor is it unique to mathematics … our colleagues in other disciplines experience the same problem.  The difference is that we, in mathematics, expect students to deal with short (often cryptic) descriptions of situations in a variety of areas; students are expected to see mixing two levels of milk fat to be mathematically equivalent to mixing acid solutions of different percent concentrations even though the phrasing is often significantly different.

Elements of a course should support the instructional objectives of the course.  This implies that verbally stated problems should contribute to the mathematical outcomes for a student.  We should be using verbally stated problems to encourage and build a more complete understanding of basic mathematical ideas, and these verbal problems should also contribute to linguistic literacy for our students.  Achieving correct answers is not nearly as important as being able to paraphrase the situation, summarize it, state the known and unknowns, identify relationships between quantities that might be helpful, and write at least one mathematical statement that can be used to ‘solve’ the problem.  These abilities (which combine the linguistic and the mathematical) are much more related to a good prognosis for employment and other goals … more than basic skill accuracy, and more than algebraic manipulation by itself.

The emerging models for developmental mathematics (such as New Life, Pathways, and Mathways) tend to emphasize deeper processing of verbal problems, and de-emphasize repetitive ‘word problems’ which might look like the ‘apples, hats, and aliens’ spoof.  I encourage you to examine how verbally stated situations are used in your courses.  Do they contribute to both understanding basic mathematical concepts and linguistic abilities?

 
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