Language as an Impediment to Improving Mathematics Education

A recent article in the Chronicle of Higher Education was:

Remedial Educators Contest Reformers’ ‘Rhetoric of Failure’ ( http://chronicle.com/article/Remedial-Educators-Contest/145351/)

This is a good article, worth the time to read and think about.  I was drawn to the phrase “Rhetoric of Failure”, a phrase that Uri Treisman used in a presentation at the NADE conference.  However, I’ve been bothered by another aspect.

Think about the word ‘reformers’ in the title … the word is being used to describe the groups (mostly external) who are trying to impose a different design for getting students in to credit-bearing courses (Florida, Connecticut, etc) with the most common strategy being the avoidance of developmental education.

One can not reform a system by avoiding it.

Reformers are those who seek significant changes in an existing system.  I am a reformer; perhaps you are.  We seem to have little power to resist the revolutionaries who want to avoid the system.  Part of this lack of power is likely due to the fact that few people outside of our profession know of the reform work we’ve been doing.  Sure, many have heard of the Carnegie projects (Statway™ and Quantway™); as a high-profile endeavor, that work has been widely publicized outside of mathematics education.  However, few (very few) outside of our profession have heard of our effective work at truly reforming developmental mathematics — the New Life project.

Do the destroyers know that we have a better model that will accelerate students to credit-bearing courses based on a professional re-design of the curriculum combined with a modernization of teaching?  How many people know that there are far more New Life implementations than any grant funded work, past or present?

Calling a group ‘reformers’ is assigning them an intent to improve a system; when revolutionaries make drastic changes, a better word would be ‘destroyers’.  Now, sometimes we need revolutions … sometimes we need destruction.  As I understand the views in the social sciences about change, revolutions and destruction are usually ineffective at producing long-term change.  I know of no reason why mathematics education would be any different.

As long as the ‘reform’ word is used for revolutionary changes, improving mathematics education will be very limited; we are, in fact, likely to regress (which is the most common result of a revolution).  We need to articulate our visions for reform with clear statements of our rationale; we need to challenge statements that attribute ‘reform’ to a revolutionary process.  We need to be comfortable telling external groups that imposing change (a bullying behavior) is not going to fix a problem; revolutions seldom work.

Calling something a ‘reform’ does not make it a good thing.

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AMATYC Webinar on the Michigan Transfer Agreement (MTA) – March 27

I’ve posted previously about the new Michigan Transfer Agreement (MTA), which will help students considerably by identifying 3 pathways in mathematics.

AMATYC is offering a webinar next week on the MTA for community college mathematics departments.  Here is a portion of the description:

The Michigan Transfer Agreement (MTA) is the new general education transfer agreement in Michigan, meant to facilitate transfer between institutions in Michigan.  The basic MTA plan calls for a block transfer of 30 credits for students who have “MTA Satisfied” approved on their transcript.  For the first time, the requirements call for a math course – college algebra (or above), statistics, or quantitative reasoning.

Any AMATYC member can register for the webinar by logging in to the AMATYC web site and clicking on the link in the right column for the March 27 webinar (3 to 4pm, EST).  I will be presenting this webinar.

Although of special interest to Michigan AMATYC members, this webinar might be appropriate for faculty in other states who want to see how a pathways approach to general education works.

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SOAP, PEMDAS … Is there some MATH here?

For some reason, I have always found mnemonics to be irritating.  Perhaps this is based on a worry that understanding was being condensed to a ‘word’ that referenced a ‘phrase’ that had no connection to the mathematics involved.  Because we cover order of operations prior to algebra (questionable), we introduce one mnemonic to almost all students — PEMDAS.  Something about Aunt Sally (we all have one?) being excused.  The mathematical statement might be Grouping, Powers, Products and Quotients L to R, then Sums and Differences L to R.  Somehow, we don’t see “GP(P/Q)(S/D)”, even though it is better mathematically.

Another idea is reduced to a mnemonic — SOAP, for ‘same, opposite, always positive’ in factoring binomials involving two cubes.  This one at least refers to a memory process; this factoring is essentially a formula application.  The mathematics that is lost is ‘binomials of cubes’.  Perhaps this one should be ‘cubic SOAP’.  Of course, cubic-SOAP still is incomplete … it fails to capture the binomial going with the ‘Same’, and the trinomial first term (another always positive).

However, I wonder about the MATH mnemonic.  Perhaps you’ve heard it:

Man, Anything That Helps!!  (“MATH”)

Are we so desperate that we offer incomplete or inaccurate memory aids?  Perhaps we confuse correct answers with understanding mathematics.

Instead, I would like us to consider what this means:

Students should learn good mathematics in every math course.

A list of nice topics does not create a set of good mathematics.  In conversations, I usually find a good amount of consensus on the phrase ‘good mathematics’; we might have trouble articulating a single definition, but we have a good idea what it looks like at various levels of student mastery in various domains of mathematics.

Not everybody in the world uses ‘math’ as a label.  The label ‘maths’ is better, since our field has a plural nature; there is not one mathematic … there are fields of mathematics.  Perhaps if we kept using the word ‘mathematics’ instead of the inaccurate ‘math’ it would help us maintain our focus on why we are here … what we are helping our students WITH.  We are not here to get students to produce a minimal number of correct answers; we are here to help them learn mathematics with value.

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Pathways … for the New General Education

We’ve been working over the past 5 years to develop new courses for our students.  Mathematical Literacy is the first new course, and is doing very well; Algebraic Literacy is the second course, and is just beginning to get ‘traction’.  To help our students, though, we need a new plan … especially for general education.

Take a look at this map:

The Michigan Transfer Agreement (MTA) is designed to improve the transfer of general education courses in Michigan.  The MTA requires one math course; students can use one of the 3 courses ‘in blue’: college algebra, quantitative reasoning, or introductory statistics.

Notice that students can meet their general education math requirement with one developmental course and then the MTA course … unless they need college algebra or pre-calculus.  We have embraced the pathways concept, with direct benefits to our students.

This is good news for students in Michigan.  I hope that other states will create similar structures.

 
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