Does Math Exist?

Okay, you have to pick ONE answer for this question, and the only available answers are ‘yes’ and ‘no’.  What say you?

Some of us will say math exists because it provides practical answers to problems and describes the world around us.  Some of us will say that math does not exist because math itself is an abstraction about quantities — not the quantities themselves.

I got thinking about this question as I ponder again our basic label ‘math’ or ‘mathematics’ (though I like the UK version ‘maths’ better than ‘math’).  It’s ironic that there is so little difference between the english word ‘math’ and the english word ‘myth’, because very few people have an accurate picture about math.

How about we start a list of “FAQ” (frequently asked questions) about the nature of mathematics?  We would state the answers in non-technical terms to help the public, especially policy-makers, understand what maths are.  Too often, we have well-intentioned authorities or agencies decree that a specific math course (or set of outcomes) is good for all students … or they decree that all students must pass a certain math course — and place math in the position of gate-keeper.

Here is a start of the FAQ (feel free to add your own):

Question 1: Is, or should, mathematics be practical?
Answer 1: We noticed that the question was not qualified … if this was ‘always’ practical, or ‘all mathematics’, the answer would most definitely be NO.  Mathematics is a collection of sciences dealing with ideas about quantities, which means that most mathematics is practical to somebody.  However, a basic observation about the history of mathematics is that most of the ideas started out being considered impractical but most of them turn out to be practical.  People learning mathematics have to accept that some ideas may not seem practical at the time; a good mathematics course will combine practical uses with ideas that are not always applied.

What questions (and answers) would you add to this FAQ list?

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Good Teachers … Bad Math??

I was in a store today buying cat food and litter (really!!), and the person in front of me at the check-out did a double take … and he asked if I still taught math.  When I said yes he said “I pass math because of you!!”  (Warm fuzzies?)  At that point, the cashier said “Where was he when I was taking math?”  (Cold pricklies?)

Part of today’s educational climate is the push to evaluate teachers, especially in K-12 settings, partially based on student academic performance.  Those who produce higher levels of improvement, or absolute performance, are rewarded with good evaluations; those who do not produce run the risk of being dismissed.  This obsession with evaluation has not reached colleges (yet), though I am really looking forward to the evaluation system like this for politicians.  Somehow politicians can say “it’s the other guys fault” and get re-elected, while teachers saying “other factors negatively impact learning” gets ignored and then dismissed (if their evaluations are not good enough).

It is far too easy to feel smug when a student says “I passed math because of you”.  Why do people say this?  Is it because the majority of teachers are, well, ‘bad’?  Or, is it because the math involved is so distorted from any reasonable need for one person to know, that we are faced with a random function (input is teacher behavior, output is ‘success’)?    If we are facing this random function, we would observe almost all teachers having a student say “I passed because of you” … and I believe that this is, in fact, the case.

We need to push for good mathematics that people actually need to know.  At the college level, the New Life project is based on this goal.  In the school setting, there is the “Common Core” … however, I believe that the Common Core does NOT describe good mathematics that people need to know.  Instead, the Common Core seems to be a laundry-list of topics and skills that members of a group nominated, without sharing an underlying criteria the discriminate between good math and math that gets in the way.

We also need to work on ‘advancing the profession’.  Too much of our work is based on oral history and local traditions, without a common framework for building methods that support good learning.  The New Life project has a hope of facilitating this community-building, just like the Carnegie Foundations “Networked Improvement Communities” strives to build the profession.

I did, of course, thank the student for the comment about helping him pass the course.  If it wasn’t such a public venue, I normally also comment about their hard work being critical. 

I hope you will join me in building good mathematics and advancing the profession.
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Whom Do we Follow?

At the college level, most introductory mathematics has been materials-based … meaning that the curriculum experienced by our students was largely determined by the textbook used.  The vast majority of textbooks considered for a given course would be very similar in ‘objectives’, presentation, and terminology.  Authors would bring minor variations in explanations, and more substantive variations in the range of problems included.

Along comes the ‘redesign-modules-web homework’ push.  The content becomes atomized, with most content described by the algorithms used to generate the problems.  Many of us are delivering courses which emphasize students “doing problems” as a way to get them to “do mathematics”; I would argue that these are not the same, and the differences have weakened our curriculum.

Another push would be the Pathways of the Carnegie Foundation for the Advancement of Teaching (Statway™ and Quantway™), developed in partnership with the Dana Center (Univ Texas- Austin), with assistance from AMATYC.  Rather than driving the curriculum by algorithm, these materials seek to remain true to the mathematical description of the content … the homework system is much more difficult to develop (though they have the best people working on it, and they are succeeding).

So, the question for our profession is this:  Whom do we follow?  Do we follow the atomized content with algorithms defining the outcomes, or do we follow new voices that seek to deliver mathematics needed by our students? 

Perhaps the question is not fair, as some of us are not following anybody … some of us are being told that we WILL walk a certain path, with the atomized content and algorithms; frequently this is due to administrators reaching a critical point in the process, and there is no more patience for a faculty-led process.

As long as we are professionals, we should continue to advocate for our responsibilities relative to our curriculum.  When administrators push, we need to look for all avenues to push back — not to avoid change, not to deny the existence of a problem; no, we need to push back so that the responsibilities remain ours as faculty. 

I hope you, and all of us, will consider our responsibilities … whether we are able to chose whom to follow, or whether somebody attempts to tell us whom to follow.  We have our own professional standards, and our future will depend upon how well we are true to those standards.

 
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A Worthy Calling

Some years ago, my department was dealing with competing requests to add off-campus sections of our developmental courses.  One of these requests was coming from a local hospital, where the staff was very interested in enhancing their education and professional development.  We decided to invest some of our resources to provide our classes at their hospital because this seemed like a worthy calling.

I suggest that all of us who work in developmental mathematics are living such a ‘worthy calling’.  We provide support and professional instruction to students, some of whom have few other options; we help students find their own ladder to a better life.  In many cases, our passion for helping our students is what makes the difference between a student reaching their dreams … or failing again.

We definitely need to re-create what we do in developmental mathematics; far too many students do not make it through our programs, and we effectively serve as a filter in spite of our collective desire to enable our students to succeed.  I hope you will consider the New Life model and ideas.

However, hold your head up!  The calling is worthy, the purpose is noble, and our students need us.  As we start a new academic year, I hope you begin with a sense of purpose combined with a committment to improve what we do on behalf of all of our students.

Together, we can create a new developmental mathematics and look to a brighter future!

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