Category: Professional Motivation

Bias in Mathematics Education: Did You See an Elephant?

People in the profession of education — including mathematics education — are prone to exhibit some common modes of reasoning.  We tend to value linearity within learning, compliant students, and evidence which supports our current outlook.  Until we overcome this bias in evidence, there is no hope to make real progress for our students.

 

 

 

 

 

 

 

A concept used in social science research (which is what education is) is ‘confirmation bias’.  Although the image above refers to ‘facts’, for our purposes the word ‘evidence’ might be a better fit (and I also include the phrase “established scientific research”).  We are so cursed by this bias that we seldom are aware that we are extremely biased.

Some examples:

  • At a conference, we select sessions dealing with what we are currently working on … ‘what we want to hear’ becomes a guarantee of what we hear.
  • In our department, we discuss issues almost exclusively with colleagues who are known to agree with us on problems and solutions.
  • When we read professional material, we seek out mathematics or pedagogy that we are already using.

My concern today is not the ‘other’; the concern is us.  Although it is certainly true that Complete College America (CCA) and the organizations bringing us the “Core Principles” of remediation are suffering from severe confirmation bias, their problem would not be able to impact us … unless we are already in a weakened rhetorical state.

 

 

 

 

 

 

 

 

 

Our theories are often as immature as the mythical blind mind finding out what an elephant is like — we experience 1/100th of the entire domain, and conclude that we have a theory for the entirety.  Something like “students have short attention spans, so never try to have a prolonged exploration of a complex topic” or “yes corequisite remediation works after all” or “showing students I care will result in them learning”.

Not only do we have confirmation bias about the learning process, but we have the same type of bias about mathematics itself.  If you don’t rebel at the phrase “mathematics hasn’t really changed”, you have not been paying attention.  If you expect that mathematics remains stagnant, that is exactly what you will see — in spite of overwhelming evidence which conflicts that point of view.

The phrase “growth mindset” is all the rage. Apparently, this only applies to students.

 

Letting Go: The Final Vertical Asymptote

Shortly (like 2 months), I will be putting my professional work into the function which produces no output at all — retirement.  Perhaps a better metaphor is that the function has a final vertical asymptote at the end point of the domain.

 

 

 

 

 

 

 

 

 

My career has actually had several points of discontinuity, where the next function value substantially differs from the prior value.

  • The first 5 years were focused on support for my college’s large and successful self-paced “Math Lab” — which initially had 13 courses in the same room with two instructors.  One of my duties was to hire and train student workers; of these workers, one of them would eventually come back to my College as an adjunct faculty.
  • The longest period without a discontinuity (19 years) came next … I provided part of the faculty leadership for the courses and instruction in that Math Lab.  One of our students started in beginning algebra, and eventually came back to my College as a full-time faculty.
  • The largest gap occurred next — I was loaned to the College’s registrar’s office to help implement our student software system (“Banner”), and eventually I functioned as an associate registrar.  Instead of AMATYC conferences, I attended the “Banner Summits” each year.
  • After 5 years, I returned to ‘faculty’ duties though not exactly as the earlier time.  The College’s Math Lab was no longer an option seen with pride, as the administrators did not provide support and our own faculty made decisions which contributed to the downfall.  This unhappy period lasted 8 years.
  • In 2010, the Math Lab officially closed.  This was the first year where all of my teaching was in ‘regular’ classrooms with larger groups of students; my initiating work with teaching was all one-on-one or pairs in the Math Lab.
  • Although relatively small, another point of discontinuity occurred two years later as the department chair asked me to take over our quantitative reasoning class.  This class was the most fun to teach of any class I’ve done.  Within 5 years, this class went from 60 students per year to 400 students per semester.
  • The last point of discontinuity occurred when I was declared not qualified to teach that QR class.  My final 4 years have been focused on dev math — though I spent two separate periods serving as an ‘acting academic coordinator’ for the department (planning, staffing, enrollment, etc).

 

 

 

 

 

 

 

 

{image is NOT a perfect match for the metaphor 🙂   }

 

This is my final semester of teaching mathematics.  On the other side of the last vertical asymptote, awaits other type of activities — family and (hopefully) volunteer work.

Throughout my work in AMATYC and MichMATYC as well as the Dana Center and Carnegie Foundation for the Advancement of Teaching, I have appreciated the help and support of MANY people.  For that, I thank each of you.

For the curious, this blog (DevMathRevival) will continue for another few weeks.  Some posts are likely to be reflections on my career, while other posts will be the type of commentary previously seen here.

 

Re – Writing the Job Description for a Math Instructor

[A guest blog post from Larry Stone]

In the two-year colleges of the near future, what will a math instructor do to earn his/her pay? What, exactly, will his/her job involve?

The model I see emerging is: setting some software to deliver a standardized list of prefab learning items (perhaps checking a few boxes to add or delete some items),
scheduling a few automated assessments, then letting each student follow an individualized path at an individualized pace (taking individualized assessments).
Occasionally, the “instructor” should check in to view the dashboard, just to make sure everyone’s been logging enough hours. Intervening in the actual learning process is only
necessary when the software seems to be struggling in guiding some student towards the correct responses – but we may expect this to become less necessary as the software
continues to improve year after year.

So, what is the math instructor of the near future? In essence, a software jockey with some tutoring ability.

Now consider: how much skill and training does that require? Presently, we hire experts with master’s degrees to teach almost all of the classes: teaching is a profession.
Instead, one can picture a small group of programmers and content developers at the center, with lesser trained software jockeys (to be nice, let’s call them “student support
specialists”) distributed among the schools. The huge potential savings to higher education, where the cost of high-credentialed labor is the largest expense, makes it easy
to see why we are inexorably moving towards this model: it’s individualized instruction for all, which makes it sound good, but it’s cheap, which is apparently the ultimate good.

But will we lose something that we could never get back?

When I proudly entered the profession in 1999, it was still a mostly traditional environment. It felt like a perfect fit for me, because it gave me the opportunity to
exercise two of my professional strengths: I love to write-write-write, crafting and re-crafting materials to make them fit together and flow ever more naturally, and I love to
put on a show, sharing my enthusiasm for math and engineering and the great fun that comes from understanding how the world works. Instructors at that time were expected
to be heavily involved in developing their learning objectives, lectures (not a naughty word if done well), exercises, projects, and the like; and as for “putting on a good show,”
that was the main reason for teaching at a two-year college instead of a four-year college: good teaching, not voluminous research, was what mattered.

I now see how fortunate was my timing: I’ve had a great run for twenty years. What has surprised me the most is that, having a human mind interacting with a human
world, I still continue to have sudden insights about how to make things even better! It keeps the job fresh, fun, interesting, and in tune with an evolving world. Best of all, I am
free to immediately incorporate my ideas into my curriculum, assessments and all, without having to worry about how it messes up some software’s learning item
connectivity database. The master plan is entirely in my own head, and that I can easily adjust. I feel like a craftsman at work.

I even dare say, I’d be pretty good instructional software if I could be downloaded — but we’re not really there yet with the technology, are we? Are we even close? Perhaps,
before we ditch the master craftsman model in order to adopt the factory automation model of education – before we lose the generation that understands what teaching as
craft is all about, and find ourselves dissatisfied with the skin-deep, stimulus-response McEducations that will result — we should ask ourselves: how easy will it be fix THAT
situation?

Instead of sliding down that road, we should refocus the original question. What SHOULD a math instructor’s job involve, in a perfect world? I’ll offer just four ideas:

  1. Writing good learning objectives and lessons, hand-crafting exercises and assessments, and using classroom experience (and other experiences, such as
    from teacher conferences, etc.) to continually improve these materials over the course of one’s career. Besides having the basic drive to produce quality work, the
    instructor should delight in finding new ways to communicate ideas that seem to open up possibilities for ever deeper learning and insight.
  2. Close, daily grading of student work, in order to hand-write custom feedback and advice for each student, while also learning which areas may need to be re
    addressed in the main class (which can be amazingly different from class to class and term to term). It takes time, but this, in my experience, is by far the best way
    to take the true pulse of your classes. Certainly, it provides a richer feel than turning to summary statistics on a computer.
  3. Using one’s own professional and life experiences to show how learning content relates to the “world out there.” Nobody measures this, but as a student in college
    I always felt it was truly worth something to be coming into contact with so many different content experts, each applying his/her own unique background and style
    to the subjects at hand. You learn things that aren’t in the book/aren’t in the software. Believing one has a unique and valuable perspective to share that may
    inspire some students to go further is part of what motivates one to become a teacher.
  4. Getting to know each student as a person. Besides putting students in a receptive mood, it helps one know how to be personally supporting and encouraging, in
    ways indescribably more effective than pop-up messages from the software saying “your hard work is paying off!” for the sixth time this week.

 

Computers are great for taking over tedious, repetitive calculations, but this is not what math education involves. If you view any of the above tasks as potentially tedious
then, historically speaking at least, you’re in the wrong profession. Meanwhile, show me a computer that loves teaching this stuff and maybe it can learn to take over my job —
but the technology isn’t there yet, and may never be.

by Larry Stone; February 26, 2019

Theory of Everything … A Presentation on College Mathematics

Presentation done at the MichMATYC conference on October 13, 2018 at Kalamazoo Valley Community College … with a goal of understanding everything about college mathematics in the first two years.

Presentation:  Theory of Everything presentation Oct2018

References (handout): References Theory of Everything Oct2018

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