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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Faculty Standards … AMATYC IMPACT

Are you looking for guidance on the core issues in college mathematics?

• Curriculum and content
• Course design and instruction
• Learning environment
• Assessment

Here is a document developed by the AMATYC IMPACT project: AMATYC IMPACT Faculty Standards 2018

This document reflects the best professional judgment of our time, using sources such as prior AMATYC standards, MAA documents, and the “Common Vision” (https://www.maa.org/sites/default/files/pdf/CommonVisionFinal.pdf).  The primary author was Jack Rotman, with content extracted and updated from those other sources; outstanding editing was provided by Mark Monroe (Iowa Valley community college), Pat Hirschy (Asnuntuck Community College, retired), and Anthony Piccolino (Palm Beach State).

I hope that you find this resource helpful as you strive to make your curriculum and instruction modern while serving the needs of your students.

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AMATYC Standards … Where is the Math in IMPACT?

What is the role of professional standards?  Do they address instructional practices only?  Do we need or want guidance on curricular issues?

I am hoping that you consider these questions routinely.  Within college mathematics, both AMATYC and MAA have released standards over the years … with the MAA standards strongly tilted towards curricular concerns.  The AMATYC standards (in the original “Crossroads”), dealt with both instructional practices and curricular issues (see https://amatyc.site-ym.com/page/GuidelineCrossroads/Crossroads-in-Mathematics.htm), though the curricular guidance in that document was primarily a validation of the status quo.

Since that time, AMATYC has released two more standards documents — Beyond Crossroads (2006, https://amatyc.site-ym.com/page/GuidelineCrossroads/Crossroads-in-Mathematics.htm) and IMPACT (2018, https://amatyc.site-ym.com/mpage/IMPACT).  The 2006 standards focused on a process, the improvement cycle, which was to be applied to both instructional practices and the curriculum.

So, what happened with IMPACT?  Curricular issues (the mathematics) are not addressed at all.  The only math in the document arises coincidentally as instructional practices are described.  What does this exclusive focus on instruction mean?  Does it suggest that AMATYC does not see any need to update the curriculum?  No, I don’t believe so.  Is there a lack of consensus?  Very likely, but that does not prevent the development of standards on curriculum.

I think this missed opportunity was the result of a focus on perceptions of what members and faculty in general WANTED to see.  I see this as a confusion between want (a comfortable condition) and need (a challenged condition).  If we judge ‘need’ by what is popular at conferences, the need is certainly for instructional practices — especially those which can be implemented now, regardless of other instruction and regardless of curriculum.

However, leadership involves also judging what people need even when this need is not measured by session attendance.  In some ways, judging this need involves measuring need indirectly — such as the actions of state legislatures and policy makers to mandate curricular changes.  We certainly enjoy discussions about effective and cool teaching methods; it is not happy or comfortable to deal with curricular challenges.

By being even more silent on curricular issues, the newest AMATYC standards leave us (the professionals) with no guidance and no support when faced with external forces and directives.

Now, I need to disclose that I was deeply involved with this newest AMATYC standards project.  From when it started in 2014 as a vague ‘update Beyond Crossroads’ until 2017, I was on the planning team.   In late 2016, I even wrote a chapter for the new standards on faculty issues — combining curriculum and instruction.  You will not see a single word from this chapter in the final document, and that (by itself) does not bother me.  For personal reasons, I had to stop my involvement with the project last year so I had to ‘let go’ of the work.  Other people took the responsibility of creating the document, so they got the decisions.

I would not have minded if “IMPACT” had material having no connection to the chapter I wrote — as long as it supported faculty and departments in all ways.  Instead, we have a very nice catalog of good ideas for teaching … with no guidance on ‘what’ to teach.

The MAA has continued to issue guidance (sort of standards) on curricular issues; I use the CUPM 2015 material far more than I use the AMATYC standards — even though I had been a member of AMATYC for over 25 years and a member of MAA for one.

Our curriculum is under pressure to change, and our curriculum needs to change.  Much of what we teach has remained constant for over half a century, while the needs of our students and our client disciplines have changed dramatically.  If we do not have professional standards from AMATYC, we will have to update the curriculum based on MAA standards — which focus on calculus and ‘beyond’.  We are dealing with a period of change without any professional standards for the curriculum in the first two years of college mathematics.

The question becomes — how can we support each other?

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What Are Math Pathways? A Good Thing?

From what I see, it sure looks like “we” have decided that math pathways are a good thing.  What does the phrase refer to?  Are they usually a good thing?

The first question is more difficult than most people would expect.  Most definitions are implied … a set of objects is called a math pathway.  Digging a little deeper, the most common reason that set of objects is called a math pathway is that the identified objects form a sequence of courses which avoid algebra when possible.  As you know, there is a strong belief in the assertion that most people do not need algebra; calling something a ‘math pathway’ gives it a nice sound and appeals to this belief.

So, what mathematics remains in a curriculum (excuse me, a math pathway) if we generally avoid algebra?  We could choose to include deeper concepts from geometry, a strong background in proportionality including judging its validity in diverse situations, or other topics meant to strengthen the mathematical abilities of the students. What is the most common focus in math pathways?  “What do they need in statistics or quantitative reasoning?”  Are creating a curriculum for our students based on Lone Star’s direction after his Winnebago ran out of gas:

Take only what you NEED to survive!   [Spaceballs]

In some math pathways, content is only included if it passes this test of immediacy — We will teach it only if students really need it in basic statistics (or quantitative reasoning).

In other words, “math pathway” involves both algebra avoidance and restricting content on what is needed for one specific class.  Compare this to the traditional college/dev math program … which involved algebra obsession and restricting content to what is needed for one specific class (college algebra).  I would suggest that the vast majority of modern math pathways are just as faulty as the traditional math courses they replaced for those students.

Many of the math pathways are specifically targeted to statistics.  The role of statistics in mathematics education has been debated here before (see  Plus Four — The Role of Statistics in Mathematics Edation).  However, think about WHY statistics is being so commonly used as a general education ‘math’ course — people see it as “practical”.  [Many of the quantitative reasoning courses suffer from the same ‘usefulness’ syndrome.]  Few people seem to be questioning this love affair with statistics.  Sure, there are ‘studies’ which indicate that a number of occupations involve the use and interpretation of data.  Some of the largest occupations in this group are nursing and related programs.  Certainly, people with a long-term goal of being a high-level nurse (perhaps supervising and administering a clinic or hospital) will need to use statistics to carry out their work.  However, the vast majority of nursing graduates — especially at the associate degree level — are expected to have a different skill set, including a bit of algebra.  At the same time, the statistics class does nothing to help students deal with the mathematics they encounter in their science courses (proportionality and algebra).

It is my hope that we will awake from our current sleepy state and critically assess the proper role of statistics as a general education math course.

Some readers may have had the dubious pleasure of attending one of the various presentations I have made over the years, and some of this group my puzzle at the apparent lack of support for practical applications in this post.  We often hear more like we want to believe … I have advocated for mathematics that helps our students succeed, and — sometimes — this involves a focus on the practical.  Education is not achieved by learning only the mathematics a person can see applied at a point in time; that is a description of training.  We are mathematics educators, not occupational trainers.

On the other hand, ‘math pathways’ is beginning to be used to include all targets including calculus.  AMATYC, for example, has a grand committee on pathways.  That is fine, I suppose.

To the extent that math pathways help us improve the mathematics all students experience in our courses, math pathways are a good thing.  My motivation for the “New Life Project” New Life Project (AMATYC, et al) was based on this goal; the support of New Life for Pathways was coincidental.  Perhaps math pathways have improved the mathematics experienced by those students in the stat or “QR” pathways … I might be wrong that they haven’t.  However, why would we want to focus so much on the non-STEM students?  All students have dreams and aspirations; we should be encouraging and enabling many more of our students to see their STEM potentials.  Why should STEM students receive a second class education?

I believe that math pathways have been a net negative.  We have improved “outcomes” but not mathematics.

All of our students deserve good mathematics.

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