Anti-Algebra College Mathematics: What are we DOING?

Much “cool-aid” has been distributed in recent years (as in “he/she has drunk the cool aid” … become a ‘convert’).  Our institutional leadership cadre sing the praises of ‘alignment’ and pathways, and celebrate the emphasis of non-algebraic courses in college curricula.

Of course, the word ‘algebra’ itself has multiple meanings. In this post, I am referring to polynomial algebra along with the reasonable connections to geometry, trigonometry, and modeling at the curricular level of first year of college.  The delivered curriculum in ‘algebra’ has degraded to the point that the primary student outcome is ‘survival’ that qualifies them to take another course.

This is not the same discussion as “Algebra II for All” in the K-12 world; we could debate the pros and cons of that issue, though in most ways that train has left the station.  Our interest is in college mathematics in the first two years.

At the  highest level, an observation is that the enrollments in STEM-enabling math courses is declining based on increased enrollments in courses aligned with programs (by which I mean statistics and quantitative reasoning [QR]).  As a general education course for students in non-scientific programs I think a rigorous QR course is the best option.  Such a rigorous QR course includes a significant focus on algebra and algebraic reasoning.  We probably don’t reach that goal very often in QR courses.  In any case, the STEM-enabling math courses are declining in enrollment.

Why?  Why does our leadership consider these non-algebra options to be superior?  Is it because they have conferred with us about the mathematical needs of students within the context of their programs and the issues of the 21st century?  Have some of us taken on the anti-algebra mantle to the extent that we encourage excessive emphasis on statistics and QR?

Sometimes, algebra has been used as a filter to weed out students who “can’t make it”.  Let’s be honest — that is not the nature of algebra, only the nature of algebra courses used to weed out students.  A positive … and accurate … conception of algebra is this:

  • Algebra provides a set of tools for representing scientific and technical knowledge
  • Algebra provides a framework for dealing with quantitative problems which are not primarily computational exercises
  • Algebra encourages precise communication

If students do not need to deal with scientific or technical knowledge, AND will not need to deal with quantitative problems, then the emphasis of QR and statistics is not inappropriate.  As mathematicians, we value the precise communication aspect of algebra, and we might even make the case that this type of communication is just as foundational as the ‘regular’ communication areas (writing, speech, etc).  That rationale is probably insufficient to require students to take an algebraic STEM-enabling course.

Let’s just consider the first feature of algebra — representing knowledge.  Take a look at the occupations with the best employment prospects (above minimum wage), and I think you will find primarily scientific and technical fields (including health careers).  Some of the very best employment prospects are in highly quantitative professions.

We don’t need all of our students to declare a STEM major (though we can always dream of what this would be like).  However, I wonder if the rush to completion is putting a large portion of our students in programs for which they are either not prepared for the jobs available OR not prepared to handle the quantitative demands of those jobs.  That statement might not be clear; here’s an example of the latter condition: students in an associate degree nursing program take a statistics class to meet their math requirement, but they are not prepared to deal with problems requiring algebraic representations or algebraic reasoning.

The ‘elephant’ in the room is how poorly we have been delivering algebra-based courses in college.  In spite of fundamental changes in both the mathematics profession and in K-12 mathematics, we still emphasize courses which might be called “death by algebra” … which serve to weed out students rather than prepare students.  How could we, in good conscience, suggest to our leadership that these algebra courses should be used instead of the QR or statistics course?

The changes in college mathematics, so far, have been at the edges — developmental mathematics reform and co-requisites (usually for QR or statistics).  I believe that the external pressure will come to our algebra-based STEM-enabling courses:  either we make fundamental changes to those courses OR the leadership will make curricular changes that take our courses out of the normal set of student programs.  Within 10 years, we could be dealing with a situation in which the only students taking STEM-enabling math courses are those in ‘high’ STEM fields (physics, engineering, perhaps a few math majors).

What’s the future you want to see?  What’s the role of STEM-enabling math courses in your vision?

 
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Where We Are … Lansing CC

We have heard the same type of ‘statistics’ cited as evidence that developmental mathematics is a failure.  “Too many students place into remedial mathematics” … “remedial mathematics blocks students from completing a college math course” … and similar data mcnuggets.

Here at Lansing CC, we are working on a different narrative, with a story of student success within a department willing to make fundamental changes because we think those changes will result in a better experience for our students — as opposed to ‘because the state (or chancellor) told us we had to’.

Here is a representation of the progress we have made:

 

 

 

 

 

 

 

 

 

     Source:  Lansing CC Center for Data Science, Feb 2018

 

This chart is showing the proportion of students enrolled in credit level mathematics out of the total (including developmental).  Within 5 years, we have doubled the rate of students taking credit math courses.

Here is a chart of our basic curriculum:

 

 

 

 

The progress is the result of several changes and decisions:

  • Eliminating pre-algebra as a course
  • Replacing beginning algebra with math literacy
  • Using math literacy as the prerequisite to the quantitative reasoning (QR) and statistics courses
  • Removing intermediate algebra from the list of general education courses for an associate degree

The only co-requisite work involved (so far) is within developmental courses (Math Lit with Review; Fast Track Algebra).

Another piece of good news is that we have slightly more students in the initial STEM path courses (college algebra & pre-calculus) than we do in the QR and statistics courses.

Early in April, I will be delivering an AMATYC Webinar on “Dev Math: Past, Present, and Future”.  In that webinar, the conclusion will be some thoughts on what a brighter future could be for us … including a specific vision for the curriculum in the first two years.  I hope you will consider being a part of that webinar (tentatively scheduled for April 3, afternoon).

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Academic Cheerleaders as Change Agents

Like many institutions, my college is looking at fundamental changes in how we handle remediation.  My math department has eliminated arithmetic, pre-algebra, and beginning algebra as college courses; we’ve implemented a full-blown mathematical literacy course (over 700 enrolled last semester) and offer an accelerated algebra course.

However, we are still being subjected to pressures from within the institution.  Our president made several remarks critical of our work at a college-wide event, partially based on not understanding what we have already done.

Last week, my college brought in an ‘expert’ who gave a presentation on “success and equity”.  By ‘expert’ I mean that the qualifications were (A) employed (B) PhD in hand and (C) agreed with college leadership (the president in particular).  I refer to this type of expert as a “cheerleader” — their task (based on what was presented) was to motivate us to implement a different solution, just like cheerleaders in sports try to get everybody motivated.

The question is this:

Can cheerleaders be effective change agents in academic work?

I’ve actually thought about these issues for a number of years.  When I began this blog as part of the AMATYC “New Life” project, I needed to understand what forces and conditions are necessary for ‘change’ … as well as what we mean by ‘change’.  I’ve been involved with a variety of ‘change’ in my life, and have learned a bit about other scientific fields; ‘change’ is studied in several — though I have focused on sociology and anthropology specifically (groups) as opposed to psychology (individual).

Change is not just a question of ‘being different from the past’.  The concept of productive change is more like “progress” — change directed towards a goal in a manner such that the trajectory of the work reflects the values and goals of those doing the work.  When change is accomplished without these conditions, the resulting system is often unstable, as well as requiring significant resources to push people in a direction in which they did not want to travel.

However, we can’t remain content with what we have done.  Changes and progress are a reflection of the people involved, so we often see our current efforts as being more productive than they are (for our students).  A group requires leadership to make the connection between where we are now and where we want to go.  There is a quote by Dr. Martin Luther King relative to this (during an interview where he was asked about consensus and leadership).

So, back to ‘cheerleaders’ — can cheerleaders be effective leaders, connecting the present and the future?  I think this deals with issues of perception; do we perceive cheerleaders as providing information, or do we perceive them as motivation and anecdotes?  I suppose that there might be some highly skilled folks who can combine the cheerleader function with a leadership function.  Certainly, the person who came to our campus did not deliver this combination; people generally left the presentation with either no internal change or a decline in their optimism.  Most ‘policy influencers’ are cheerleaders — Complete College America, Jobs for the Future, foundations, etc.

Cheerleaders are not effective change agents — even if they have a PhD and a pocketful of data.  We need leadership willing to work with us over an extended period of time to achieve progress … with this collaboration, we can go further than the cheerleaders can imagine.

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The Doom of Developmental Mathematics

At the recent AMATYC conference, I gave my final presentation at a national conference.  That session seemed helpful to those attending, and I plan to create a video to post here for others who may wish to experience that presentation.  However, it is critical that we understand why traditional developmental mathematics is doomed.

This doom has two primary sources, one objective and one subjective.  The objective doom is our historical ties to grade levels in K-12 mathematics of a prior era; the subjective doom is the perception that we have created an exponential decay function experienced by our students which prevents them from completing their degree.  These ‘dooms’ of developmental mathematics can not be removed by debate nor by data.  That does not mean our work will end; we can create a model which avoids these dooms … and (more importantly) works for our students.

First, the objective doom:  historical ties to grade levels in K-12 mathematics.  The traditional developmental mathematics courses were created as clones of high school courses — 8th grade math copied as pre-algebra or basic math, 9th grade Algebra I copied as our ‘beginning algebra’, 11th grade Algebra II copied as our ‘intermediate algebra’ with some copying 6th-7th grade math as ‘arithmetic.  All this copying was based on facts from the 1960’s: not all students completed Algebra II in high school, and we needed to get them ready for college algebra.

The result is a sequence of courses prior to college mathematics which exhibits the exponential decay function property … no matter how high the pass rate in a given course, the net result of the sequence is that only a small minority can finish.   Even ignoring that, we have a curriculum which is inconsistent with current course taking patterns in high school; we are not serving current needs — the ‘need’ is an image from 50 years ago.  This doom, this conflict with reality, is as obvious as it is deterministic.

Second, the subjective doom: developmental mathematics prevents students from completing their degrees.  Why is this ‘subjective’ when we have seen data supporting it?  Perhaps it would be more accurate to say that this is a hypotheses which has not yet been statistically supported by data.  The data used to support this viewpoint uses observed correlations to support a conclusion — a large portion of non-degree-completers did not complete their developmental math courses, therefore the developmental math courses caused the non-completions.

Nobody has (yet) shown that removing the ‘dev math barrier’ results in a significant increase in degree completion.  Yes, there have been reports that removing dev math results in more students completing a  college math course.  By itself, that is a small improvement.  We don’t know if more students are completing degrees … or if we are just changing which courses students complete on their way to non-degree status.

The fact that this is an unproven hypotheses does not matter for our purposes.  For our purposes, the doom is present regardless of evidence:  our presidents and provosts and chancellors generally accept this conjecture as ‘the truth’.  We would need years of effort to counter this subjective truth; we lack the time.  Once accepted, this conjecture causes a failure in the patience circuits.  We have passed the tipping point, and few of our collegiate leaders support traditional developmental mathematics.

How do we avoid the dooms?

  1. Replace traditional developmental math courses with new courses which do not clone K-12 mathematics
  2. Avoid the word “algebra” in all course titles (ALL … including college level)
  3. Avoid the words “developmental” and “remedial” when describing our work; perhaps use the label “pre-college mathematics”
  4. Allow no more than two pre-college courses at any institution
  5. Establish placement processes which allow at least 90% of all students to reach their college math course with one year

It is my view that traditional developmental math courses will NOT survive; within 5 to 7 years, they will be eliminated … either by our planning or by external directives.  We can not escape the doom of dev math.  However, we can greatly help our students by re-creating pre-college math courses which provide modern content in an efficient curriculum.

If we fail to create a new curriculum, stand-alone dev math courses will become extinct.  Is that what we want?  I hope not!

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