Co-Requisite Remediation in Tennessee

Has Complete College America (CCA) collaborated with the Tennessee Board of Regents (TBR) to create a great solution … or, have they inflicted an invalid model on the students of the state?  I suggest that “data” will not answer this question. #CCA #CorequisiteRemdiation

To summarize some key features of the Tennessee plan in mathematics, implemented state-wide this fall (2015):

• All students are placed in to college-credit mathematics
• If the ACT Math score is below 19, that college level math course will be statistics or quantitative reasoning
• If the ACT Math score is below 19, the student is required to enroll in a co-requisite ‘support’ course
• This co-requisite support course involves all developmental math learning outcomes

These elements are taken from a TBR memo (http://www.pstcc.edu/curriculum/_files/pdf/cdc/1415/Features%20of%20Corequisite%20Remediation%20-%20Memo.pdf)

From what I can see, actual practice is pretty close to this plan … learning support classes are paired with a QR course and an intro statistics course (but not college algebra or pre-calculus).  The learning support courses list topics from arithmetic, algebra, geometry and statistics.  I noticed that the QR courses tend to be more of a liberal arts math course — set theory, finance, voting, etc (the course is called ‘contemporary mathematics’).  In the 4-year college setting, this type of liberal arts math course is usually offered without any math prerequisite.

The initial data from the Tennessee pilot look very good; in fact, my provost is smitten with the Tennessee program, and wants us to consider doing the same thing.  I think the plan will “work” fairly well in Tennessee because of the non-symbolic nature of their QR course (intro statistics is notoriously non-symbolic, in the algebraic sense) … and the fact that they block students from STEM.  [They also had an inappropriate prerequisite on the non-STEM courses; see below.]

In Michigan, we have tried to establish 3 paths in math … college algebra/pre-calculus, statistics, and QR.  For statistics and QR, we have established a ‘beginning algebra level’ prerequisite (algebra or math literacy).  This level maps roughly to an ACT math score of 17, and we require more algebra in my QR course than in the Tennessee course. When the Tennessee plan ‘works well’, part of that is due to the fact that students never needed any remediation for stat or QR if their ACT math was 16 to 18.

In other words, the good results from the co-requisite pilot is due, in significant part, to the math prerequisite for college level courses.  ACT math = 19 (the Tennessee cutoff)  is a bit low for college algebra, but it is too high for statistics and QR (even if the QR is more algebraic, like mine).  Tennessee could have achieved the benefits for about 30 to 40% of their students by changing the prerequisite on two courses to be more realistic; they had established a ‘intermediate algebra’ prerequisite for all college math when that is not appropriate.  Changing the prerequisite would have helped many of the students without requiring them to take another class.

The problem we face is not that there are ‘bad ideas’ being used; the problem is that policy makers are evaluating ideas at a global level only, when the meaning of any statistical study is derived from analysis done at a fine-grain level.  Aggregated data is either useless or dangerous, and ‘aggregated’ is all policy makers consider.

CCA says “the results are in”.  Nope, not at all … we have some preliminary data about some efforts, which are not necessarily showing what the aggregated data suggests.

 Join Dev Math Revival on Facebook:

Walking the STEM Path V: Intermediate Algebra’s Role

We’ve got some problems to solve in college mathematics.  The most important problems involve the role of Intermediate Algebra.  Currently, that intermediate algebra course operates as a filter … a barrier with extremely limited benefits to students.  #STEMPath #IntermAlg #AlgLiteracy

Historically, intermediate algebra is an altered copy of a ‘typical’ “Algebra II” course from the K-12 world.  That Algebra II content was driven by a variety of forces, none of which involved STEM preparation.  For one thing, the Algebra II content was created knowing that a significant portion of those teaching the class would be non-math majors.  In addition, “easy replication” was given a higher priority than “important mathematics”; it was more important that the course could be easily delivered in most schools, than the content have benefits to the students in college.

Now, we have (sort of) the Common Core math standards.  Even in states where the Common Core is not being opposed by political forces, the impact is limited.  In my state, the opposition has been focused on the assessment using high-stakes tools; the schools can still ‘implement common core’.  However, we are seeing the results of the Common Core paradox:

Any course ever taught in K-12 exists as a subset of Common Core, even those courses clearly opposed to the outline of mathematical practices.

Algebra II is not going away in K-12 work; it’s not even changing that much.  What this means is that Algebra II, our source for Intermediate Algebra, is  just as disconnected from student needs in college.

The Intermediate Algebra focus, just as in Algebra II, is on 3 priorities:

1. Topics
2. Procedures
3. Answers

On occasion, an intermediate algebra course will coincidentally do some good mathematics on the road from ‘topic’ to ‘procedures’.  However, since this good mathematics is done in a disconnected way in a minor part of the course, the result is a huge mis-match with student needs:

1. Understanding
2. Connections
3. Reasoning

To paraphrase a student complaint at my college:

You take my money every semester, knowing that this course will not do any good.

[The actual student complaint was ‘not pass’ the course.]

In many ways, the reason for the Algebra II content is pretty similar to the reasons Intermediate Algebra has survived — we don’t require strong ‘math credentials’ to teach developmental mathematics, and replication is more important.  We have the additional force of ‘online homework systems’.

However, the intermediate algebra fiasco can not continue.  The tragedy will be ended when our best teaching mathematicians work on preparing students for STEM work (calculus-bound and others).  The New Life “Algebraic Literacy” course was created to fit this goal, and the Dana Center “Reasoning with Functions” courses also work in this direction.

So, what are YOU doing to end the tragedy named “Intermediate Algebra”?

 Join Dev Math Revival on Facebook:

Does College Mathematics Have a Future?

I have been wondering about something over the past few months. The concerns originated much earlier, as it seems that people are trying to avoid algebra within college math classes for non-STEM students.  More concerns were added as policy experts suggest that we align mathematics requirements with programs and, ideally, contextualize math for non-STEM students.  #CCA #STEM #MathPaths

There seem to be two premises at work:

1. STEM students need lots of algebra, like we’ve been doing.
2. Non-STEM students are harmed by algebra, and need something less ‘challenging’.

You can see by my phrasing that I am not objective about these premises.  Many people — mathematics educators, policy experts, and more — presume that STEM students, especially those headed towards calculus, are well-served by a college algebra experience.  The problem is that (1) the typical college algebra experience lacks development of covariational reasoning needed in calculus, and (2) our client disciplines have a more diverse need than we work with.  We continue to dig deep into symbolic calculus (which is one of our great achievements) but we downplay the usefulness of numeric methods that are heavily used in engineering, biology, physics, and more.

The STEM life is much more than putting calculus on top of algebra.

A brief story:  At a recent state MAA meeting, I attended a student session on mathematical modeling in biology.  The presenters where all about to get the BS in biology, and reported on fitting models using Matlab (Matrix Laboratory).  After the session, I asked one of the presenters where they learned the techniques … in a math class?  Nope — their biology professor taught them mathematical modeling because their math courses did not.

The non-STEM students are being tracked into statistics or quantitative reasoning, with statistics having the bigger push.  Policy experts push statistics because it is ‘practical’, and people will ‘use it’; these statements are true to some extent.  The problem is that almost all mathematical fields are practical.  In particular, algebra is practical.  Mathematics courses have failed to present algebra as a practical tool for living and for basic science & technology.

Even in a quantitative reasoning courses, we tend to de-emphasize great mathematical ideas.  Sure, we cover finances and statistics, voting and logic; however, the symbolic work combined with the concepts for transfer to new situations tends not to be there.  We use one of the best QR books on the market, and I supplement heavily on functions and related concepts; still, I do not think it is enough.  Some QR courses only apply a couple of concepts (such as proportional reasoning, or math in the news); great components of a QR course … terrible foundations for a QR course.

The risk I see is this: At some point, mathematics will be eliminated.  Non-STEM students get tracked into statistics and weak QR courses; mathematics is thereby eliminated for these students.  STEM students outside of mathematics are only required to show some basic background, and then all of their mathematics is taught by other departments (see biology story above).  The only mathematics students around will be mathematical science majors, and (in most institutions) this is far too small to support mathematics.

We need to do two difficult things:

• Get our heads out of the sand, in terms of modern mathematics (what we should be teaching)
• Effectively argue against the decay of mathematics requirements (especially in two-year colleges)

Fortunately, we have resources from people wiser than I … such as the Mathematical Sciences 2025 material (http://www.nap.edu/catalog/15269/the-mathematical-sciences-in-2025 ).  Please take a look at the diverse nature of mathematics needed in STEM fields, and think about how narrow of a focus we have.

The major threat to mathematics requirements comes from policy influencers (CCA, JFF, Lumina, etc).  Just because they say it, and have ‘data’, does not mean the idea is good or safe.  The degree requirements in institutions are the responsibility of faculty (including mathematics faculty).  It is our job to honor that responsibility, which does not belong to these external agencies.

Let’s keep mathematics as a valid component in a college education.

 
Join Dev Math Revival on Facebook:

GPS Part IV: CCA as a Dot Com Bubble

Many states and colleges are engaged with the Guided Pathways to Success (GPS) program and other methodologies supported by Complete College America (CCA).  In this post in the series, I will suggest that this observation if essentially true:

The influence of CCA will be similar to the dot com bubble of the 1990s.

In other words, the CCA is advocating dramatic action using unproven methods for a large group of investors (states and colleges).  Some methods involve components which have sufficient evidence for scaling, but the magnitude of change being created exceeds any reasonable prediction for a positive return on investment.  Even if the labels (like GPS) stick, the market will collapse within a few years as states and colleges get data indicating the large amounts of money are being lost with little gain for students.

To understand why this observation is made, take a look at a quote from the CCA materials:

But game changers don’t spontaneously happen: They are caused by people who act boldly and decisively in response to challenges.  http://completecollege.org/the-game-changers/

The ‘game changer’ reference is designed to pull in the big investors; investors are drawn to promises of large returns, especially when there is an apparently simple plan for the large returns promised.  The declaration of ‘boldly and decisively’ is a propaganda tool meant to turn off any inclination to be skeptical of the rationale for the components of the plan.

The question is this:  Why do we need ‘game changers’ in the first place?  Few of us would like the process of education being equated with any game or set of games; let’s set that valid concern aside.  “Game changer” is defined (Merrian-Webster) as “a newly introduced element or factor that changes an existing situation or activity in a significant way”.  Some components of the methods suggested by the CCA would meet this definition (such as ‘full time is 15’); however, the methods are more accurately summarized as “changing the game” rather than “game changers”.

The push toward GPS and other ‘game changers’ is accompanied by a rationale that sounds reasonable to those with smaller amounts of understanding of culture of our institutions … community colleges in particular.  I am reminded of the many novice arguments presented by my students for why their incorrect mathematics was actually ‘correct’: such arguments convince other novices, and perhaps some professionals who turned of their skeptical (critical) functions.

In spite of the obvious and reasonable doubts about the “CCA Game”, their marketing has worked very well.  Several states are deep in to the “CCA com” (like dot com) bubble.  The press for CCA has been extremely one-sided … partially because they create much of the press themselves.  No organization has stood up to question the CCA messages, even though the messages lack significant professional history.

I commend the CCA for a hustle well played.  It’s disappointing that so many leaders and policy makers have been hustled like this.  The prediction for the collapse of this CCA bubble is supported by the track record of prior changes … prolonged change tends to be consistent with, and supported by, the work of professional organizations.  The CCA bubble is supported by a network of change agents, much like the ‘dot com’ bubble.

The unanswered question: How long will the CCA bubble last?

 Join Dev Math Revival on Facebook: