Case Closed … Mind Closed?

We are again being bombarded with ‘information’ about co-requisite remediation working.  The “we” in that statement would be everybody involved with college remediation — practitioners, administrators, policy makers, and boards.  One of the recent notes from Complete College America begins with “Case Closed on Traditional Remediation”.  Good propaganda … bad education.

The most basic issue before us is NOT “should we have stand-alone developmental math courses”.  No, the core issue is:

What ‘mathematics’ do students need to ‘know’ for various educational goals?

Non-mathematicians have considerable difficulty understanding this question, because of the two words in quotes — ‘mathematics’ and ‘know’.  For many, mathematics consists of arithmetic and algebraic procedures with some memorization of geometric formulae; ‘knowing’ consists of being able to recall barely enough of those procedures to pass a college math course.  In other words, non-experts tend to see mathematics as training in skills, and they tend to view our courses as barriers to an education.

We certainly can agree, at some level, that the mathematics being taught in basic courses (whether remedial or college algebra) is both badly out of date and not well suited to the educational needs of our students.  Therefore, when the primary evidence for co-requisite remediation comes from comparisons between the experimental treatment and ‘traditional’, the results have meaning mostly for people who do not understand the problem space.  So what if 70% of students in the treatment succeed compared to 54% of those in the traditional classes!  Neither group is getting good mathematics (most likely).

My message continues to be:

Design NEW courses with modern content designed to meet the educational needs of our students.

For some students, this will mean that they take a college statistics course with extra support (co-requisite).  For other students, this means that they will take one pre-college course which provides strong understanding of concepts and relationships with good fluency in being able to deal with quantitative problems in both symbolic and numeric methods.  For a few students, this means that they will need to take two pre-college courses.  And, for some students (half?), they can start in the college mathematics course because their recent Common Core mathematics experience has provided them sufficient fluency.

A declaration that the “case [is] closed” reflects the bias of the speaker, not the factual situation.  The speaker is hoping that we will have a closed mind to other interpretations (especially if we are leaders or policy makers).  The worst thing about Complete College America is the message that a problem has been solved and there is nothing further to understand.   We see closed minds in education, but the results are never good.  I can only hope that most of us will keep an open mind, and consider the basic problem so that we can work on real solutions for our students.

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How to Impact Student Success

College leaders (presidents, trustees, chancellors, etc) have discovered “student success” as an issue, and they promptly implement systemic changes which impede student success.

In some ways, their errors are understandable.  We’ve got plenty of data which shows …

• Traditional remediation in mathematics most often functions as a barrier to students
• Students who complete college math in their first year are more likely to complete their program/degree
• Placement by single-measure tests tends to underplace 20% to 30% of the students

Leaders have also accepted the surface logic of “alignment” (At the Altar of Alignment  ), just like some folks accept the logic of ‘trickle-down-economics’.  Alignment takes many forms … from aligning K-12 and college expectations to selecting a math course for a student’s program.  Little data exists to show that alignment improves student success; like tax cuts, alignment is difficult to argue against — even though we should.

When I talk about student success, I am referring to the important measures of student success — learning, preparation, and a liberating education.  Passing my math course is not a measure of student success … being able to deal with mathematics in other situations IS.  Curiously, I asked by college president about measuring student learning as a component of student success; the response was that we should drop course grades and move to a portfolio.

So, here is the type of thing I mean by student success.

In a conversation with a small group of science faculty, they shared their frustration with student’s inability to apply math — algebra in particular — to scientific contexts.  A low level example was a simple temperature conversion:  T[sub C] = (5/9)(T[sub F] – 32), given temperature of 40 degrees C, convert to degrees F.

Many students treat this as a calculation problem (5/9)(40 – 32), instead of algebraic.  It seems to make no difference if subscripts are used or the letters C and F instead.

Student success is being able to reason (algebraically) in this case to get the job done.

In this case, we have ‘alignment’. The math course students took before the specific science course included replacements for both independent and dependent variables.  Alignment is a very (VERY) weak estimate of preparation for student success.

My goal of student success is not especially lofty.  In a nutshell, this is it:

Given a situation involving application of concepts and skills easily within the mathematical reach of the students, they will formulate a reasonable solution method and execute this solution with reasonable precision.

This goal is quite a bit above the useless definition of student success seen by college leaders: course completion one-at-a-time.  Student success means that my colleagues in other disciplines would be pleasantly surprised by how well our students apply mathematical concepts and relationships which arise in that discipline.  Those faculty would not need to dilute the scientific rigor of their course (in whatever discipline) just because the students we send to them lack quantitative understanding.

We live in an era of ‘completion obsession’.  It’s not that program completion is bad … completion is a great thing; the best day of my year is getting to see some of my students walk across the stage to get their degree.  The problem is that the obsession with completion devalues the education we are supposed to be providing to our students.  In the completion fixation, we watch students on the marathon course to make sure that they pass each critical point — without noticing that many students are running without understanding strategy or skill.  It’s like perseverance is the only trait we value.

Our job is to keep education in mathematics.  Student success means that we’ve made a difference in how our students are able to deal with quantitative situations; mathematics is an enabler of multiple career options for all students, not a subject to be gotten-done-with.

 
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Corequisiste Remediation as a STEM Recruiting Tool

Seems like much of the world (in higher education) has gone ‘crazy’ with reforms intended to remove mathematics as a barrier.  Are we happy with that vision of mathematics?  Are we content with a system which minimizes the learning of mathematics in college?

Perhaps we have not seen some potential opening doors which could support the vision for mathematics we would advocate.  Corequisite remediation has been implemented as a disruptive influence on an algebraic-based mathematics requirement … if a student does not qualify for “college algebra”, put them in a non-algebraic course (statistics, liberal arts math, QR, etc) with a support course which will cover a minimum of mathematics (just enough to learn that stat/Lib Arts/QR course).

Take a step back, and think about these questions.

• Do these non-algebraic courses typically have high needs for ‘remediation’? Or, did we have artificially high prerequisites for these courses … so now corequisite remediation allows us to save face while not providing any significant advantage to students?
• Do the initial STEM-enabling courses (such as college algebra and pre-calculus) have high needs for remediation and support?

To the extent that the answers are “no” and “yes” (respectively), the reform process has been mis-directed.

In addition, we have students who have the potential to be STEM majors — but are intimidated by the prospects of passing the STEM-enabling math course (college algebra, pre-calculus, calculus I).  The current reform work deliberately pushes these students into programs outside of STEM.

Let’s re-direct the reform work to meet student needs and enable many more students to achieve their STEM dream.  Instead of attaching co-requisite support classes to non-algebraic math, attach them intentionally to STEM-enabling math courses.  Whether a student barely places directly in to such a course, or minimally passes a prior math course, their prospects are not good currently.   Think about students within 1 standard deviation above the cutoff on a placement assessment, and those with 2.0, 2.5, C, and C+ grades.  Maybe something like this:

Where do we want students to succeed?  If we are okay with students succeeding if they avoid STEM-enabling mathematics courses, then continue doing the current reforms.  On the other hand, if you want students to choose STEM and succeed, it might be time to consider a better use for co-requisite support classes.

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The Power of Understanding Math

One of the most rewarding experiences we can have is when a student exceeds our expectations.

This is a story of a student who initially struggled with everything and is now being successful within an individualized course structure.  In this class, I never ‘lecture’ to a group of students.  Class time is used for studying, help, consultation, and testing; we call it the “Math Lab” though it’s not what most people mean by that phase.  The common meaning of “Math Lab” is a drop-in help center open to a variety of students in a set of math classes.  Our Math Lab is a way to take a few math courses … our math help for other classes is separate from the Math Lab.

This particular student (I’ll call him Philip) was clearly having trouble on the first day.  He did not want to use the online homework system, and that was not a problem for me.  However, he opened the book to the first page of the first section and had lots of questions about the names for types of numbers, about order of numbers on a number line, and (shortly after) about adding signed numbers.  The second day brought questions about the meaning of words in statements of properties, and about the meaning of variables.

It’s not that most students “get” these things, nor that they do not need to work on them.  What was unusual was the level of the struggle (basic) along with the sheer quantity of questions.  I never tell students what my prognosis is for them (I’m sometimes wrong) but I thought this student was going to spend weeks on every chapter.

Philip did, indeed, spend weeks on chapter 1 … a chapter about real numbers in a beginning algebra course.  Following those weeks, Philip then missed several classes due to medical problems related to his PTSD and physical injuries.  With over 6 weeks gone, Philip had only tried that first chapter test.  He was about to encounter the chapter on linear equations and applications, a classic “speed bump” for students struggling to learn algebra.

Somewhere in the month after that, however, Philip began making consistent progress.  In fact, he was getting through the third chapter faster than many students.  That progress has continued, and Philip is very likely to pass the course.

The main point is that something in the way Philip dealt with the struggle made a difference in how he succeeded in the entire course.  Philip works towards understanding everything, including ideas the are relatively minor.  He writes down lists of both vocabulary to learn and problems that he needs help with.  My guess is that his turn-around from struggle to success was caused by his hard work at understanding (and not just knowing what to do).

We all have students in this level of course who interact with the material at a low level; for them, it’s more about remembering what to do than it is about understanding.  I think Philip’s intense effort at understanding provided him with a cumulative positive improvement in the ability to learn new material.

Like most of us, I strive to have all students look for that understanding in learning mathematics regardless of the specific math course.  With other students, I end up trying to pull them someplace they have no intention of going (understanding) while Philip approached the material that way without any influence from me.

As a minor point in this post, I will point out that a struggling student such as Philip will be lost prior to getting any success.  Taking several weeks on one chapter is not an option within a fixed-pace class; instead of accumulating benefits, struggling students accumulate bad grades on assessments.  Our Math Lab, with its focus on individual learning, allows a struggling student to truly become a successful student.

A fixed-pace class has a limited capacity for helping struggling students; they need to be within a relatively small range of struggle in order to succeed.  Our Math Lab expands that range considerably (though there are still limits).

Understanding … a focus on understanding … enables students to obtain power in mathematics by raising their level of functioning to a higher point.

 
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