Skills, Abilities, and Readiness

So, I’ve been thinking about “replacing them all” (a recent post here), and wondering what types of reactions that idea would receive.  Do the old courses have something valuable?  Would we harm students by getting rid of them?  #NewLifeMath #SaveMath

Not all implementations of arithmetic, pre-algebra, beginning algebra and intermediate algebra are equivalent to other implementations of those courses.  Certainly, some instructors (and perhaps some institutions) deliver a course that is qualitatively different from the accepted norms for those courses.

However, the norms for those 4 courses essentially define the courses as:

The student will use n procedures to get correct answers in the topics ________.

The courses are designed to maximize the value of n, often while maximizing the list of topics.  Our textbooks reflect these priorities; in fact, many of our courses are set up so that there is no textbook — just the class and the online homework.

Part of this set of norms is a fact that the New Life Project has focused on since the beginning.

Most commonly, developmental mathematics is taught by adjunct instructors.

The problem here is not the employment status of adjuncts.  The biggest problems deal with support for adjuncts and expectations — adjunct faculty do not receive the same level of support as full-time, and adjuncts are expected (in general) to follow the normal expectations.  For us to make any significant improvements, this pattern needs to be broken.

As long as we offer the traditional courses, there will be a very strong trend towards doing exactly what we’ve been doing — focus on skills, measure by correct answers, and avoid reasoning.  The traditional dev math courses produce completers who are the same as the starters, except for a finite number of specific skills which tend to be forgotten before they can be used again.

The reform dev math courses (all similar to the New Life courses at this basic level) focus on student abilities (reasoning in particular) along with a focus on strategically chosen skills.  The courses are qualitatively different in several ways.

Adjunct faculty can certainly teach Math Literacy and Algebraic Literacy.  However, in most cases, this will require an increase in institutional support in professional development.  Our hope is that this will become “the new normal”, which will tend to integrate adjunct faculty more completely into the math department.

We’ve approached “readiness” as a check-list of skills … frequently including far too many ‘skill’s … with no emphasis on reasoning abilities.  Skills can be quickly reviewed, as needed — IF the student has the reasoning to support it.  Reasoning is the ability that can not be ‘reviewed’.

The traditional dev math courses, with their focus on skills, provide such a limited benefit to students that we can safely replace them.  This is especially true if their replacements are engineered to develop a healthy combination of reasoning and skills, which the New Life courses do.

This change from ‘old’ to ‘new’ is more of a problem for us, than our students.  Are we ready to offer math courses which focus on central ideas and reasoning?  Can we give up the ‘easy’ path of doing the same old stuff?  This change issue is true for all college mathematics in the first two years; external forces are causing us to start with developmental courses, though pre-calculus and calculus courses will go through similar changes.

We are not changing “for changes sake”.  We are changing for the sake of our students … we are are changing to save mathematics.

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Time to Replace Them All (dev math courses)

My college is undertaking a major change, motivated in some ways by applying the federal financial rules about remediation with integrity:  courses need to be at least at the high school level in order to be included in a student’s financial aid load.  I’m also getting ready for the National Math Summit (next month, Anaheim).

When we began the New Life Project back in 2009, the core group working on the curriculum stated that there was no need for a course prior to Math Literacy … that Math Literacy can replace beginning algebra for ALL students (STEM and non-STEM) … and that Algebraic Literacy can replace intermediate algebra.  Since that time, more has been understood about the college algebra/pre-calculus curriculum and problems.

So, here is an updated curricular map that puts this together:

The small box at the start of this image represents a non-course preparation for Math Literacy.  My college is exploring the other option — including the needed prerequisites within the Math Literacy course.  We have not made any decisions, though we are going to do something along these lines.  At this point, we will not offer any arithmetic nor pre-algebra course.

One of the changes in the map is the courses after Algebraic Literacy.  The original map made reference to reform college algebra (for general education).  However, the recent discussions have focused more on revising pre-calculus to be a modern course … so the map uses that terminology, and maintains the college algebra ‘box’ for the non-calculus paths.

Several colleges are known to be ahead of my college on this path — some have totally replaced their dev math sequence with the Math Lit and Algebraic Lit courses.  More have replaced beginning algebra with Math Lit, and would consider replacing intermediate algebra with Algebraic Literacy if the materials were readily available.

I want to remind all of us that one of the goals of our Project was to replace the old courses for all students.  STEM-bound students deserve the good stuff in Math Literacy.

In my presentation at the National Math Summit, I will be sharing data on how (poorly) the beginning algebra course serves students.  The data on this question is glaring, and should encourage more of us to walk down this path of ‘replacement’.  The data on intermediate algebra is also consistent with the goal of replacing the old courses (though the data is not as ‘bad’).

The up-to-date information on the National Math Summit is available at http://www.nade2016.net/math-summit.html  As of the first of this week, registration is still open (the event has a definite maximum).

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Co-Requisite Remediation and CCA (Saving Mathematics, Part V)

Complete College America (CCA) released a new report on co-requisite remediation this week.  Actually, that statement is not true … the CCA released a web site which shows some data on co-requisite remediation, with some user interaction.  What’s missing?  Anything that would help a practitioner judge whether they should consider co-requisite remediation!  #CCA #Corequisite #SaveMath

Many of us are dealing with policy makers in our states or institutions who see co-requisite remediation as the solution to the “developmental math problem”.  There are, in fact, serious problems in developmental mathematics; there are also serious problems with how ‘college math’ has been defined, and how policy makers are defining a problem away instead of solving it.

Within developmental mathematics, we have been working hard teaching the wrong stuff to our students, frequently using less-than-ideal methods to help them learn.  Our curriculum has too many courses, and the combination is lethal … not many students reach their dream.  When students proceed from developmental math to college algebra or pre-calculus, they often find that the gap in expectations between the two levels is very difficult to deal with.

Co-requisite remediation steps in to this complex problem domain, and declares that all will be fine if we just put students into college math with some support.  The most common (and sometimes the ONLY) co-requisite remediation done is in Intro Statistics and Quantitative Reasoning [QR] (or Liberal Arts Math).  The history, frequently, is that students had to pass intermediate algebra prior to these courses … even though that background has nothing to do with the learning; the requirement was to establish “college level”.

So, the CCA and allies declare that students can take Stat or QR instead of developmental math.  Of course this is ‘successful’; the old prerequisite was unreasonable, and the co-requisite method puts students directly in to courses they are relatively ready for, and also provides extra support (in some cases).  Many colleges, including mine, had already lowered the prerequisite for Stat and QR years ago; our results from both Stat and QR are better than what the CCA states for their co-requisite model.

The co-requisite ‘movement’ is an illusion.  The work succeeds (almost totally) because students are placed in to math courses that have minimal needs for algebra.  I get better results by just changing the prerequisite to Stat and QR.

We also face a risk to mathematics in this illusion:  students with dreams that involve STEM are frequently told that this dream is being shelved in favor of co-requisite remediation, that they will take either Stat or QR.  The path to calculus is either not available or involves work that is not articulated well to students.  Policy makers are treating math as a barrier to cope with, a problem to solve with the least remediation.  The need for mid- and high-skill STEM workers is well documented, but the co-requisite ‘solution’ often blocks the largest pool of students from those fields … the minorities, the poor, the students served by under-performing schools.

Society needs our work to succeed for all students.  We can not accept a solution which reduces upward mobility; a solution which does not provide ‘2nd chances’ is a risk to both mathematics and to a democratic society.

Don’t get me wrong — Stat and QR have a major role to play in our curriculum, and these courses might be the most common math courses students should take in college.  My main message is that we need to question the illusion called ‘co-requisite remediation’, AND we need to articulate a vision of our curriculum which enables ALL students to consider STEM and STEM-like careers.   [The New Life Project provides a vision of such a curriculum.]

If you really want to read the CCA “Report”, go to http://completecollege.org/spanningthedivide/#the-bridge-builders

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Saving Mathematics, Part IV: This is College, Right?

For whatever reason, we in the mathematics community have an obsession with high school … we define college mathematics by assigning a prerequisite that suggests a level above high school (often the prerequisite is intermediate algebra).  We also accept the notions about people not being good at mathematics, which results in the contradictory policy of allowing intermediate algebra to meet a degree requirement in college.  What’s up with THAT?  #remediation #FinAid

All of our institutions (with very few exceptions) must comply with financial aid laws and regulations.  Those regulations make a distinction between remediation at the high school level and remediation at the elementary level (K-8); courses at the elementary level (like arithmetic, pre-algebra) can not be used to determine eligibility for financial aid.  Courses at the high school level can be used for financial aid, though there is a limitation on the total remediation.  (see https://ifap.ed.gov/fsahandbook/attachments/1415Vol1Ch1.pdf)

The K-12 professional standards of the past 25 years (NCTM) and the Common Core provide a way to judge the level of our courses.  Most of our intermediate algebra courses map to 9th and 10th grades in those standards; even prior to that, intermediate algebra was considered 10th or 11th grade level.  Overall, 57% of our enrollments (community-college-type) is in pre-college mathematics … 32% of that enrollment is in remediation at the elementary level.  [CBMS 2010 data; http://www.ams.org/profession/data/cbms-survey/cbms2010-Report.pdf]

My position is that these high numbers in remediation are the result of artificial parameters for ‘college level’ and our obsession with high school.  Many of us accept the position that the mathematics actually needed for college work (whether STEM-path or not) is not delivered by our basic-math > pre-algebra >beginning-algebra > intermediate-algebra filtering system.  Our curriculum in those courses is often inferior to what our K-12 colleagues are using.

• Remediation does not mean high school mathematics

We need to throw out our traditional developmental courses (as well as most college-algebra-level courses).  Convenient copying of courses does not help students.

The question is:

• What does a COLLEGE student need prior to a college math course?

The needs do vary somewhat depending on the particular college math course.  We need to show our integrity by offering courses designed to serve the purpose for which we use them:

• Only require students to take courses with validity for the purpose!

This is not a quick process, but it is something we can do together … and even be inspired by.

In the meantime, let’s show our professionalism by doing the following:

1. Always classify arithmetic and pre-algebra as “elementary level” remedial courses
2. Always classify beginning algebra and intermediate algebra as “high school level” remedial courses, which have no role meeting a college degree requirement
3. Identifying appropriate college-level math courses required for each degree

Complete College America says much that I disagree with; quite a bit of their communication is rhetoric to support pre-determined solutions.  However, one thing from CCA I really agree with:

College students come to campus for college, not more high school. Let’s honor their intentions — and refocus our own good intentions to build a new road to student success.
http://www.completecollege.org/docs/CCA-Remediation-final.pdf

To get started on a path to replace the traditional developmental math courses, take a look at the New Life Project courses (Mathematical Literacy and Algebraic Literacy).  I hope that you will join me and hundreds of other professionals working to create better models to serve our students and communities.

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