Scaling Mathematical Literacy Courses

My college (Lansing CC) has implemented a second version of Math Literacy, which allowed us to drop our pre-algebra course.  I posted previously on the ‘without a prerequisite (see http://www.devmathrevival.net/?p=2516).

Here is a summary of where we ended up in the first semester of having both Math Lit courses.

  • Math105 (Math Lit [with math prereq] has 8 sections with about 165 students.
  • Math106 (Math Lit with Review [no math prereq] has 9 sections with about 225 students

With these 17 sections of Mathematical Literacy, we have quite a few instructors teaching the course for the first time.  Most of the instructors new to this teaching have been involved with the development of the course and policies, where we discussed text coverage and technology expectations for students.

As part of our collaboration, we are having bi-weekly meetings with as many of the instructors as can manage the ‘best time’.  The leading issue being dealt with is the textbook purchase; we’re helping as best we can with that, but buying the textbook is outside of our control.

We are talking about learning and teaching issues.  For example … how to balance an emphasis on concepts to enable reasoning with an emphasis on procedures so that students can actually ‘do something’ with the math (like have an answer to communicate).  We are talking about which small-group structures seem to work well in this course.

Our approach to scaling up Math Literacy is based on a long-term professional development approach.  Our bi-weekly meetings will continue as long as there seems to be a need (one semester, one year, or longer).  We are looking in to setting up a shared collaboration space for the instructors, which will enable those not able to attend to be involved.

In our structure, students who do not place at beginning algebra (or higher) are required to start with Math Literacy; those at the beginning algebra have the option to use the Math Literacy course.  After the Math Literacy course, students have 3 options:

  1. Take our Quantitative Reasoning course (Math119) … required for most health careers
  2. Take out Intro Statistics course (Stat170) … required for some other programs
  3. Take our Fast-Track Algebra (Math109) which allows progression to pre-calculus

Unlike some implementations, our vision of Math Literacy includes all students … even “STEM-bound”.  Faculty teaching our STEM math courses are pleased with the strong reasoning component of Math Literacy.  We will be collecting data on how the various progressions work for students, and can implement needed adjustments to make improvements.

For those near Michigan, we will be making a presentation at our affiliate (MichMATYC) conference next month (Oct 15 at Delta College).  See http://websites.delta.edu/math/michmatyc2016/ for details.

 
Join Dev Math Revival on Facebook:

Alignment of Remediation with Student Programs

My college is one of the institutions in the AACC Pathways Project; we’ve got a meeting coming up, for which we were directed to read some documents … including the famous (or infamous) “Core Principles” for remediation.  [See http://www.core-principles.org/uploads/2/6/4/5/26458024/core_principles_nov4.pdf]  In that list of Core Principles, this is #4:

Students for whom the default college-level course placement is not appropriate, even with additional mandatory support, are enrolled in rigorous, streamlined remediation options that align with the knowledge and skills required for success in gateway courses in their academic or career area of interest.

What does that word “align” mean?  It seems to be a key focus of this principle … and the principle also implies that colleges are failing if they can not implement co-requisite remediation.  In early posts, I have shared data which suggests that stand-alone remediation can be effective; the issue is length-of-sequence, meaning that we can not justify a sequence of 3 or 4 developmental courses (up to and including intermediate algebra).

The general meaning of “align” simply means to put items in their proper position.  The ‘align’ in the Core Principles must mean something more than that … ‘proper position’ does not add any meaning to the statement.  [It already said ‘streamlined’ and later says ‘required or’.]  What do they really mean by ‘align’?

In the supporting narrative, the document actually talks more about co-requisite remediation than alignment.  That does not help us understand what was intended.

The policy makers and leaders I’ve heard on this issue often use this type of statement about aligning remediation:

The remediation covers skills and applications like those the student will encounter in their required math course.

In other words, what ‘align’ means is “restricted” … restricted to those mathematical concepts or procedures that the student will directly use in the required math course.  The result is that the remedial math course will consist of the same stuff included in the mandatory support course in the co-requisite model.  The authors, then, are saying that we need to do co-requisite remediation … or co-requisite remediation; the only option is concurrent versus preceding.

If the only quantitative needs a student faced were restricted to the required math course, this might be reasonable.

I again find a basic flaw in this use of co-requisite remediation in two flavors (concurrent, sequential).  We fail to serve our fundamental charge to prepare students for success in their PROGRAM … not just one math course.  As long as the student’s program requires any quantitative work in courses such as these, the ‘aligned’ remediation will fail to serve student needs:

  • Chemistry
  • Physiology
  • Economics
  • Political science
  • Psychology
  • Basic Physics

Dozens of non-math courses on each campus have strong quantitative components.  Should we avoid remedial math courses just to get students through one required math course … and cause them to face unnecessary challenges in several other courses in their program?

In some rare cases, the required math course actually covers most of the quantitative knowledge a student needs for their program.  However, in my experience, the required math course only partially provides that background … or has absolutely no connection to those needs.

Whom does remediation serve?  Policy makers … or students?

 Join Dev Math Revival on Facebook:

Equity and Stand-Alone Remedial Math Courses

One of the key errors that co-requisite (mainstreaming) advocates make is the treatment of ‘developmental mathematics courses’ as a single concept.  We would not expect college students who place into arithmetic to have comparable outcomes to those who place into intermediate algebra.  However, most ‘research’ cited with damning results uses that approach.  We need to have a more sophisticated understanding of our work, especially with respect to equity (ethnicity in particular).

A local study by Elizabeth Mary Flow-Delwiche (2012) looked at a variety of issues in a particular community college over a 10 year period; the article is “Community College Developmental Mathematics: Is More Better?“, which you can see at http://mipar.umbc.edu/files/2015/01/Flow-Delwiche-Mathematics-2012.pdf   I want to look at two issues in particular.

The first issue is the basic distribution of original placement by ethnicity.  In this study, ‘minority’ means ‘black or hispanic’; although these ethnicity identities are not equivalent, the grouping makes enough sense to look at the results.  The study covers a 10 year period, using cohorts from an 8 year period; partway through the 8 year period, the cutoffs were raised for mathematics.

Here is the ‘original’ distribution of placement by ethnicity using the data in the study:
Distribution by level Flow-Delwiche 2012 Original

 

 

 

 

 

 

 

 

After the cutoff change, here is the distribution of placement:
Distribution by level Flow-Delwiche 2012 New HigherCutoffs

 

 

 

 

 

 

 

 

Clearly, the higher cutoffs did exactly what one would expect … lower initial placements in mathematics.  However, within this data is a very disturbing fact:

The modal placement for minorities is ‘3 levels below college’ (usually pre-algebra)

This ‘initial placement’ data appears to be difficult to obtain; I can’t share the data from my own college, because we do not have ‘3 levels below’ in our math courses.  However, the fact that minorities … black students in particular … place most commonly in the lowest dev math course is consistent with the summaries I have seen.

We know that a longer sequence of math courses always carries a higher risk, due to exponential attrition; see my post on that http://www.devmathrevival.net/?p=1685    Overall, the pass rates for minorities is less than the ‘average’ … which means that the exponential attrition risk is likely higher for minorities.

The response to this research is not ‘get rid of developmental mathematics’; the research, in fact, shows a consistent pattern of benefits for stand-alone remedial math courses.  This current study shows equivalent pass rates in college math courses, regardless of how low the original placement was (1-, 2-, or 3-levels below); in fact, the huge Achieve the Dream (ATD) data set shows the same thing.  See page 46 of the current research study.

The advocates of co-requisite (mainstreaming) focus on the fact that 20% or more of the students ‘referred’ to developmental mathematics never take any math AND the fact that only 10% to 15% of those who do ever pass a college math course.  The advocates suggest that a developmental math placement is a dis-motivator for students, and claim that placing them into college math will be a motivator.  Of all the research I’ve read, nothing backs this up — there are plenty of attitudinal measures, but not about placement; I suspect that if such studies existed, the advocates would be including this in their propaganda.

However, there is plenty of research to suggest that initial college courses … in any subject … create a higher risk for students; it’s not just mathematics.  So, the issue is not “all dev math is evil”; the issue is “can we shorten the path while still providing sufficient benefits for the students”.    This goes back to the good reasons to have stand-alone remedial math courses (see http://www.devmathrevival.net/?p=2461 ); although we often focus on just ‘getting ready for college math’, developmental mathematics plays a bigger role in preparing students.  The current reform efforts (such as the New Life Project with Math Literacy and Algebraic Literacy) provide guidance and models for a shorter dev math sequence.

Even if a course does not directly work on student skills and capabilities, modern developmental mathematics courses prepare students for a broad set of college courses (just like ‘reading’ and ‘writing’).  It’s not just math and science classes that need the preparation; the vast majority of academic disciplines are quantitatively focused in their modern work, though many introductory courses are still taught qualitatively … because the ‘students are not ready’.  Our colleagues in other disciplines should be up in arms over co-requisite remediation — because it is a direct threat to the success of their students.

Developmental mathematics is where dreams go to thrive; our job is to modernize our curriculum using a shorter sequence to give a powerful boost for all students … especially students of color.

 Join Dev Math Revival on Facebook:

The Difference Between Mathematical Literacy & Algebraic Literacy

As more colleges implement Mathematical Literacy courses, we are running in to a point of confusion:  what is the difference between Algebraic Literacy and Mathematical Literacy?  The easy reference is problematic … comparing these courses to the traditional beginning & intermediate algebra courses; those traditional courses are at the ‘same level’ in a general way, but this fact does not help us deal with the details of new courses.

I’ve written previously on the comparison of the new courses to the old, especially Algebraic Literacy compared to the traditional course (http://www.devmathrevival.net/?p=2347 and http://www.devmathrevival.net/?p=2331 ).  However, I’ve not talked that much about the difference between these new courses that share a word in the title (“Literacy”).  That’s the goal of this post.

First, the course titles are not perfect … the word ‘literacy’ was meant to imply that the courses deal with pre-college material; ‘mathematical’ was meant to suggest that we did not start with algebra directly … while ‘algebraic’ was meant to suggest some directionality (headed towards STEM and STEM-like courses).  We have focused on the goals and outcomes documents for the new courses as a way to clarify what the courses are designed to deliver.

MLCS Goals and Outcomes Oct2013 cross referenced 2 by 2

Algebraic Literacy Goals and Outcomes Oct2013 cross referenced

Since these courses diverge from the traditional curriculum, these documents were not sufficient to clarify “what belongs in each course” for shared topics (especially algebra).

So, here is a side by side chart meant to provide some additional clarification.

Math Lit vs Algebraic Lit July2016

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The intent is not to avoid any overlap between the courses, though there is less overlap than the traditional courses (in general).  As an example, many Math Lit courses introduce systems of linear equations; the solution methods are usually limited to numeric (graphing & intersect) and some substitution.  In an algebraic literacy course, the problems would be more diverse and so would the solution methods presented.

Another example is factoring polynomials.  The classic Math Literacy course might cover “GCF” factoring only (pardon the redundancy) … though that is not assumed.  The intent is that Math Literacy avoid most factoring beyond that which is a direct application of the distributive property; Algebraic Literacy picks up most of the factoring concepts necessary.  We note that most ‘needs’ to include factoring are contrived; a deep understanding of functions (the core goal of pre-calculus) does not depend upon all the typical methods presented in the albatross “Intermediate Algebra”.

A solid Mathematical Literacy course will involve some algebraic manipulation (limited in types as well as in complexity), and these procedures would be further enhanced Algebraic Literacy.  Therefore, the distinction between Math Lit & Algebraic Literacy can not be reduced to a particular ‘problem’ being present in one course but not the other.  We really want to keep the focus on the purposes of each course; see the ‘goals’ part of the course documents listed above.

If you have questions about the distinction between the two new courses, I would be glad to provide any information I have.

 Join Dev Math Revival on Facebook:

WordPress Themes