Implementing Better Math Courses, Part III: Connecting All the Dots

The traditional developmental math sequence focuses on school mathematics, biased by an algebra fixation … narrowly defined to be algebraic procedures.  Although some have the perception that this sequence serves ‘STEM students’ well, professional standards and research indicates that the sequence does not serve them well.  In this post, I will focus on truly connecting all the dots — to STEM math and most college mathematics&nbsp. #NewLifeMath #AlgebraicLiteracy

The prior posts on implementing better math courses focused on the beginning algebra level.  The Level I implementation (Pathways) described a side-by-side model; the Level II implementation (Medium) provided a total replacement of beginning algebra as well as all courses prior to that.  The next level (III) involves replacing intermediate algebra with Algebraic Literacy (AMATYC New Life project).

Here is an image of this implementation model:

Algebraic Literacy provides a modern course connecting students to STEM and related college mathematics.  I’ve posted information on the course and research for Algebraic Literacy at https://www.devmathrevival.net/?page_id=2312; here, I will focus on the implementation aspects.

One benefit of this ‘high’ implementation is that we can minimize remedial enrollments while providing intentional preparation.  Because Algebraic Literacy focuses on communication and reasoning, we provide an accessible course with higher expectations — more students can start in the 2nd course, and they will be better prepared for what follows.  For example, if intermediate algebra required a 77 on a placement test, algebraic literacy can succeed with a cutoff of 60 to 65; if an ACT Math 19 is required for intermediate algebra, algebraic literacy can manage with a 17.  These numbers are very generic, and are simply meant to illustrate the increased access.

The preparation is also improved in this model.  The cumulative message of the college math standards is:

Focus on learning core ideas in mathematics to a high level. (AMATYC; MAA – CRAFTY and CUPM)

Even if students flow from Algebraic Literacy to a traditional college algebra course, they will have more capabilities.

However, the curriculum at the college algebra level (and above) is in desperate need of modernization.  Those courses are almost all modifications of either a 19th century college algebra course in college algebra or slight variations of calculus from the mid-20th century.  We live in a golden age of mathematical sciences, but our students still take courses on dead (aka obsolete) mathematics.  Having the Algebraic Literacy course in place will provide both the motivation and safety needed for our departments to begin updating the STEM math courses.

This “High” implementation results in a total replacement of obsolete dev math courses and the beginning of renewal in the courses which follow.  The New Life Project dev math courses share much with the work of the Carnegie Foundation (Pathways) and the Dana Center (New Mathways).    The Carnegie work builds an option after the pathways courses (Statway or Quantway) to enable the student to take college algebra; the Dana Center work provides a different replacement model, where the STEM path (pre-calculus) begins right after a Math Literacy-type course.

Many in our profession would like to teach Algebraic Literacy instead of intermediate algebra; Algebraic Literacy is better mathematics and is consistent with modern teaching methods.  The main barrier to progress right now is ‘textbooks’, since there are no commercial materials available (Pearson; McGraw Hill; Cengage; Hawkes; etc).   The path out of this ‘chicken-egg’ dilemma is YOU … talk to the publisher representatives at every opportunity about the books you want to see.

A primary goal of this “High” implementation is a combination of improved preparation and the minimizing of the remedial math enrollment function.  I believe that we can achieve a situation where the mode of remedial math enrollments is 0 and 1, with a mean between those values.  We don’t need to eliminate remedial math courses … we need to modernize them to better serve our students.

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National Math Summit — resources, handouts, …

The National Math Summit 2016 was held in mid-March, with over 250 people attending.  We had a very productive 2-day event.

Now, you can access much of the information shared during the “NMS” (national math summit).  Resources and handouts have been posted to a drop-box.

The drop box is https://www.dropbox.com/sh/c3p3lizhfqjjic5/AAARt_ynsNIoeAvuZVOzPn5xa?dl=0

You can share this link, and download the materials from the drop box.  If you have questions about a particular item, contact the primary author.

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Implementing Better Math Courses, Part I: A Starting Point

I want to share some specific options for implementing courses from the New Life Project, both to encourage more people to consider using those courses and to also increase our collective understanding of changes in the field.  In this Part I, I’ll talk about the easiest implementation; later parts will describe increasingly complete replacements of the traditional curriculum.  #NewLifeMath #MathLiteracy

The easiest curriculum reform to implement is often the side-by-side approach, also called ‘pathways’.  In this structure, the existing courses are left intact but some students are referred out of beginning algebra … based on a target of either statistics or quantitative reasoning.

This pathways model looks something like this:

Overall, about half of the known implementations of New Life courses is done within this ‘low’ implementation (side-by-side, or pathways).

The advantages of the low (pathways) implementation are:

• Easier to get ‘buy-in’ from other math faculty
• Allows for learning process (for teaching differently, with different content)

Some of the disadvantages are:

1. Depends upon effective advising for ‘recruiting’ students
2. Complicated structure and communication
3. Perhaps too easy to get buy-in from other math faculty
4. Provides benefits to some students, while the remainder experience an unimproved curriculum

In general, this pathways model (also called ‘low implementation’) is done by colleges.  When states implement the courses, they usually do so at the next level — replacing beginning algebra with “MLCS”.  In my view, the pathways (side-by-side) structure is not sufficiently stable to survive long-term.  As in my institution, however, this pathways model allows a math department to begin the process of curriculum reform without major disruptions.

The disadvantages listed for this model may actually be an advantage for some institutions.  In coping with the advising and communication challenges, the college may see improvements in those general processes.  I’ve heard of those types of outcomes happening at some institutions, though the positive outcomes depend upon good planning and lots of hard work; in my institution, for example, those disadvantages did not result in significant improvements in general systems.

Within the mathematics community, this pathways model is what ‘got traction’ a few years ago.  The side-by-side nature is not a long-term solution, and tends to reinforce that antiquated curriculum in college algebra or pre-calculus.  A more mature response to our curriculum would achieve some level of replacement; those replacement models will be explored when I talk about “medium” (MLCS instead of beginning algebra) and “high” (MLCS and Algebraic Literacy instead of traditional developmental algebra courses).

Overall, this pathways (side-by-side) low implementation model is an excellent choice for how to start the long-term process of improving our curriculum.  The key is to judge what your department and institution are ready for … pushing for a replacement of the old courses can be counter-productive, if the readiness is not there.  Once a department is working in the pathways model, we can more easily build the readiness for the replacement stages.

Nationally, the Carnegie Foundation’s Pathways (Quantway, Statway) are pretty much limited to the ‘low’ implementation; the purpose of those pathways is to accelerate math for students who are not in the ‘STEM’ path.  On the other hand, the Dana Center’s New Mathways Project is flexible enough to allow for both pathways (side-by-side) and replacement models.  Like the New Life project, the Dana Center work includes the MLCS course (called “Foundations of Mathematical Reasoning”, or FMR).  Differences emerge when we get to the replacement models.

If you are considering implementing a new course like MLCS or FMR, I hope the points above are helpful.  Feel free to leave a comment or send me an email for clarification or further information!

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What is Co-Requisite Remediation?

Several posts here have involved a critique of “Co-Requisite Remediation”, which usually results in questions of “what do you mean by co-requisite remediation?”  Let’s take a look at what is usually meant by the phrase.  #CCA #Corequisite #SaveMath

The first thing to know about corequisite remediation is that it is a new and ill-defined phrase.  Before about 2011, corequisite remediation was a micro strategy — to help with specific weaknesses, a course would include focused remediation within a limited portion of the class.  Most math faculty do remediation within courses, and this initial use of the phrase ‘corequisite remediation’ seems to have been an effort to focus on this work to support collaboration across institutions.

Within the past 5 years, the phrase “corequisite remediation” has been almost exclusively being used by Complete College America (CCA) and their co-conspirators.  The methodologies they suggest are goal-driven, which means that the actual practice is ill-defined.  That goal is:

Place students directly into college-level courses instead of developmental course(s) followed by college-level.  http://completecollege.org/tag/corequisite-remediation/

The CCA agents have been very effective at using their rhetoric to support this ‘method’; unfortunately, for us practitioners, corequisite remediation is implemented in such diverse ways that we have small probabilities of interpreting the results in practical ways.  Further complicating our interpretation is the fact that the CCA agents will report that the “results are in” and “data supports” co-requisite remediation.

Sadly, we find  ourselves in the situation where almost all supporters of corequisite remediation are policy makers or administrators, while the majority of practitioners are skeptical or ‘non-believers’.  Neither side can convince the other, as long as the problem is ill-defined and we lack practical research on various methodologies used.

Like I said, corequisite remediation is a goal statement, not a single method.  Here are some common implementation patterns:

• Students in gen ed math (statistics or quantitative reasoning) who did not place at that level are required to register for a second class — a class providing the remediation.
• Students in gen ed math who did not place at that level are required to register for special sections of the course which incorporate additional time for the remediation.
• Students in gen ed math who did not place at that level are required to complete a remediation workshop (before the semester, during the first week or two).

In general, (1) The methods for remediation are not uniform and often not shared, and (2) pre-calculus is almost never used.  And, although I use the tag “quantitative reasoning”, the course is sometimes liberal arts math or an everyday-math type.

So, the corequisite remediation targets college-level math courses which tend to have a smaller set of prerequisite abilities.  Intro statistics is a course widely believed to have minimal requirements on the behalf of students; the liberal arts math course is often very similar in the demands for ‘skills’.  In most cases, the prerequisite was intermediate algebra or comparable test level.  Therefore:

Co-requisite remediation is often used for courses which have had an artificially high prerequisite in the past.

Separate from the remediation issues, we should correct our prerequisites for college math courses.  AMATYC has a position statement on this … see http://www.amatyc.org/?page=PositionInterAlg

I suspect that we will begin to see presentations at our conferences (AMATYC and affiliates) documenting the practices and results of co-requisite remediation; that will help the rest of us make an informed judgment on any possible validity.  I do not expect any “gold standard” research in this area (randomized, controlled studies which can be replicated), due to the politicized context.

Perhaps this has helped a little.  I remain a skeptic of the rhetoric surrounding corequisite remediation.

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