Intermediate Algebra is NOT College Math ! :(

I actually spend a fair amount of time looking at other colleges math courses, partly from my interest in seeing how many colleges are doing New Life Project courses (Mathematical Literacy, Algebraic Literacy).  From that work, it is clear that the landscape is changing in both beginning algebra and general education mathematics.  However, two patterns are still present:

1. We continue to offer one or more courses in arithmetic focusing on procedures.  The presence of these courses is a tragedy on our campuses, since they negatively impact exactly the student groups we want to help (minority, poor).  I’ve posted on these issues earlier this year.
2. We frequently classify intermediate algebra as a college course, and commonly use it as a general education requirement.  Using a course which mimics a high school course in this way is professional embarrassment.  That’s the topic of this post.

We all know that “intermediate algebra” varies considerably between colleges, states, and regions.  In some cases, the intermediate algebra course has content at the level of the Common Core Mathematics (see http://www.corestandards.org/Math/ ) within the algebra and functions categories.  In most cases, however, our intermediate algebra courses fall below those expectations.

Intermediate algebra is a remedial course!!

The primary distinction between K-12 algebra and intermediate algebra is assessment — the college intermediate algebra course most likely requires a higher level of performance by the student in order to earn a passing grade.   It’s like “So, you were supposed to have learned this stuff in high school but NOW you are going to have to REALLY know that stuff.”

However, in many ways, our intermediate algebra (IA) courses are inferior copies of the K-12 curriculum.  Our IA courses are still descendants of copies of Algebra II from the 1970’s; much emphasis on procedures and correct answers … not much dealing with reasoning.  Given that we don’t deal with most of the discipline issues that occupy a K-12 teacher’s time, we should to better.    The K-12 content has responded to a series of standards (NCTM, Common Core) while our intermediate algebra has been standing still.

The Algebraic Literacy (AL) course is a modern system to help students get ready for college mathematics.  However, AL is still “not college math”, even though AL raises the expectations for students.

Entire states use intermediate algebra (IA) as an associate degree requirement.  In Michigan, which lacks a central governing body for community colleges, most colleges use that as one option for degrees.

We can, and must, do better.  If students do not need a course like Pre-Calculus, then we should use quantitative reasoning (QR) or statistics for their degree requirement … or even a course like ‘finite mathematics’.

Personally, I think intermediate algebra must die (and soon).  The issue in this post is whether a K-12 level standard course should be used for associate degree requirements.  Beyond the criteria of ‘expediency’, there is no rationale for that use.  IA is remedial, not college level.

Let’s MOVE ON!!

 
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TPSE Math … Transforming Post Secondary Ed Mathematics

One of my Michigan colleagues recently reminded me of a national project on transforming post secondary education mathematics “TPSE Math”, which you can find at http://www.tpsemath.org/

This broad-based effort seeks to engage faculty and leadership from all segments of college mathematics, with an impressive leadership team.  I encourage you to check it out.

One of the first things I explored on their site deals with equity; they have a 2016 report on equity indicators (see http://www.pellinstitute.org/downloads/publications-Indicators_of_Higher_Education_Equity_in_the_US_2016_Historical_Trend_Report.pdf)  Interesting reading!

Another part of their web site I want to look at in more detail … “MAG” (Mathematics Advisory Group), which is focused on an ‘action oriented role’.  Take a look at http://www.tpsemath.org/mag

I’m expected that we will all be involved with this TPSE work, to varying degrees.

 
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Progression in Math — A Different Perspective

Much is made these days of the “7 percent problem” (sometimes 8%) — the percent of those placing in to the lowest math course who ever pass a college math course.  This progression ‘problem’ has fueled the pushes for big changes … including co-requisite remediation and/or the elimination of developmental mathematics.  The ‘problem’ is not as simple as these policy advocates suggest, and our job is to present a more complete picture of the real problem.

A policy brief was published in 2013 by folks at USC Rossier (Fong et al); it’s available at http://www.uscrossier.org/pullias/wp-content/uploads/2013/10/Different_View_Progression_Brief.pdf.  Their key finding is represented in this chart:

The analysis here looks at actual student progression in a sequence, as opposed to overall counts of enrollment and passes.  This particular data is from California (more on that later), the Los Angeles City Colleges specifically.  Here is their methodology, using the arithmetic population as an example:

1. Count those who place at a level: 15,106 place into Arithmetic
2. In that group, count those who enroll in Arithmetic:  9255 enroll in Arithmetic (61%)
3. Of those enrolled, count those who pass Arithmetic: 5961 pass Arithmetic (64%)
4. Of those who pass Arithmetic, count those who enroll in Pre-Algebra: 4310 enroll in Pre-Algebra (72%)
5. Of those who pass Arithmetic and enroll in Pre-Algebra, count those who pass Pre-Algebra: 3410 (79%)
6. Compare this to those who place into Pre-Algebra: 68% of those placing in Pre-Algebra pass that course
7. Of those who pass Arithmetic and then pass Pre-Algebra, count those who enroll in Elementary Algebra: 2833 enroll in Elementary Algebra (83%)
8. Of those who pass Arithmetic, then pass Pre-Algebra, and enroll in Elementary Algebra, count those who pass Elementary Algebra: 2127 pass Elementary Algebra (75%)
9. Compare this to those who place into Elementary Algebra: 70% of those placing into Elementary Algebra pass that course
10. Of those who pass Arithmetic, then Pre-Algebra, and then Elementary Algebra, count those who enroll in Intermediate Algebra: 1393 enroll in Intermediate Algebra (65%)
11. Of those who pass Arithmetic, then Pre-Algebra, and then Elementary Algebra, then enroll in Intermediate Algebra, count those who pass Intermediate Algebra: 1004 pass Intermediate Algebra (72%)
12. Compare this to those who place directly into Intermediate Algebra: 73% of those placing into Intermediate Algebra pass that course

One point of this perspective is the comparisons … in each case, the progression is approximately equal, and sometimes favors those who came from the prior math course.  This is not the popular story line!

I would point out two things in addition to this data.  First, my own work on my institution’s data is not quite as positive as this; those ‘conditional probabilities’ show a disadvantage for the progression (especially at the pre-algebra to elementary algebra transition).  Second, the retention rates (from one course to the next) are in the magnitude that I expect; in my presentations on ‘exponential attrition’ I often estimate this retention rate as being approximately equal to the course pass rate … and that is what their study found.

One of the points that the authors make is that the traditional progression data tends to assume that all students need to complete intermediate algebra (and then take a college math course).  Even prior to our pathways work, this assumption was not warranted — in community colleges, students have many programs to choose from, and some of them either require no mathematics or basic stuff (pre-algebra or elementary algebra).

The traditional analysis, then, is flawed in a basic, fatal way — it does not reflect real student choices and requirements.  For the same data that produced the chart above, this is the traditional analysis (from their policy brief):

This is what we might call a ‘non-trivial difference in analysis’!  One methodology makes developmental mathematics look like a cemetery where student dreams go to die; the other makes it look like students will succeed as long as they don’t give up.   One says “Stop hurting students!!” while the other says “How can we make this even better?”

So, I’ve got to talk about the “California” comment earlier.  The policy brief reports that the math requirement changed for associate degrees, in California, during the period of their study: it started as elementary algebra, and was changed to intermediate algebra.  I don’t know if this is accurate — it fits some things I find online but conflicts with a few.  I do know that this requirement is not that appropriate (nor was elementary algebra) — these are variations of high school courses, and should not be used as a general education requirement in college.  We can do better than this.

This alternate view of progression does nothing to minimize the penalties of a long sequence.  A three-course-sequence has a penalty of about 60% — we lose 60% of the students at the retention points between courses.  That is an unacceptable penalty; the New Life project provides a solution with Mathematical Literacy replacing both pre-algebra and elementary algebra (with no arithmetic either) and Algebraic Literacy replacing intermediate algebra (and also allowing about half of ‘elementary algebra students’ to start a course higher).

Let’s work on that question: “How can we make this even better?”

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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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