The Big Missed Opportunity: Forty Five Years of Dev Math, Part III

This is part of a series of posts reflecting on our history in developmental mathematics … especially at community colleges in the USA.  We’ve talked about the ‘origins’, about a ‘golden age’ (or not), and now we move to the first half of the 1980s.

Two major movements were active at about the same time in the early 1980s … one dealt with placement policies, and the other dealt with the content of mathematics courses at this level.  When more than one movement is impacting a profession at the same time, there is always an opportunity for fundamental change.  That is not what happened in this case, and we continue to deal with the ‘incorrect’ responses to that opportunity.

The use of standardized assessments for placement was widespread (though with varied instruments) at the start of this period, as we moved from home-grown placement measures to assessments used at a larger scale (state, region, or nation).  Those tracking data quickly noticed that these measures, often used with mandatory placement, were impacting certain groups at a disproportionate rate.  In some cases, the items on the assessments had been tested for bias; even with tests using only these tested items, the results showed an uncomfortable level of differential impact.

Clearly, “something” had to be done.  A professional response might have been to develop an effective short term intervention that would equalize the results.  Another professional response might have been to establish collaborations between community college math faculty and the local K-12 school’s math program.  In general, neither of those responses occurred.  Instead, there was a decline in the rate of mandatory placement:

Students have the right to fail.  If they disagree with the placement measures, they can take the higher course.

I still hear this “right to fail” statement, which I see as a abrogation of our responsibilities:  We let students make a decision known to put them at unnecessary risk (we knew they were likely to fail).  Most colleges did not continue this ‘worst practice’ (as opposed to best practice), with the result that the placement system continued to have a differential impact on known groups of students.  That problem continues to the present day, as a general condition.  [Some colleges, systems, and states use either placement systems that moderates the impact (true multiple measures) OR have implemented new curricula which make the results more tolerable (pathways).]

For some history of placement policies, see https://ccrc.tc.columbia.edu/media/k2/attachments/college-placement-strategies-evolving-considerations-practices.pdf  .

The content movement impacting developmental mathematics in the early 1980s was a ‘trickle-up’ reaction to K-12 math reform in the prior decade or two.  The K-12 math reform is usually called “new math”, which failed because the curriculum was designed by university math education professors with little attention to the teachers who would try to deliver it.  Even though we can see the “DNA” from this New Math within the modern curricular standards of NCTM, AMATYC, and MAA, there was a back-lash in K-12 that drifted up to college … “BACK TO BASICS”.

There were very few college level books that implemented New Math designs; most were (and still are) very similar to the K-12 math predated New Math.  However, here was an opportunity for college math faculty to create developmental mathematics courses with balanced and effective approaches to multiple levels of learning — including reasoning and communication.  Our collective response was to regress even further on the levels we sought to deliver in our curriculum.  We reduced the amount of reading in our books, added examples, grouped the student practice by type, and generally made choices guaranteed to limit the student benefit for their efforts.

The two movements (right to fail, back to basics) involved forces that could have had that synergy necessary for significant long-term change.  We should have had one response to resolve both issues … change our curriculum in a basic way so that entering memory levels of particular skills do not determine success; rather, the entering level of understanding would determine success.

In my view,  the “New Life Project” represents this type of approach with developmental courses that are far less sensitive to remembered skills (Math Literacy, Algebraic Literacy), which means that they are far more accessible to all parts of our student population.  The fact that this solution appeared and gained support 30 years after the first opportunity indicates to me that our profession has been resistant to progress.  It’s not that dev math did not change between 1985 and 2010; it’s that all of the other changes did not address the core problems we face.  We needed other external forces acting upon our work before we were willing to try something different enough to possibly make real progress towards helping all students succeed.

We currently are in the ‘next big opportunity’ to make progress.  Let’s be sure to do things this time that will get us significantly closer to our goals.

 
Join Dev Math Revival on Facebook:

Math Literacy: Placement, Prereqs, and Access

In response to a recent post on placement tests, a colleague made this comment:

In my experience, many of the people who struggle with arithmetic really aren’t ready for Math Literacy. [S. Jones]

This colleague teaches at one of the premier colleges in the “Math Literacy Movement”, with experience and wisdom.  I think this is one of the most important issues we face in community colleges.

The intended curriculum in a Math Literacy course has very limited prerequisites.  Among these are basic number sense (place value and order), and some understanding of basic operations within contextual situations.

If a student struggles with these items, yes … they are likely to be ‘not ready’ for Math Literacy:

• Add 24.1 + 1.3     [know place value ‘across’ the decimal]
• Which of these is smallest?   0.23, 0.201, or 0.1065?  [order of numbers]
• A set of bleachers has 6 rows, and 10 people can sit in each row.  How many people can sit on the bleachers?  [operations in context]
• A recipe calls for 24 ounces of diced dried fruit.  The packages I’m buying contains 3.5 ounces; how many packages will I need for that recipe?  [operations in context]

On the other hand, struggles with these items are far less related to readiness for Math Literacy:

• Add 3/4 + 5/6 and write as a mixed number if necessary
• Which of these is smallest:   3/13, 5/14, or 2/7?
• Divide (without a calculator):  19.3 ÷ 2.56
• If the area of a rectangle is 56 square feet, find the width if the length is 6 feet.

To understand what the prerequisites are for a course like Math Literacy, we need to think about the end point of that course.  The goal of Math Literacy is to build readiness for the next math course (quantitative reasoning, statistics, or Algebraic Literacy).  This goal drives the content of Math Literacy, which is outlined in four areas in the document mlcs-goals-and-outcomes-oct2013-cross-referenced

This goal, as operationalized in the content, seeks to have students meet the necessary and sufficient conditions for readiness in the next math course … any of those next math courses.  None of these courses are arithmetic in nature, though all of them depend upon numeracy skills to some extent.

The problem with our conceptualization of arithmetic in a college setting is that we attribute “here is what we would like students to know” to that content.  Of course, we’d like people to be able to perform fraction operations and decimal operations without depending upon a calculator.  Of course we would like students to know some basic geometric relationships.  In fact, most implementations of Math Literacy will assist students in those areas, but not as a core goal of the course nor as a prerequisite.

The truth is … that arithmetic was never a prerequisite for algebra, based on content structure.  Sure, some parts of arithmetic had a role.  In fact, we might call those parts ‘numeracy’ just like we do in the conversations about Math Literacy.  However, competency in arithmetic procedures is (and has been) unrelated to readiness for a subsequent math course.

Too often, we create artificial barriers to students reaching their goals.  One of the largest barriers in a college environment is the “arithmetic placement test”.  We have a situation where:

1. A content analysis does not support the treatment of arithmetic as a prerequisite to a math course.   AND
2. No data exists to suggest that there is any practical connection between competence in general arithmetic and readiness for a math course.

My college is currently using an arithmetic placement test merely for the purpose of sorting students relative to our two Math Literacy courses … the Math Literacy with Review course has a lower cutoff than the Math Literacy without review.  We no longer offer any math course ‘before’ Math Literacy.  Eventually, we might be able to make the determination about which Math Literacy course from other measures.

Think about this aspect of the situation: Most of the students who might take an arithmetic test have experienced 12 years of mathematics with over half of this time focused on arithmetic.  Do we expect to ‘fix’ most of their problems in arithmetic within a few months?  Also, what do the students look like who get lower scores on placement tests (especially arithmetic)?  The polite phrase is “this group is very diverse”.  The fact is that tests on arithmetic impact certain minority groups (race, poverty) more than others.  Unless we can show a very strong connection between ‘arithmetic’ and success (in a specific math course, or in general), we have a moral obligation to NOT impose an arithmetic barrier.

Using an arithmetic placement test to identify students required to take an additional math course is a fundamental access issue.  Such courses are obsolete relics of a different era, and lack connections to both school mathematics in this century and to other math courses in colleges.  We can help thousands of students by following one simple plan.

Just stop it!!

 Join Dev Math Revival on Facebook:

The Placement Test Disaster ?

For an internal project at my institution, I’ve been looking at the relationships between Accuplacer test scores, ACT Math scores, and performance in both developmental and college-level courses.  Most of the results are intended for my colleagues here at LCC.  However, some patterns in those relationships are important for us to explore together.

So, the first pattern that is troubling is this:

Students who place into a pre-calculus course based on their ACT Math score have lower outcomes than those who place based on the Accuplacer “College Level Math” test … and lower than those who needed to take intermediate algebra before pre-calculus.

We use the ‘college readiness’ standard on the ACT Math test of 22 (see https://www.act.org/content/act/en/education-and-career-planning/college-and-career-readiness-standards/benchmarks.html ).  The pattern in our data for the ACT Math is similar to some references found at other institutions … though we tend not to talk about this.

Of course, the use of an admissions test (ACT or SAT) for course placement is “off label” — the admissions tests were not designed for this purpose.  We tend to use the ACT option for placement in response to political pressure from administrators (internally) and from stakeholders (externally), and sometimes under the guise of “multiple measures”.  The patterns in our data suggest that the ACT Math score is only valid for placement when used in a true multiple measures system … where two or more data sources are combined to create a placement.  However, most of us operate under ‘alternative measures’, where there are different options … and a student can select the highest outcome if they wish; alternative measures is guaranteed to maximize the error rate in placement, with a single measure placement test almost always providing better results.

The second pattern reflecting areas of concern:

The correlations are low between (A) the ACT Math and Accuplacer College Level Math test, and (B) the Accuplacer Algebra and Accuplacer Arithmetic tests.

The second combination is understandable, in itself; the content of the Algebra and Arithmetic tests have low levels of overlap.  The problem deals with our mythology around a sequence of math courses … that the prerequisite to algebra is ‘passing’ basic math.  Decades of our research on algebra success provide strong evidence that there is little connection between measures of arithmetic mastery and passing a first algebra course.  In spite of this, we continue to test students on arithmetic when there curricular needs are algebraic:  that is a disaster, and a tragedy.

The first ‘low correlation’ (ACT Math, College Level Math) is not what we would expect.  The content domains for the two tests have considerable overlap, and both tests measure aspects of ‘college readiness’.  As an interesting ‘tidbit’, we find that a higher proportion of minorities (African American in particular) place into pre-calculus based on the more reliable College Level Math test compared to majority (white, who have a higher proportion placed based on the ACT Math) — creating a bit of a role reversal (whites placed at a disadvantage).

Placement testing can add considerable value … and placement testing can create extreme problems.  For example, students with an average high school background will frequently earn a ‘college ready’ ACT Math score when they have too many gaps in their preparation for pre-calculus.  A larger problem (in terms of number of students) comes from the group of students a bit ‘below average’ … who tend to do okay on a basic algebra test but not-so-good on arithmetic, which results in thousands of students taking an arithmetic-based course when they could have succeeded in a first algebra course (or Math Literacy).

Those two problems are symptoms of a non-multiple-measures use of multiple measures, where alternative measures allow students to select the ‘maximum placement’ while other measures (with higher reliability) suggest a placement better matched for a success situation.

As a profession, we are under considerable pressure to avoid the use of placement tests.  Policy makers have been attacking remediation for several years now, and more reasonable advocates suggest using other measures.  The professional response is to insist on the best outcomes for students — which is true multiple measures; if that is not viable, a single-measure placement test is better than either a college-admission test or a global measure of high school (like HS GPA).

And, all of us should deal with this challenge:

Why would we require any college student to take a placement test on Arithmetic, when their college program does not specifically require proficiency in the content of that type of test?

At my institution, I don’t think that there are any programs (degrees or certificates) that require basic arithmetic.  We used to have several … back in 1980!  Technology in the workplace has shifted the quantitative needs, while our curriculum and placement have tended to remain fixated on an obsolete view.

 Join Dev Math Revival on Facebook:

Talking About Equity as an Avoidance

My department has begun a process which will (hopefully) lead to meaningful and sustained improvements in our equity picture.  Current, and historical, data makes it clear that our program is not serving all groups adequately.  Black students (aka “african american”) almost always have a pass rate significantly lower than other groups, after accounting for their level of preparation.

I am very pleased with my colleagues and their willingness to spend time working on a problem which involves some discomfort … it’s not always easy to talk about race and equity.  Much of our initial discussion focused on our point of view and problems that make sense to us … phrases like “student skills”, “role models”, and “tutoring” we very common.  “Compassion” and “empathy” were also used.  These are all good thoughts, but tend to focus on the surface and symptoms.

However, I am sure that our conversation will need to progress to deeper levels of understanding.  One reason to believe this is that this conversation has occurred hundreds of times in other institutions and organizations without producing an accepted basket of ‘best practices’ for eliminating the inequity as we generally would like.

One perspective that might help our profession actually make progress on this comes from Danny Martin (University of Illinois at Chicago).  Dr. Martin delivered a talk entitled “The Collective Black and Principles to Actions” (available at http://ed-osprey.gsu.edu/ojs/index.php/JUME/article/view/270/169) .  The ‘Principles to Actions” part of the title refers to the 2014 publication by NCTM of that name.  The “collective black” in the title refers to a way to understand a social structure in the United States.

A quote from near the end of that article is:

Does this document represent, symbolically and in spirit, the kind of disruptive violence to the

status quo that can move the last to first?  Can it truly help in improving the collective conditions

— not isolated examples of success — of African American, Latin@, Indigenous, and poor

students? By success, I do not mean slow growth and incremental gains.

The “disruptive violence” in this quote might bother some readers.  Remember that Dr. Martin is speaking of social institutions, not a personal philosophy of political change.

I think Dr. Martin’s point, perhaps shared by Dr. Martin Luther King as well, is that incremental change and “stuff around the edges” will not produce meaningful changes at the level necessary.  Our  problems are too well established in the existing structures, and even in the vocabulary we use to describe ‘the problem’.  For example, millions of white people have had “compassion” and “empathy” for a wide variety of students (including the group ‘black students’ my department is focused on).

Here is a point … Perhaps “white people” only support working on “equity” when this work does not involve any change in the white power relationships and social structure.  Are we willing to share power and authority to reach the lofty goals we seek?

Perhaps we will find that reaching equity in our department depends upon fundamental changes in the  local community.  The urban schools have old buildings, few resources, and other significant challenges; this district is heavily ‘minority’ (black students in particular) … because our state allows “school of choice’, where THOSE WITH RESOURCES can take their students to a ‘better’ school in the suburbs.   Can ‘separate and sort of equal’ ever allow us to achieve equity in higher education?  [The local condition amounts to sanctioned segregation of schools, especially at the high school level.]

We are likely to encounter large-size problems in our work to eliminate inequity in our courses.  We have only begun the conversation, and I’m proud that my colleagues are willing to begin this journey.  Our success will likely involve changes that would have been difficult to imagine prior to beginning the process.  So … I appreciate your “moral support”.

Is your department ready to face the challenges of doing effective work to reduce inequity?

 
Join Dev Math Revival on Facebook: