Placement: Does HS GPA Add EQUAL Value?

Many people are talking about ‘multiple measures’ placement, especially the option of using high school grade point average as an input variable.  In some locations (like mine) ‘multiple measures’ is translated ‘HS GPA instead of placement test’, where ‘multiple’ means ‘alternative’. True multiple measures has some appeal.  Conceptually, there is an advantage to using more than one variable as input when the variables measure different traits.  The HS GPA involves several issues, with equity being high on my list.

As mathematicians, the first thing we should say about HS GPA is that this variable is a mis-use of the raw data.  The grades in any class are barely ordinal in nature (rankings); the average used (mean) is based on ratio variables (equal intervals AND a 4 represents twice something compared to 2).  When a variable has statistical flaws such as this, any further use in analysis should be suspect.  Whatever the disadvantages of tests (ACT, SAT, or placement), at least they involve appropriate use of the measures from a statistical point of view.

High school GPA has a number of confounding variables, some of which are shared by most tests used today.  In particular, economic level (SES) and ethnicity are both factors in the HS GPA picture (as they are in college GPA).  This type of analysis is widespread and the results consistent; one such report is from the Educational Testing Services (see http://www.ets.org/Media/Research/pdf/RR-13-09.pdf ).  Using HS GPA does not level the playing field, given the high correlations normally found between the measures.  In fact, my view is that using HS GPA in addition to a test will benefit mostly majority students from comfortable homes … and will again place minority and poor students in lower levels.

As an anecdotal piece of data, I was at a conference session recently on co-requisite remediation where the placement method involved tests or HS GPA.  Through the first year of their work, the co-requisite ‘add-on’ sections were almost totally minority … even more than their traditional developmental classes had been.  [The institution used a co-requisite model where all students enroll in the college course, and those not meeting a cutoff were required to enroll in the add-on section as well.]

When people try to explain the predictive ‘power’ of HS GPA, they often use ill-defined phrases such as ‘stick-to-itness’.  I suspect that our friends teaching high school would have a different point of view, where grades in the C+ to B range reflect not skills but attitudes (primarily compliance).  How can we justify using an inappropriate statistic (grades are ordinal) which measures “who knows what”?  Whatever the HS GPA measures, it is indirectly related to preparation for college mathematics.  The connections are likely to be stronger for writing.

The arguments FOR using the HS GPA in placement are based on studies which indicate an equal or higher predictive validity, versus tests alone.  One of the better studies within mathematics is one done by ACT (see http://www.act.org/content/dam/act/unsecured/documents/5582-tech-brief-joint-use-of-act-scores-and-hs-grade-point-average.pdf).  Here is their graph:

This graph is showing the probability of passing college algebra, with the 5 curves representing ACT Math levels (10-14, 15-19, etc).  If a student’s ACT Math is below 20, their HS GPA does not improve their probability of success — until we get between 3.5 and 4.0.  The 20 to 24 groups and above have a pattern indicating that it might help to include the GPA; since most of us use cutoffs in the 19 to 22 range, this shows some promise when using BOTH variables.

However, notice the negative indications … if the ACT math is high (over 25) and the GPA is low, the data indicates that we should place the student differently because the student has a dramatically lowered pass rate.  Perhaps THIS is the place for co-requisite remediation!  I would also point out the overall picture for HS GPA at the high end … the probability of success is varied, and depends upon the test score.

SUMMARY:
We know that both HS GPA and tests tend to reflect inequities, where the results tend to place more minorities in developmental courses.  Although predictive value increases (correlation), we are using an inappropriate statistic (HS GPA) with little connection to preparation for college mathematics.  The available research suggests some minor gains for using HS GPA:

• for students just below the college math test cutoff with a very high HS GPA
• those with high scores and low HS GPA
• use of HS GPA alone results in an almost random assignment of students

Placement has never been a confident endeavor; even the best measures (tests or other) are incomplete and impacted by other variables.  Placement Tests have taken a beating in recent years, a treatment which I think was not justified.  Modernizing the placement tests is a more appropriate response … an idea which I will pursue in an upcoming post.

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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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Making Up For Twelve Years

How can we make up for what students did not get from twelve years of math?  Is it possible to have just one or two pre-college math courses, regardless of the entering level of students in a community college?  This is the big issue of our era, and the truth lies in a deeper understanding of the problems we face.  #CoRequisiteMath #NewLifeMath #CollegeMath

The origins of remedial mathematics, which formed developmental mathematics, are in the “college student” concepts of universities.  Being a college student meant that you had a solid high school academic background, and (almost coincidentally) meant that you could register for college algebra.  If a student could not show this high school background, remediation was used to fill it in.

This “college student” approach was originally based on the K-12 curriculum, which has never been very standardized in the USA.  Even with the recent Common Core, great variations exist.  The remediation provided, in mathematics, was usually a package that estimated the most common content as measured by topics and procedures.  We often referred to developmental courses as the “same as high school, only faster and LOUDER”.

In a basic way, remediation was done to estimate the desired college readiness measures (ACT, SAT); those measures, do correlate with placement in to college algebra.  The studies I’ve seen show correlation coefficients between 0.2 and 0.4; significant and meaningful, although these values indicate that only 5% to 15% of the variation is explained.

Meanwhile, we have no validation that the K-12 content as identified by topics and procedures has any causative connection to college mathematics success.  The entire set of them correlates somewhat, but we lack the professional validation of what members of the set (or a different set) are necessary.

Now, all of this means:

K-12 mathematics has a vague connection to readiness for college mathematics.

The conjecture we are exploring, in the current reform efforts, is that only some members of the K-12 math set are needed along with some members of another set (not taught in K-12).  [The reforms are the New Life Project, Dana Center New Mathways, and Carnege Pathways.]

In other words, the issue is not “making up for twelve years”.  The issues involve the particular abilities needed for success in specific college math courses.  Perhaps it really does not matter if a student can not tell me what 8*9 is, or what -4 + (-2) is; perhaps it is more important that students can reason about numbers and quantities at a level necessary for the college course.

In the current reform work, we in the New Life Project have identified some prerequisite learning outcomes needed before our first course (Math Literacy).  Here is what our document states:

Prerequisites to MLCS Course:
Limited quantitative skills are required prior to the MLCS course. Students should be able to do the following prior to this course:

• Understand various meanings for basic operations, including relating each to diverse contextual situations
• Use arithmetic operations to solve stated problems (with and without the aid of technology)
• Order real numbers across types (decimal, fractional, and percent), including correct placement on a number line
• Use number sense and estimation to determine the reasonableness of an answer
• Apply understandings of signed-numbers (integers in particular)

The New Life Project recommends that students be provided any needed instruction for these areas in either a short-term format (‘boot-camp’) or just-in-time (within the course).

These outcomes are vague, because we did not engineer down to the details.  My college is about to begin this process for a new version of our Math Lit course; our initial estimate is that we will need something like 20 hours of class time (perhaps 30) to help students develop the necessary abilities.  We do not have a goal of making up for twelve years … that goal is both unrealistic and not productive.  Instead, we will work on the much smaller set of “what does the student need to succeed in THIS course”.

The same conjecture would extend to other levels.  Whether it is Algebraic Literacy or Intermediate Algebra, what abilities does the student need?  The New Life Project suggests that the Math Literacy course is a good match.  For college algebra needs, the Algebraic Litercay course was designed to provide the abilities needed.

“Covering twelve years” is a bad solution to the wrong problem.  Student readiness for particular math courses is not a matter of ‘twelve years’ … it is a matter of specific abilities, and dealing with those is much more efficient.

Do not confuse these comments with support for “co-requisite remediation”.  Co-requisite remediation takes the extreme step of saying that essentially all students can start a college math course with enough support.  My position is that some portion can do this (more than we might think) … but taking the extreme position of co-requisite remediation is foolish and lacks the professional judgment that we are supposed to apply to our work.

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Who needs developmental math? Who needs remediation?

In our beginning algebra class, we started our work in ‘exponents’.  I use an activity (guided, discovery) to start this work and talk with students and groups as they answer the questions.  The range of questions and confusion is both encouraging and discouraging.  Some of the questions showed thoughtfulness and insight; others indicated a naive knowledge of our language system. #placement #tests

A large component of the issues relate to “grouping”, in 3 categories:

• The meaning of required, shown grouping
• The meaning of optional, shown grouping
• The meaning of implied grouping

Many of us have commented on an example of the last group:   -5², where the implied grouping exists on the base (5) not the opposite.  Students do struggle with this, and … on its own … this type of problem is not worth the trouble.  However, many of the same students misinterpret 5x²; when a value of x is provided students will square the 5 as well as the x … if the replacement value is negative, students will either leave off parentheses on that value or write the parentheses but not use them in evaluating.  The implied grouping is a key feature of mathematical languages, and it harms students that we are not consistent in the meaning of implied grouping.  [Just think about what sin² 3x means … there are two implied groupings in that expression, and both are inconsistent with almost all other implied groupings.]

When a problem had optional grouping shown, as in (5xy)(x²y³), students do not always understand that the meaning has not changed … and often, they think of a different process (like distributing) when they would not if the problem had no grouping at all.  Another example would be (5x + 3) – (2x – 5) [required grouping on the 2nd expression] when the student distributes the ‘negative’ and writes (5x + 3) (-2x + 5) … and proceeds to multiply; that’s a case where we would say the grouping is optional but correct with the ‘plus’ between the groups.

So, what do these comments have to do with ‘needing developmental math’ or ‘needing remediation’?  These misunderstandings are not gaps in knowledge, nor forgotten information … they are wrong ideas (called ‘baggage’ by some colleagues).  Wrong ideas are known to be resistant to instruction; the most common outcome is that the wrong ideas are temporarily covered up by memorized correct information but then re-appear in the behavior after a short period of time.

Much criticism has been leveled at the placement tests we use.  The words “evil” and “invalid” often are included in statements about those tests.  However, the problem is us not the tests.  The tests are constructed to meet ‘market demands’ … we have told the companies that we need to measure skills, so that is what we got.  The problem is that skills are a very poor way to identify students needing either a developmental math course or a remedial math course.  Missing a skill problem can be caused by either a wrong idea OR a forgotten procedure, resulting in much ambiguity with scores.

Developmental mathematics is not going away.  Change is happening … the new courses like Mathematical Literacy and Algebraic Literacy focus first on developing right ideas about the mathematical objects then on procedures.  What we need is a new set of specifications for placement tests to determine who needs a course versus those who are either ‘ready now’ or ‘have forgotten some’.  I suspect that the ‘entrance tests’ (SAT, ACT) are better measures than the placement tests because the ACT & SAT are not as focused on skills.  We need placement tests that identify wrong ideas as well as some fundamental skills.

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