The Arithmetic Financial Aid Liability

At a session this week (at the National Math Summit), one comment led to some looks of surprise and follow-up discussion.  This comment dealt with the federal financial aid policies that our institutions are required to follow (if they accept any federal student aid money, which pretty much all colleges do). #ArithCollege #FinAid #NewLifeMath

Here is the basic idea:

Courses at a level below high school can not be counted to determine a student’s enrollment level (which determines their actual aid).   [See https://ifap.ed.gov/fsahandbook/attachments/1415Vol1Ch1.pdf on page 1-4]

In other words, courses primarily at the K-8 level can not be counted.  The determination of which category a given course belongs to … is left up to one of three bodies (a state legal authority, an accrediting body, or a state agency which approves vocational programs).  Two of those decision-making bodies are state level, while the other would normally be one of the regional accreditation bodies.

Perhaps you know what the determination is, within your state.  A logical assumption is that any course below the level of beginning algebra would be considered “K-8” level, and that this would include any arithmetic, basic math, or pre-algebra course.  One of the things I find interesting is that the information on this classification is very difficult to find.

In my own state (Michigan), we do not have a state legal authority for higher education; there is an office for reporting higher education data, and they do not classify remedial courses by level (K-8 or high school).  We have an agency responsible for vocational programs, but they make no determination (as far  as I can tell) about remedial course work.  Our accrediting body (HLC) does not have an answer.  In our college, our administration asked the math department to classify each course.

As remedial education remains in the spotlight, we can expect some added scrutiny based on the financial aid regulations.  Can we defend, with professional integrity, a position that a course in arithmetic or basic math or pre-algebra is ‘at the high school level’?  This is not a question of whether such courses exist in high schools; high schools offer a wide variety of courses, and some of them are below or above high school level.  The issue here is more about standards and expectations:  are students expected to have mastered arithmetic, basic math and pre-algebra before they reach the 9th grade?  From all perspectives that I am aware of, the answer is ‘yes’.

Of course, financial aid rules should not determine what courses we offer in a given college.  [Sadly, at my institution, that is exactly what happened this year.]  However, we have considerable evidence that offering courses at the K-8 level results in more damage than benefits.  Part of this evidence comes from the completion studies, which generally show single-digit completion for those who start in the K-8 math courses; this is for completion of a college-level math course within an extended period (often 3 years in the data).

Another source of evidence against offering K-8 level math courses comes from more scientific progression data.  Over a 40 year period, I’ve checked this progression data at my institution; I’ve never seen a benefit for passing a pre-algebra course prior to algebra … the data does not even show a ‘level playing field’.  Part of the problem contributing to this progression issue is that most courses in arithmetic or basic math or pre-algebra are very skill & procedure oriented.  Our courses and books focus almost exclusively on calculating answers (along with fairly routine ‘applications’), and this approach does not provide any preparation for courses which follow.

I see this as a situation where our best option is over-determined:  We should stop offering K-8 level math courses in college.

If we can justify requiring students to learn specific content from the K-8 mathematics, we should provide those in an accelerated or pre-requisite method.  My own conjecture is that there is a limited set of such content required in college, perhaps equivalent to 3 weeks of a regular course; we can use boot camps or just-in-time remediation, and get better results than our old system of separate course(s) at the K-8 level in college.

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New Life Project presentation at National Math Summit (March 2016)

The New Life session (at the 2nd National Math Summit) involves these materials.

• Presentation slides:  AMATYC New Life Project NADE Math Summit March 2016
• References:  References NewLife NMS 2016
• Implementation Maps and curriculum:  Implementation Maps AMATYC New Life Project 2016
• Math Literacy Learning Outcomes:  MLCS Goals and Outcomes Oct2013 cross referenced 2 by 2
• Algebraic Literacy Learning Outcomes: Algebraic Literacy Goals and Outcomes Oct2013 cross referenced 2 by 2

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Avoiding the Beginning Algebra Penalty

The most commonly taken math course in two-year colleges is beginning algebra; if we select a math student at random, there is a 21% probability that they are enrolled in a beginning algebra course.  On average, taking a beginning algebra course either does not improve the odds of passing intermediate algebra … or actually decreases the odds of passing.  #NewLifeMath #MathLiteracy

According to the 2010 Conference Board of Mathematical Sciences report (CMBS, http://www.ams.org/profession/data/cbms-survey/cbms2010-Report.pdf) about 428,000 students enrolled in a beginning algebra course at community colleges, compared to a total of 2.02 million enrolled.  The next most common enrollment was intermediate algebra (344K) followed by college algebra (230K) and pre-algebra (226K).  These extreme enrollments in courses in a long sequence have got to stop … see other posts on ‘exponential attrition’.

The main point today is this:

Evidence suggests that students incur a penalty when they enroll in a beginning algebra course.

Progression data is difficult to obtain, at the cross-institution level.  When the progression data is available, the format is often an overly simplistic comparison of those who placed at level N compared to those who took course N-1 then course N.  These summaries provide little information about the results of course N-1 (beginning algebra in this case).  At my institution, for example, those taking beginning algebra prior to intermediate algebra have a slightly higher pass rate in intermediate algebra compared to the course average.

However, this data is not research on the impact of beginning algebra.  Fortunately, our friends at ACT routinely conduct research on various components of the college curriculum.  In 2013, ACT released a research study on developmental education effectiveness (see http://www.act.org/content/dam/act/unsecured/documents/ACT_RR2013-1.pdf).  This ACT study used a regression discontinuity method, with a very large sample (over 100K), to examine the impact of taking certain courses with ACT Math score as a basic variable.  Since most two-year institutions do not use ACT Math as a placement test (at this level), their sample included large numbers of students at varying levels … a portion of which took beginning algebra first then intermediate algebra, and a portion which took intermediate algebra only.

The results were strong and negative:

The ‘dashed’ lines are students taking beginning algebra prior to intermediate algebra.  The upper set of lines represents ‘receiving a C or better in intermediate algebra.  For all ACT Math scores, the data suggests that students would be better served by placing them in to intermediate algebra (6% or higher probability of success, regardless of ACT Math score).

This is not what we want, at all; our personal experience might suggest that reality is different from this research study.  I believe that the research study is accurate, and that our own perceptions are misleading about generalities.

What strikes me about this research is that the results form a consistent pattern even though we lack a standard for what is ‘beginning algebra’ and what is ‘intermediate algebra’.  In some states, this is defined by a governing body; overall, though, we have operational definitions — beginning algebra is a course called beginning algebra, using a book titled beginning algebra.

Both courses (beginning and intermediate algebra) are heavily skill and procedure based,  organized around discrete chapters and sections.  In practice, intermediate algebra involves enough complexity that some understanding is required … while beginning algebra tends to reward memorization techniques.  To me, the research findings make sense

We need to avoid the beginning algebra penalty by replacing beginning algebra with a modern course that builds reasoning (like Mathematical Literacy).  Students are ill-served when we ‘keep it simple’ … students are not prepared for the future, and we also reinforce negative messages about mathematics (“I am not a math person”).  As long as we teach beginning algebra, we harm our students — we help some, but harm a larger group.

The beginning algebra course is beyond rescue; no amount of tweaking and micro-improvements will result in any significant improvement.  It’s time to start over.

At my institution, we are expecting that our beginning algebra course will decrease over the next few years while Math Literacy grows.  [We also expect to move away from intermediate algebra, but that might take longer.]  I know of other institutions, like Parkland College in Illinois, which have gone further on this path.

What is your plan for getting rid of beginning algebra at your institution?

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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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