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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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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Saving Mathematics, Part IV: This is College, Right?

For whatever reason, we in the mathematics community have an obsession with high school … we define college mathematics by assigning a prerequisite that suggests a level above high school (often the prerequisite is intermediate algebra).  We also accept the notions about people not being good at mathematics, which results in the contradictory policy of allowing intermediate algebra to meet a degree requirement in college.  What’s up with THAT?  #remediation #FinAid

All of our institutions (with very few exceptions) must comply with financial aid laws and regulations.  Those regulations make a distinction between remediation at the high school level and remediation at the elementary level (K-8); courses at the elementary level (like arithmetic, pre-algebra) can not be used to determine eligibility for financial aid.  Courses at the high school level can be used for financial aid, though there is a limitation on the total remediation.  (see https://ifap.ed.gov/fsahandbook/attachments/1415Vol1Ch1.pdf)

The K-12 professional standards of the past 25 years (NCTM) and the Common Core provide a way to judge the level of our courses.  Most of our intermediate algebra courses map to 9th and 10th grades in those standards; even prior to that, intermediate algebra was considered 10th or 11th grade level.  Overall, 57% of our enrollments (community-college-type) is in pre-college mathematics … 32% of that enrollment is in remediation at the elementary level.  [CBMS 2010 data; http://www.ams.org/profession/data/cbms-survey/cbms2010-Report.pdf]

My position is that these high numbers in remediation are the result of artificial parameters for ‘college level’ and our obsession with high school.  Many of us accept the position that the mathematics actually needed for college work (whether STEM-path or not) is not delivered by our basic-math > pre-algebra >beginning-algebra > intermediate-algebra filtering system.  Our curriculum in those courses is often inferior to what our K-12 colleagues are using.

• Remediation does not mean high school mathematics

We need to throw out our traditional developmental courses (as well as most college-algebra-level courses).  Convenient copying of courses does not help students.

The question is:

• What does a COLLEGE student need prior to a college math course?

The needs do vary somewhat depending on the particular college math course.  We need to show our integrity by offering courses designed to serve the purpose for which we use them:

• Only require students to take courses with validity for the purpose!

This is not a quick process, but it is something we can do together … and even be inspired by.

In the meantime, let’s show our professionalism by doing the following:

1. Always classify arithmetic and pre-algebra as “elementary level” remedial courses
2. Always classify beginning algebra and intermediate algebra as “high school level” remedial courses, which have no role meeting a college degree requirement
3. Identifying appropriate college-level math courses required for each degree

Complete College America says much that I disagree with; quite a bit of their communication is rhetoric to support pre-determined solutions.  However, one thing from CCA I really agree with:

College students come to campus for college, not more high school. Let’s honor their intentions — and refocus our own good intentions to build a new road to student success.
http://www.completecollege.org/docs/CCA-Remediation-final.pdf

To get started on a path to replace the traditional developmental math courses, take a look at the New Life Project courses (Mathematical Literacy and Algebraic Literacy).  I hope that you will join me and hundreds of other professionals working to create better models to serve our students and communities.

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Intermediate Algebra Must Die!!

“Intermediate Algebra Must Die!” … I said this at two recent meetings (first at a conference, then at my college).  The need for this demise is ‘over-determined’, to use a social science phrase:  several factors, each of which would be sufficient, are present to create a conclusion with multiple rationales from different perspectives.  #IntermediateAlgebra #AlgebraicLiteracy  #NewLifeProject

The first rationale for the necessary demise of Intermediate Algebra comes from data concerning preparation for ‘college math’ (most often college algebra or pre-calculus).  The CCRC and ACT both have discontinuity regression research showing that intermediate algebra does not prepare students.  [See the first part of my presentation on Algebraic Literacy at https://www.devmathrevival.net/?p=2331.]  The most optimistic results show a 2% to 5% gain in pass rates after an intermediate algebra course compared to students with similar backgrounds; of the 4 data sets, 1 had this very small positive result … 2 have ‘null’ (no gain), and 1 has ‘negative’ (students do worse after intermediate algebra, compared to similar students who did not).

The second rationale for the necessary demise of Intermediate Algebra comes from the policies about degree requirements at our institutions.  At hundreds of institutions, students can meet a general education requirement for a degree by using the remedial math course called ‘Intermediate Algebra’.  This policy makes two horrible statements at once:  first, that we don’t think it is important for students to learn additional mathematics; second, that we don’t think students have sufficient abilities to learn additional mathematics.  We are not just accommodating negative perceptions about learning mathematics, we are reinforcing them.

The third rationale for the necessary demise of Intermediate Algebra comes from its origins:  Intermediate Algebra was copied from the high school curriculum during a period when procedure and repetition were emphasized (in reaction to the original ‘new math’) in a design based on low standards for teacher credentials (the thought was ‘make it teacher-proof’).  This origin of the course is clearly related to the data referenced above; however, this rationale is based on the contradictory nature of the course compared to any set of modern curricular standards (as in Common Core, or even the original NCTM standards).  Intermediate Algebra is a professional embarrassment.

The last rationale for the necessary demise of Intermediate Algebra comes from the politicization of developmental mathematics:  as long as we are teaching ‘high school courses’, policy makers are going to attack our curriculum in colleges.  These stakeholders do not see why they should pay a second time for the same treatment, and many do not see any appropriate benefit from the course.  This rationale, like the third, suggests that all traditional developmental mathematics be removed ASAP and replaced (to the extent needed) by modern courses designed for college use (such as the New Life Project courses, Mathematical Literacy and Algebraic Literacy).  A course being “pre-college” does not mean “high school”.

We need to ‘own our problem’; for too long, we have continued our weak copies of weak high school courses to stand in the way of actually preparing students.  We have taken the easy road, sometimes creating a significant revenue source for our colleges, when we should have focused on our students’ needs in college.  We have reinforced the “I can’t do math” belief, and sold our profession short.  We have placed our entire curriculum at risk by requiring many students to take high school courses in college.

Intermediate algebra must die!

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