Equity in College Mathematics: What does the data tell us about poverty and race?

I am very proud of my department for our decision to do some serious work on equity.  We are having focused discussions at meetings and in hallways, we are bringing up equity in other discussions, and have examined quite a bit of data.  I want to highlight a little bit of that data.  This post will focus on the role of poverty in the pursuit of equity in college mathematics.

Like many colleges, my institution provides access to a centralized data reporting function (“Argos” in our case).  We can use this database to extract and summarize data related to our courses, and the database includes some student characteristics (such as race, ethnicity, and sex … self-reported).  In addition, the database connects to direct institutional records dealing with enrollment status and financial aid.  The primary piece of data from the financial aid record is a field called “Pell Eligible”.

As you know, Pell Grants are based on need; this usually means an annual income of less than $30,000.  Students are not required to apply, even if they would qualify for the maximum award.  However, we do know that students do not receive a Pell ‘award’ unless they have a low income.  For us, this “Pell Eligibility” is the closest thing we have to a poverty indicator.

When we summarize student grades by race and Pell Eligibility (across ALL courses in our department), this is the result.

This graph has two “take aways” for me.  First, poverty is likely associated with lower rates of passing.  Secondly, the impact of race on outcomes is even stronger.  Note that the “Pell” group is lower than the non-Pell group for all races, and that the “Black non-Pell” group has lower outcomes than the non-Pell hispanics or whites.

The situation is actually worse than this chart suggests.  The distribution of ‘poverty’ (as estimated by Pell eligibility) is definitely unequal: 70% of the black group is Pell eligible, while only 40% of the white group is Pell eligible (with hispanics at a middle rate).

I am seeing a strong connection between our goal of promoting equity and the goals of social justice.  As long as significant portions of our population live in poverty, we will not achieve equity in the mathematics classroom … awarding ‘financial aid’ does not cancel out the impacts of poverty.  In addition, as long as some groups in our population are served by under-resourced and struggling schools, we will not achieve equity in the mathematics classroom.  This latter statement refers to the fact that many states have policies like Michigan’s which allow those with resources to have a choice about ‘better schools’, while limiting state funding for public schools (and simultaneously attacking the teaching profession).

In our region, the majority of the black students attending my college came from the urban school district.  This urban school district had a proud history through the 1980s, with outcomes equal to any suburban school in the area.  However, dramatic changes have occurred … even though that district has made significant progress in recent years, there is no doubt that the urban schools are not preparing students for college.  Poverty plays a role within that school district, and the interaction between race and poverty is again unequal: more blacks live in poverty within the city than other races.

The social justice movement seeks to provide all groups with equal access to upward mobility, combined with a reasonably high probability of escaping poverty, based on a presumption of effort.  Barriers to progress are addressed as systemically as possible.  College mathematics is currently one of the barriers to progress in social justice.  Modern curricula do not solve this barrier, given the data I’ve seen (though we are early in that process of change).

If we see our role as separate from equity and social justice, we are enabling the inequities to continue.  This is a set of issues that we can not remain silent about.  Even if we are not committed to social justice, we need to work on these barriers for the good of our profession.  You might begin by discussing social justice issues with your friends or colleagues who teach sociology or anthropology, quite a few of whom have a background in ‘social problems’.

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Culture of Evidence … Does it Exist? Could it Exist??

Perhaps you are like me … when the same phrase is used so extensively, I develop an allergic-type reaction to the phrase.  “Awesome” is such a phrase, though my fellow educators do not use that phrase nearly as much as our students.  However, we use ‘culture of evidence’, and I have surely developed a reaction to it.

Part of my reaction goes back to a prior phrase … “change the culture”, used quite a few years ago to describe the desire to alter other people’s beliefs as well as their behavior.  Education is based on a search for truth, which necessarily implies individual responsibility for such choices.  Since I don’t work for Buzz Feed nor Complete College America, my priority is on education in this classic sense.

The phrase “culture of evidence” continues to be used in education, directed at colleges in particular.  One part of this is a good thing, of course … encouraging the use of data to analyze problems.  However, that is not what the phrase means.  It’s not like people say “apply the scientific method to education”; I can get behind that, though we need to remember that a significant portion of our work will remain more artistic and intuitive than scientific.  [Take a look at https://www.innovativeeducators.org/products/assessing-summer-bridge-developing-a-culture-of-evidence-to-support-student-success for example.]

No, this ‘culture of evidence’ is not a support for the scientific method.  Instead, there are two primary components to the idea:

• Accountability
• Justification by data

Every job and profession comes with the needs for accountability; that’s fine, though this is the minor emphasis of ‘culture of evidence’.

The primary idea is the justification by data; take a look at the student affairs professional viewpoint (https://www.naspa.org/publications/books/building-a-culture-of-evidence-in-student-affairs-a-guide-for-leaders-and-p  ) and the Achieving The Dream perspective (http://achievingthedream.org/focus-areas/culture-of-evidence-inquiry  ).

All of this writing about “culture of evidence” suggests that the goal is to use statistical methodologies in support of institutional mission.  Gives it a scientific sound, but does it make any sense at all?

First of all, the classic definition of culture (as used in the phrase) speaks to shared patterns:

Culture: the set of shared attitudes, values, goals, and practices that characterizes an institution or organization  (Merriam-Webster online dictionary)

In an educational institution, how many members of the organization will be engaged with the ‘evidence’ as justification, and how are they involved?  The predominant role is one of data collection … providing organizational data points that somebody else will use to justify what the organization wants to justify.  How can we say ‘culture of evidence’ when the shared practice is recording data?  For most people, it’s just part of their job responsibilities … nothing more.

Secondly, what is this ‘evidence’?  There is an implication that there are measurements possible for all aspects of the institutional mission.  You’ve seen this — respected institutions are judged as ‘failures’ because the available measurements are negative.  I’m reminded of an old quote … the difference between the importance of measurements versus measuring the important.

There is also the problem of talking about ‘evidence’ without the use of statistical thinking or designs.  As statisticians, we know that ‘statistics’ is used to better understand problems and questions … but the outcome of statistics is frequently that we have more questions to consider.

No, I think this “culture of evidence” phrase describes both an impossible condition and a undesirable goal.  We can’t measure everything, and we can’t all be statisticians.  Nor should we want judgments about the quality of an institution to be reduced to summative measures of a limited set of variables covering a limited range of ‘outputs’ in education.

The ‘culture of evidence’ phrase, and it’s derivatives (‘evidentiary basis’, for example) are used to suggest a scientific practice without any commitment to the scientific method.  As normally practiced, ‘culture of evidence’ often conflicts with the scientific method (to support pre-determined answers or solutions) and has little to do with institutional culture.

Well, this is what happens when I have an allergic reaction to the written word … I have a need to write about it!

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Don’t Tell, Active Learning, and Other Mythologies about Learning Mathematics

For one of the projects I’m involved with, I was providing feedback on a section providing concepts and suggestions for the use of active learning in college mathematics classrooms.   One of the goals of this project is to connect practice (teaching) with research on learning … a very worthy goal.

This particular section included “quotes from Vygotsky” (Lem [or Lev] Vygotsky); see https://en.wikipedia.org/wiki/Lev_Vygotsky for some info on his life work.  I put the reference in quotes (‘quotes from …’) because none of the quotes were from Vygotsky himself.  Vygotsky wrote in Russian, of course, and few of us can read the Russian involved; most “quotes” credited to Vygotsky are actually from Cole’s book “Mind in Society” (https://books.google.pn/books/about/Mind_in_Society.html?id=RxjjUefze_oC).  That book was “edited” by scholars who had a particular educational philosophy in mind, and used Vygotsky as a source (both translated and paraphrased).

I talked about that history because Vygotsky was an influential early researcher … in human development.  As far as I know, the overwhelming portion of his research dealt with fairly young children (2 to 6 years).  That original research has since been cited in support of a constructivist philosophy of education, which places individual discovery at the center of learning.

Most of the research in learning mathematics is based on macro-treatment packages.  The research does not show whether this particular feature of learning results in better learning … the research looks at treatments that combine several (or dozens) of treatment variables.  Some “educologists” use this macro-treatment research to support very particular aspects of those treatments (like inquiry based learning [IBL]).

The “don’t tell” phrase in the title of this post comes from the original NCTM standards, which told us not to tell (ironic?) based on some macro-treatment research.  I’ve never seen any research at the micro-level showing that “telling” is a bad thing to do.  Some of us, however, have concluded that the best way to teach any college math course (developmental or college level) is with discovery learning in context with an avoidance of ‘telling’.

I want to highlight some micro-level results from research, but first an observation … in addition to the problems listed above about macro-treatment research, the Vygotsky research dealt with children learning about material for which they had little prior learning.  In our math classes, the majority of students have had some prior exposure to the concepts up to pre-calculus; when these students are placed in to an IBL situation, the first thing that will happen is that the process will activate their prior knowledge (both good and bad).  This existence of prior knowledge complicates our design of the learning process.

So, here are some observations I offer based on decades of reading research as close to the micro-treatment level as possible.

• Lecturing (un-interrupted talking by the instructor) can be effective as a component of learning.
• Small group processes can be effective as a component of learning.
• The effectiveness of either of those treatments depends upon the expertise and understanding of learning on the part of the teacher.
• Teachers need to deliberately seek to develop expertise and understanding about learning the mathematics in their courses.
• Students assume that their prior knowledge is sound and applies to everything.
• The  amount (frequency) of formative assessment should be directly proportional to the amount of inaccurate prior knowledge in the students.
• Feedback on student learning should not be instantaneous but timely, and qualitative feedback is just as important as information on accuracy.
• The primary determinant of learning is student effort in dealing with the material at the understanding levels (as opposed to memorizing).
• Repetition practice (blocked) is okay, though mixed practice (unblocked) is more effective.
• Classrooms are complicated social structures, and the teacher does not have influence over significant portions of those structures.

Those are the “Rotman Ten”, presented without their references to research.  Many of them are based on a sabbatical I took a few years ago, and much of this is based on extraction from multiple sources.  A few (like blocked and unblocked practice) have an extremely sound historical basis in micro-treatment research.  None of them suggest that the adoption of a particular teaching method will result in general improvements.

Hopefully, you see some wisdom in that “Ten List”, and perhaps some food for thought.

 
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Are Our Students Changing?

In most ways that matter, college mathematics has not changed in the past five decades.  Whether we are looking at developmental math, college algebra, or calculus, the mathematics has not changed … the changes have been in the mediating tools (computers), not in matters of substance.

Of course, that assessment is too harsh with respect to developmental mathematics.  At this writing, perhaps greater than 10% of students in remedial mathematics are enrolled in a modern course (Math Literacy, Foundations of Mathematical Reasoning, Quantway, or Statway).  However, those modern courses are too often implemented around the edges … only students needing non-STEM math courses are allowed to take the improved dev math course.

At the same time, our students have changed in basic ways.  One shift is the high school math they have experienced.  When our current remedial courses were designed, the median high school math experience ended in Algebra I.  Currently, the median experience includes Algebra II … and more, in many cases.

The lighter bars represent the graduating class of 2009; 76% of them completed Algebra 2 … and 35% completed something like pre-calculus in high school.  [This data is based on a detailed study of a sample of transcripts.]

Note that the high school courses have changed in basic ways, in response to the NCTM standards and even the Common Core State Standards.   Our college courses have held on to the abandoned property at the corner of 1965 and Elm Street.

Student intended majors have also shifted.  Using data from 4 year colleges, this is the pattern over an extended period.

[From “Insights and Recommendations”, MAA Calculus Project  http://www.maa.org/sites/default/files/pdf/cspcc/InsightsandRecommendations.pdf ]

That chart is not especially clear.  Notice the curve upward for one of the trends?  The steepest increase is in biological sciences, which used to be less than half the size of engineering majors … though now the bio sciences majors outnumber all other groups.  Our college math courses continue to emphasize the needs of 1965 engineering programs, with a fixation on ‘the calculus’.

I am not as concerned with whether students have ‘more skills’ now; they likely do, based on the long-term trends in national assessments.  However, talking about ‘more skills’ often limits our discussion to particular subsets of either high school or college mathematics.  My point is that we, in college mathematics, are significantly blinded by our viewpoint in the traditions of college mathematics … and that we would not notice changes in student mathematical knowledge because we are looking in the wrong places.

It’s time for ALL college students to experience a modernized mathematics curriculum, one which reflects student backgrounds and goals while providing content based on professional college standards.    Take a look at the guiding principles in the Common Vision document … http://www.maa.org/sites/default/files/pdf/common-vision/cv_white_paper.pdf

The status quo is not just unacceptable.  The status quo is a professional failure on our part.  We can fix that, and help both our students and society thrive.

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