Math Literacy without a teacher at the center

We are trying something different this fall.  As we’ve eliminated our basic algebra class in favor of Math Lit, we are adding a student-directed format. I’m doing two of these classes as part of my teaching load this semester, and I hope to post commentary each week.

What’s different?  Well, the big difference is that students in this “Math Lab” (student directed) format work on the material without me standing in front of them.  The online homework system has videos in support of the workbook, which focuses on context and concepts; students will be following these detailed assignments for each section, and they are encouraged to work with other students.  [Of course, the students also face the usual assignment of problems to be done after this studying.]  The instructor is available to help when needed.  The goal is to get every student actively engaged with the mathematics (no sleeping in class 🙂 ).

I am testing a conjecture that students can learn significant mathematics (concepts and reasoning)  mostly ‘on their own’, even at this level.  Sometimes, I think we place too high a value on what we say or do.  In my view, all learning is essentially “on my own”.  Help is often needed, but is not always best prior to the learner recognizing that there is a need.  It’s not that one way is better for all students at all times; it’s that a different approach enables more students to succeed — and that this sometimes leads to students understanding the learning process a little better.

We’ll see how it goes!

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Algebra Lament

Woe, my name is algebra.

I help people communicate about important relationships; people use me to predict future conditions.

Woe, my name is algebra.

I have been shunned and made fun of.  The fault is not mine; no, the fault is almost entirely that of ‘algebra courses’ taught without a focus on understanding, without attention to communication about the world.  The quadratic formula is not my fault!!

Woe, my name is algebra.

People think that I am another name for right answers to meaningless questions, that I am the effort to emulate some perfect series of steps to solve those meaningless questions.  I am not some worthless set of dance steps, steps being marketed in the absence of music or creativity.  Just because I can’t carry a tune doesn’t mean that I lack creativity!

Woe, my name is algebra.

I am the written language to communicate about matters quantitative.  Rejecting me is the rejection of the basic goals of education in the modern era.  For, how can people understand the world when all they can do is vaguely describe the qualitative traits … or calculate values for a few specific cases?  I may have faults, but ‘lack of clarity’ is not one of them!

Woe, my name is algebra.

My properties allow people to transition from a sum to a product, and to discover the almost magical explosion of options for working with expressions.  My properties allow people to express functions of variables in ways which uncover critical features of the relationships.  Instead of this beauty, most people are told that overly complicated trivial work is ‘algebra’.

Woe, my name is algebra.

I live in the core of science and society, despised solely for the company I’ve kept.  Did I have any say in that company?  Is it my fault that school mathematics is often taught in poor ways and with ‘outcomes’ which add no value for the learner?

Woe, my name is algebra.

My reputation has been ruined by others.  I am like a poor citizen who needs to be represented by public defenders who do not see my value.  The public defenders have good intentions about our students, but represent me in such a negative fashion that the majority of students conclude that I am worthless … and that they (the students) can never understand me.  My remote cousin with a similar name, ‘linear algebra’, has much better respect and cred.

Woe, my name is algebra.

I have been placed in two boxes.  One box is labeled “use only enough to get an answer”, perhaps to questions students might care about.  The other box is labeled “recipes for right answers to artificial questions”.  Does anybody put geometry in these boxes?  Does anybody put statistics in these boxes?  I can tell you that I seldom have any company in these boxes, and never for very long.  Let me out of the box!!

Woe, my name is algebra.

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Transitioning Learners to Calculus in Community Colleges (TLC3)

You might have heard of the MAA project “National Study of College Calculus”  (see ).  That work was very broad, as it studied calculus in all 3 settings (high school, community colleges, and universities).

A recent effort is focused on community colleges  with the title “Transitioning Learners to Calculus in Community Colleges”   (info at  )  Take a look at their web site!

One component of their research is an extensive survey being completed by administrators of mathematics at associate degree granting public community colleges, including the collection of outcomes data.  A focus is on “under represented minorities” (URM), which relates closely to a number of recent posts here (on equity in college mathematics).

I am expecting that the TLC3 data will show that very few community colleges are successful in getting significant numbers of “URM” students through calculus II (the target of this project).  The ‘outliers’, especially community colleges succeeding with numbers proportional to the local population of URM, will provide us with some ideas about what needs to change.

Further, I think the recent emphasis on ‘pathways’ has actually decreased our effectiveness at getting URM students through calculus; the primary assumption behind this (based on available data) is that minorities tend to come from under-performing K-12 systems which then results in larger portions placed in developmental mathematics.  The focus on pathways and ‘completion’ then results in more URM students being tracked into statistics or quantitative reasoning (QR) pathways — which do not prepare them for the calculus path.  [Note that the basic “New Life” curricular vision does not ‘track’ students; Math Literacy is part of the ‘STEM’ path. See ]

Some readers will respond with this thought:

Don’t you realize that the vast majority of students never intend to study calculus?

Of course I understand that; something like 80% of our remedial math students never even intend to take pre-calculus.  Nobody seems to worry about the implication of these trends.

Students are choosing (with encouragement from colleges) programs with lower probabilities of upward mobility.

The most common ‘major’ at my college is “general associates” degree.  Some of these students will transfer in order to work on a bachelor degree; most will not.  Most of the other common majors are health careers (a bit better choice) and a mix of business along with human services.  Upward mobility works when students get the education required for occupations with (1) predicted needs and (2) reasonable income levels.  Take a look at lists of jobs (such as the US News list at )  I do not expect 100% of our students to select a program requiring calculus, nor even 50%; I think the current rate (<20%) is artificially low … 30% to 40% would better reflect the occupational needs and opportunities.

Our colleges will not be successful in supporting our communities until URM students select programs for these jobs and then complete the programs (where URM students select and complete at the same rates as ‘majority’ students).  Quite a few of these ‘hot jobs’ require some calculus.  [Though I note that many of these programs are oriented towards the biological sciences, not the engineering that often drives the traditional calculus curriculum.]

I hope the TLC3 project produces some useful results; in other words, I hope that we pay attention to their results and take responsibility for correcting the inequities that may be highlighted.  We need to work with our colleges so that all societal groups select and achieve equally lofty academic goals.

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Segregation in College Mathematics: Corequisites! Pathways?

So, this post will mostly apply to those of us located in urban colleges (more than rural).  The idea is to remind of the societal costs of “separate and not equal”.

As a general statement, urban public schools have more challenges than suburban schools (and more than rural schools).  The role of poverty in this situation appears substantial, and the burden of this poverty tends to fall on ‘minority’ students more than ‘majority’.  In this post, I’m focusing on two categories — black/African American and white/Caucasian.

If you track the proportion of each course that is black, you are likely to get a chart like this one.  Note that “0” represents a college-level math course (most commonly ‘college algebra’ … more on that later).











This comes from a college where black students represent about 10% of the population; the college does not have a “-3 course” (pre-algebra).  The pattern in course enrollment is a similar pattern to the ‘placement levels’ of each group … the mean placement level for black students is about -1.4 compared to -0.6 for white students.  If all students are in a sequence (‘path’) that produces an equal chance of succeeding to all college mathematics, there is ‘equality’ (given the unequal starting points).

However, two current trends break that ‘equality’ and produce a system of separate and unequal.  In many co-requisite models, students who do not place into college mathematics are given only the option to take a non-STEM math course (statistics or quantitative reasoning aka ‘QR’).  In general, colleges using a co-requisite model find that their ‘support sections’ (ones taken by non-placing students) are predominantly minority.  I know some colleges have tried to use co-requisite models in college algebra (though more often ‘intermediate algebra’); these results are seldom published, and I think this is due to the much lower ‘results’ than statistics or QR.  The result of this type of system is an unequal result for minority students — they are discouraged (or even prevented) from pursuing a STEM or high-tech program.  A new segregation is being sold to colleges, in the name of ‘better results’; more on that later!

Some ‘pathways’ implementations also produce this same unequal pattern.  Those placing ‘lowest’ and ‘struggling students’ are strongly encouraged to take a stat or QR pathway program; some of these programs actually do allow students to select a STEM or high-tech program, but many do not.  The most common model is a side-by-side design … Math Literacy (or similar course) as an option to beginning algebra, where the Math Literacy course only leads to stat or QR.  In the K-12 world, this is called “Tracking”.  Pathways often create a segregated condition, due to the impacts of the lower-performing K-12 schools.

One argument is that the co-requisite models (and pathways) at least get students to complete a college math course, most commonly stat or QR.  The question remains … so WHAT?  There is an assumption that this stat/QR approach results in more students getting a degree (likely to be true).  But … what good is the degree?  Are there actually jobs for that program?

Obviously, the answer to that last question is ‘in some cases’.  In some regions, nursing requires either statistics or QR for their associate degrees, and the employment outlook is often good.  However, these health careers programs can be ‘selective admission’.  My experience has been that students accepted in to a nursing program tend to be ‘whiter’ than the college population in general … which likely goes back to the urban school system problems.  As a practical matter, I don’t think that a focus on stat or QR, in either co-requisite or pathways, results in ‘equal’.  We are creating separate in a deliberate strategy, without ensuring that they are equal.  [Of course, it’s also reasonable to say that we should avoid “separate” in the first place.]

Now, I’m not saying that co-requisite and pathways have no place in college mathematics.  The concern deals with the ‘scaling up’ that is often sought with them, as well as the target population.  Co-requisite remediation can be quite effective at the boundary … students who “just miss” qualifying for their college course (stat, QR, or college algebra); this system can be used to partially offset the negative impacts of lower-performing K-12 schools.  Pathways keep our focus on getting out of the way as much as possible … get them to their college course quickly; however, all pathways should preserve student options.  Any pathway that blocks student options is very likely to result in ‘unequal’ conditions.

Both of these efforts (co-requisites, pathways) remind me of the segregation caused by ‘school of choice’.  Do we really want to institutionalize segregation in these new ways?

I think the better response is to modernize the entire mathematics curriculum in colleges.  Start by replacing arithmetic and basic algebra courses with Math Literacy with an intentional design to provide students options at the next level.  Replace intermediate algebra with Algebraic Literacy with its intentional design to prepare students for modern college mathematics courses.  Replace college algebra with a course likewise designed to actually prepare students for calculus.  Reduce the calculus curriculum to fewer courses while incorporating more numeric methods (see “Common Vision”).

We do not need to create separate conditions for students, not nearly as much as we need to modernize our curriculum.

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