Why We Will Stop Doing Pathways in Mathematics

Currently, and for the past few years, “pathways” has been a big thing in community college mathematics education. For students not needing calculus or similar courses, alternate paths have been established — with a focus on courses such as Statway™, Mathematical Literacy, and Foundations of Mathematical Reasoning. The fact that all three of those courses are very similar in content is not an accident, and the fact that the three organizations involved collaborated is a key reason for their success.

The reasoning behind the creation of pathways is essentially “give them what they need, not what they don’t need”. Students with a pre-calculus target are still placed into the old-fashioned developmental math courses, and students with other targets are placed into a ‘pathway’. All students are generally required to meet some arithmetic criteria before starting at the Math Literacy level or beginning algebra.

My own work has certainly played a role in this creation of pathways. However, that was not the intent of the efforts beginning this work. Neither do pathways have a good prognosis for long-term survival.

Let’s go through some of the reasons why “pathways” are not a long-term strategy.

Reason 1: Pathways are a dis-service to “STEM” (calculus-bound) students!
The original design of the major pathways courses (Quantway™, Math Literacy and Foundations of Mathematical Reasoning) was based on identifying what all students needed in college-level mathematics — statistics, quantitative reasoning, AND pre-calculus. These outcomes were then categorized in two clusters … those needed by ALL students became the core of the Math Literacy course, and those primarily needed by pre-calculus students became the core of Algebraic Literacy. [Algebraic Literacy also includes some outcomes needed for technical programs.]

In effect, “pathways” is preventing STEM (calculus-bound) students from getting the learning they need for success. We have accumulated data showing the the traditional developmental algebra courses do not add significant vale for these students when they take pre-calculus. In addition, we also know that the traditional courses were not designed for this purpose — they were designed to replicate the 9th to 11th grade content of a 1970’s high school.

Pathways create a better experience for non-STEM students, at the price of harming (relatively) those bound for pre-calculus.

Reason 2: Curricular complexity costs too much
One of the extreme cases I have seen is a college with SIX different courses at the Math Literacy level. Clearly, half of these are quite specialized for students in particular occupational programs. However, half were general in nature — a Math Literacy course, and two basic algebra courses.

Curricular complexity raises the cost of support functions at an institution, advising in particular. Few colleges can support this extra work in the long-term, even when the initial launch of those efforts is strongly supported by the then-current administration & governing board. As time goes on, the focus on advising slips … mistakes are made … and a later administration will question why things are so complicated.

This curricular complexity also raises costs within the mathematics department. More courses at the same level means more difficult scheduling, less predictable enrollments in each course, and a host of faculty coordination issues. Unless an institution has excess resources not needed for other situations, the mathematics department will realize in a few years that they can not support the complex curriculum.

Reason 3: Pathways allow the continuation of arithmetic courses at colleges
The presence of arithmetic courses at a college involves several problems and costs; the fact that our profession has not accepted these are overwhelming rationales for discontinuing arithmetic courses is a failure with moral and economic dimensions.

First of all, these extra courses at the developmental level are primarily taken by students of poverty and minorities. This is the moral dimension for us: these are the students coming to college to get out of poverty, who are then required to take one or more courses prior to the course that is a prerequisite to their required course. No possible benefit from learning arithmetic can justify this process; in fact, there is no evidence of any significant benefit for taking such arithmetic courses in college.

Secondly, arithmetic courses in a college create costs for the mathematics department. We often have a fairly discreet set of faculty (heavily adjunct), and these faculty are seldom qualified to teach a college mathematics course. In many colleges, the arithmetic courses are administered in a separate department. As faculty, we should want to design a curriculum that does not depend on a course at the arithmetic level.

Thirdly, the presence of arithmetic courses at a college will tend to perpetuate the outdated focus on procedures and answers. This conflicts with the design of Math Literacy, and impedes development of basic reasoning needed even in a traditional basic algebra course.

Reason 4: External Forces Will Continue to Push Us To Change
So far, the evaluation of ‘pathways’ has focused exclusively on the impact for students taking Math Literacy (or companion course) as preparation for statistics or quantitative reasoning courses — specifically, students who enroll in stat or QR after passing Math Literacy.

Curricular complexity means that there will be a less successful experience for students needing pre-calculus … by definition, because those students need two courses (beginning algebra, intermediate algebra) compared to the one & done of Math Lit. There are also operational causes for other ‘bad’ data to show up — students taking Math Literacy instead of the course they were supposed to take, for example.

In addition, we can predict that these change agents will critique our developmental math courses compared to modern standards (whether Common Core, or NCTM standards). We are not ready for this critique, and have no response for the results that are bound to come from such a critique — that developmental mathematics operates as if the year is still 1975, ignorant of the fundamental changes in our students’ experiences in K-12 mathematics.

In a way, I am reminded of something I learned at a conference session on graph theory and traffic design. Our intuition might say that it is better to have more options in street designs, where there are several north-south options and several east-west options. The traffic design results were the opposite … that the best throughput for a traffic system is the fewest possible streets.

A pathways curricular design presumes the presence of at least two courses at the same level in a sequence. This design is not particularly stable, as a system. In the long term, I think the system will collapse down to one of the options.

We need to be prepared for the demise of pathways so that we can maintain the improvements from those efforts. The danger is in assuming that both Math Literacy AND the old courses will ‘always’ be there. Within a few years, one of them will be gone. Which type of course do YOU want to survive?

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Algebraic Literacy course, Math curriculum in general, Mathematical Literacy Course | Jack Rotman | March 20, 2017 9:37 am

7 Comments

By schremmer, March 20, 2017 @ 10:01 am

Re. “Pathways create a better experience for non-STEM students, at the price of harming (relatively) those bound for pre-calculus.”

American “educators” seems always to have had a predilection for atomizing things. E.g. Skinner.

How about just developing the ability to make one’s case in more and more complicated situations (AKA understanding)? Then, as WE all did, the students will be able to realize the point at which to quit.

Any “path” is authoritarian and thus doomed from the outset.

The real problem is that, for a variety of reasons, adults do not all learn at the same speed. But experience has shown that neither “tracking” nor “pathing” is the answer. And experimenting on human beings is supposed to be criminal.
By Jack Rotman, March 22, 2017 @ 7:38 am

Re: “Path” is authoritarian and thus doomed … we’ve had paths in mathematics for a LONG time, and specific ones are doomed. I don’t think this is a one-to-one mapping (‘path’ and ‘doomed’).
Re: Experimenting on human beings is supposed to be criminal … We’d have to check with a lawyer type, but I think the law speaks to using untested treatments being used on humans which the treatment has a reasonable expectation of doing harm. We all ‘experiment’ on humans, when we try something ‘new’. I think educators sometimes violate the concept behind this type of law. However, I don’t see how the post being discussed has any connection to ‘experimenting’. In fact, one of the basic tenets is that our practice should align more with professional judgments about appropriate ‘treatments’ for humans as mathematics students.
By schremmer, April 1, 2017 @ 8:39 pm

1. And, has a path ever led anyone anywhere worthwhile? And I have been around for a long time. I still say that a path is authoritarian by definition and I note that you haven’t argued to the contrary.

2. What happened to the demands of the subject matter itself? The insistence on “teaching” has completely killed any understanding of mathematics by most two-year math teachers. If I want students to understand a piece of mathematics, the first thing I do is to analyze what that piece of mathematics rests on, what are its analogues elsewhere, how it is related to other pieces of mathematics, in other words, what drives it. Then, either the case I make is convincing or it isn’t but my delivery method doesn’t have much to do with it.

3. I wasn’t joking when I quipped about experimenting on live subjects: Any “teaching method” that assimilates human beings to computers and/or animals cannot possibly not harm them. And, when you look at what is being done, that is what is left when you have jettisoned the educando.
By Jack Rotman, April 3, 2017 @ 1:46 pm

1) I don’t enter into debates framed in a biased manner; ‘authoritarian’ is a very imprecise word, and stating that paths are authoritarian by definition leaves no entree for a reasonable discussion.
2) I like the idea of ‘the demands of the subject matter’ within the process of designing courses and the sequence. There are people who believe that we should cover only the mathematics students will actually use, or only the mathematics that we can show an application understandable to our students. I am not in either camp. My refrain has been “show them some useless and beautiful mathematics in every course!”
3) I knew you weren’t joking. Like many of our colleagues, I lose sleep worrying about whether my choices concerning the classroom will result in harm to some students. I would submit that all of us, including you, use untested treatments on students … and sometimes even expose them to treatments that lack a professional validity. As long as education is a process based on human interaction, I do not see a way to avoid ‘experimenting’. I think we need to get better at sharing evaluations and assessments along with the design of our ‘experiments’ so that we can develop a stronger professional basis for our work.
By schremmer, April 3, 2017 @ 10:31 pm

1) The Oxford does not seem to agree with you: “favoring or enforcing strict obedience to authority, esp. that of the government, at the expense of personal freedom” and that is exactly what I meant.

2) The utilitarian excuse has never worked. It used to be, not long ago, that we had to teach arithmetic in a certain way in order to check what the cashier at the supermarket was doing. Nobody did back then, nobody does it today. On the other hand, there is no such thing as useless mathematics. It all is in what you do with it. I “use” it as a simple area where students can learn to be logical.

3) That, too, would be worth discussing. In my case, by the way, I would agree that I push my students as hard as I can to stand on their own feet. And that could bring them one day on the wrong side of “authority”. But, to return the compliment, “experimenting” is a very imprecise word. Last, but not least, my stuff is completely open and freely available and arguable.
By Jack Rotman, April 6, 2017 @ 8:37 am

“Pathways” do not always remove elements of student choice (and frequently include a professional advice function).
Of course, there exist pieces of mathematics which are currently ‘useless’ — both in the global sense and the local sense. I was especially referring to the local sense (relative to a set of students in a given cousre).
By schremmer, April 6, 2017 @ 3:13 pm

Re. ““Pathways” do not always remove elements of student choice”

OK, I will go along with “not always”. But, based on a very long experience, only very reluctantly.

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