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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A recent effort is focused on community colleges with the title “Transitioning Learners to Calculus in Community Colleges” (info at http://occrl.illinois.edu/tlc3 ) 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 http://www.devmathrevival.net/?page_id=8 ]

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 http://money.usnews.com/careers/best-jobs/rankings/the-100-best-jobs ) 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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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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When the NCTM released it’s standards in 1989, people teaching developmental mathematics could immediately see the implications for our work. The conceptualization of the dev math curriculum was a one-to-one mapping to 9th to 11th grade mathematics (in ‘the old days’). The NCTM calls for increased attention and decreased attention had a lot of appeal.

During this same time period, the graphing calculator became a reasonable tool for mathematics classrooms; both TI and Casio had good machines, with some design elements driven by what math teachers wanted. [The HP calculators of the time were designed for engineer use, so they seldom had much traction in schools.] These graphing calculators provided a tool that would help teachers implement the NCTM standards.

In the Spring of 1992, Ed Laughbaum had an opinion piece published in the AMATYC journal (called “The AMATYC Review” at that time), with the title ** A Time for Change in Remedial Mathematics**. One of Ed’s main points was:

To change the current pattern of instruction, I propose that teaching methods be changed to support implementation of the graphing calculator into the remedial sequence.

Ed’s article is primarily an agreement with Lynn Arthur Steen that most mathematics remediation is a failure. You might notice that this is the same message being sent in the last 5 years by change agents such as Complete College America. Twenty-five years ago, we were saying it. What happened?

One thing that happened was that I wrote a response, which appeared in the AMATYC Review a year later, with the title “** Time, Indeed, for a Change in Developmental Mathematics**“. http://files.eric.ed.gov/fulltext/ED373817.pdf This was written just as I was about to become chair of the AMATYC Dev Math Committee (the first time, 1993 to 1997). My response was a little too soft in terms of critiquing our work at the time; I regret that now.

This response was the first time I used the phrase “mathematical literacy”, written in the general sense (not course specific). Sadly, one of the things I said was that graphing calculators should not be used in courses at the beginning algebra level. My position on this changed over the subsequent five years, but my comments resulted in a number of AMATYC members thanking me … they felt supported in doing their traditional courses (which was not my intent).

My conclusion in that article had this:

The basic issue facing mathematics educators today is how to integrate the various forces attempting to drive our mathematics curriculum. The solution involves dialogue and consensus building. Institutions such as AMATYC provide a needed forum and structure for this work. As we work together, our theories and standards will converge, resulting in changes in our curriculum which will certainly integrate technology in many ways.

It’s clear that this change process did not occur … in spite of the NCTM standards resonating with our own interests as shown in the first AMATYC Standards (“Crossroads”). What happened?

Our collective resistance to the graphing calculator is the primary reason that we did not make any progress when there was another opportunity. Partially, this was due to the overwhelming resistance to calculators at the college math level (college algebra, pre-calculus) … and much of this still exists today. The fact that students could not use numeric methods in the next course meant that our use of those methods in developmental mathematics was a possible risk to our students.

In some ways, the content of our courses became ‘locked in’ by 1990. We resisted professional calls for numeric methods, we collectively ignored the NCTM standards; we even ignored most of our own AMATYC standards (which were being written during the early 1990s). From 1995 to 2010, fewer natural opportunities for change would arise. Our default support for an antiquated curriculum is exactly why dev math was an easy target for policy makers and change agents in 2012 … 20 years after the early 1990s.

We are facing a similar call for change today. The Common Vision suggests that our courses emphasize numeric methods alongside symbolic ones, as well as suggesting that our teaching methods change. This is the danger of ‘pathways’ … that only non-STEM students get a modern course with numeric & symbolic methods; STEM students are required to survive a series of courses overly focused on symbolic methods with little emphasis on reasoning, and far too little emphasis on connections between concepts. “Right Answer” still is the goal in these courses, which is the wrong answer for students.

I am hopeful that we individually and collectively will respond today with “let us build better courses for ALL students”. No student should be required to take a course known to be defective. In particular, I am hoping that AMATYC will develop a project that links the Math Intensive committee with the New Life Project to work on revitalizing the courses which follow developmental mathematics.

If our profession fails to seize the current opportunity for creating our own modern curriculum, external change agents will control the primary playing field: the initial college level math course(s) such as college algebra, pre-calculus, and similar courses. These courses suffer the same defects as the traditional developmental mathematics curriculum — antiquated topics delivered inefficiently and with harm to the overwhelming majority of college students who will never take a calculus course. [Our calculus courses are just as antiquated and inefficient; external change agents just don’t care about calculus very much. They should!]

We have a problem NOW (2017) because we did not have sufficient motivation to make systemic changes 25 years ago. The profession let a few visionaries create boutique programs which were locally successful but totally isolated from the mainstream of our work. Today’s boutique program is “Pathways”. We need systemic change to create modern mathematics courses for ALL students. Do we really think that non-STEM students deserve a modern course while STEM students slog thru disfunctional artifacts clustered as pre-calculus & calculus courses?

It really is “Time for a Change” … not just in remedial mathematics, but in all college mathematics.

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That post quickly led to the natural question: What about books for courses AFTER math literacy? (Thanks, Eric!)

Ideally, we would have 3 books for “Algebraic Literacy” … a course designed to replace intermediate algebra. However, much of the Math Literacy work is still stuck in a pathways approach, where Math Literacy is only used for “non-STEM” students. I don’t think this pathways emphasis can survive that long (see http://www.devmathrevival.net/?p=2779) In this period, however, most uses of math literacy courses is as an alternative to beginning algebra for those who “don’t need algebra” (as if that was possible or desirable).

To review, here is the New Life vision of basic mathematics courses at colleges & universities:

So far, the reform work in our college curriculum has been limited, with the most systemic work being done at the Math Literacy level. Many people are holding off on Algebraic Literacy until there is a textbook, and publishers are interested in creating those texts. We need to achieve a higher level of interest before those “AL” books will be developed and published. Authors want to write them, publishers are willing to support them … IF the market interest is there. Lesson:

Always tell publishers that you want to see textbooks for Algebraic Literacy, and that Algebraic Literacy is not an intermediate algebra with a new ‘cover’.

There are colleges who are implementing Math Literacy for all students, replacing beginning algebra in their curriculum (mine, for example). Most often, this means the use of a typical intermediate algebra book for the course following math literacy … a bit like getting to use an iPhone 7 one semester and then being handed a rotary phone the next semester. If only there were better options!! [Some folks use the “Math in Action” materials, which are not Algebraic Literacy at all … they just provide great context and applications.]

Both publishers with good Math Literacy texts (McGraw Hill, Pearson) have considered algebraic literacy books; they may even have them ‘under contract’ (I would not necessarily know about that). Keep telling them that you really want an algebraic literacy book, and they will develop them.

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First, I’ve got to point out that some books are being marketed for “Pathways” with very little change in content. Math Literacy is not just a name for a modified old course; Math Literacy is the first new course in developmental mathematics with content drawn from modern standards, with an emphasis on reasoning and communication. This comment applies to books from most major publishers; in particular, Cengage and Hawkes do not have a Math Lit textbook (though they do have books for pathways).

I recognize 3 textbooks available which faithfully implement the Math Literacy learning outcomes (whether as Math Lit, Quantwayâ„˘, or Foundations of Mathematical Reasoning). Quantway courses run differently from the others in the sense that colleges join the collaborative, and use shared materials & online system; colleges not in the collaborative do not have access to those same materials. However, the Quantway materials were the basis for the Foundations of Mathematical Reasoning (FMR) from the Dana Center.

**Foundations of Mathematical Reasoning**(FMR); Pearson

https://www.pearsonhighered.com/product/Dana-Center-Student-In-Class-Notebook-for-Foundations-of-Mathematical-Reasoning/9780134467481.html**Math Lit**(Almy/Foes); Pearson

https://www.pearsonhighered.com/product/Almy-Math-Lit/9780321818454.html**Pathways to Math Literacy**(Sobecki/Mercer); McGraw Hill

http://www.mheducation.com/highered/product/1259278751.html

If you want the ‘most different’ materials, you’d choose the FMR materials. There is not really a ‘textbook’ with FMR; the lessons are a series of contexts and problems with the mathematics tied in to those situations. The core of FMR is the classroom work (highly group based). The lessons are presented in ’25-minute’ pieces, and the instructor has a set of supportive materials including suggestions for processes. A number of colleges (mostly in Texas) are using the FMR materials as part of a larger project; other colleges adopt them as they would any textbook. (Again, the Quantway materials are very similar to FMR but only used ‘in the network’.)

The Almy/Foes Math Lit shares some of those properties. The lessons are highly group based, focused on contexts and problems; instructors have support materials. The Almy/Foes structure is not as finely grained as FMR, which I think fits what most faculty prefer (though I have been known to be wrong … on occasion!). This was the “original” math literacy text, written before most of us thought about offering the course. Unlike the FMR materials, the Almy/Foes text is definitely geared towards the non-STEM pathway. If you are pretty sure that you can support a discreet path for non-STEM, this text is a good alternative.

The Sobecki/Mercer “Pathways to Math Literacy” combines some of those properties within a slightly more traditional structure. The lessons employ significant group work, but also significant whole-class work. This book includes slightly more mathematical content, and a little less divergent lesson work (where students might create 4 different methods to ‘solve’ a problem). Instead, the Sobecki/Mercer text tends to keep a goal or outcome in mind. If your dev math program is highly adjunct-based (as mine is), this text probably is a good choice. As does FMR, the text does not assume that all students are non-STEM — though the contexts are generally non-STEM.

Each of these sets of materials has advantages, and they all deliver the core learning outcomes of Math Literacy. All 3 are doing well in the market, from what I can tell.

If you have specific questions about a specific set of materials, I can try to help get an answer.

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Today, I wanted to follow that up with some similar data on the role of gender (technically, ‘sex’) in the outcomes of students, accounting for poverty and race. This seems especially important given the national attention to “men of color” (http://cceal.org/about-cceal/). As a social justice issue, I agree that this focus on MEN of color is important given the unequal incarceration rates.

However, this is what I see in our data for all Pell eligible students in math courses:

As for the prior chart, this reflects data over a 6 year period … which means that the ‘n’ values for each group are large (up to 10000 for ‘white’). Given those sample sizes, almost any difference in proportions is statistically significant. All three comparisons ‘point’ in the same direction — females have higher outcomes than males, within each racial group.

However, notice that the ‘WOMEN” of color have lower outcomes than men “without color” (aka ‘white’). A focus on men of color, within mathematics education, is not justified by this data. Here is what I see …

- There is a ‘race thing’ … unequal outcomes for blacks and hispanics, compared to white students.

[This pattern survives any disaggragation by other factors, such as different courses and indicators of preparation.] - There is a ‘sex thing’ … unequal outcomes for men, compared to women.

[This difference is smaller, and does NOT survive some disaggregations.]

There is a large difference in ‘effect size’ for these; the black ‘gap’ in outcomes approaches 20 percentage points (about 2/3 of the white pass rate), while the ‘male’ gap is 5 percentage points or less (90% to 96% of the female pass rate). In other words, it does not help to be a woman of color; it just hurts less than being a man of color.

I think that pattern fits the social context in the United States. The trappings of discrimination have been fashioned in to something that looks less disturbing, without addressing the underlying problems. We have actually retreated in this work, from the period of 40 to 50 years ago; there was a time when college financial aid was deliberately constructed as a tool in this work, and this was effective from the information I have seen. Current college policies combined with the non-supportive financial aid system results in equity gaps for PEOPLE of color.

Most of us have a small role in this work, but this does not mean the role is unimportant. If your department and institution are critiquing your impact on people of color, terrific; I hope we have an opportunity to share ideas on solutions. If your department or institution are not deeply involved in this work, why not? We have both the professional and moral responsibility to consider the differential impact of our work, including unintended consequences.

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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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It might be difficult to believe that there was a time before people talked about standards. The first great effort on standards came from NCTM in 1989 (“Curriculum and Evaluation Standards”, summarized at http://www.mathcurriculumcenter.org/PDFS/CCM/summaries/standards_summary.pdf ) which was a follow up to “An Agenda for Action (http://www.nctm.org/Standards-and-Positions/More-NCTM-Standards/An-Agenda-for-Action-(1980s)/ ). Whether these standards were even discussed at a college was more a coincidence of faculty connections than any organizational cooperation.

The period we are talking about preceded these initial standards. However, collaborative activity across institutions and regions was increasing in the latter 1980s. It is not a coincidence that my first AMATYC conference was in 1987 (“Going to Kansas City” theme song). We, as a profession, were looking for stability and support. The AMATYC Developmental Mathematics Committee (DMC) had several active subcommittees on issues such as “Student Learning Problems” and “Minimal Competencies”, as well as “Handheld Calculators”. I served as the editor of the DMC Newsletter for several years, a newsletter produced by printing stuff on a dot-matrix printer and physically cutting & pasting to make the pages of the newsletter. Ah, for the good old days …

We entered this period having missed the great opportunity, which naturally led to the primary outcome of the time:

The existing pre-college and college curriculum was normalized and accepted as a “good thing”, or at least “the way it should be”.

Some of us knew that NCTM was working on their standards, though none of us were involved in any way (no community college faculty served on a team or as a writer). In this period prior to the first AMATYC work on standards, we explicitly supported the grade-course structure (from K-12) which had been our inheritance. When a problem was identified (such as low pass rates), our response was to double-down … we created split courses for beginning algebra, and split courses for intermediate algebra; we often added a basic math course separate from a pre-algebra course. This double-down trend resulted in horrific sequences for students. We often went from our old sequence of 3 courses to a system where some students took 9 terms or semesters of developmental mathematics. [These structures still exist, relatively intact, in some places … parts of California, for example.]

Another aspect of the ‘double-down’ response was an attempt to identify THE list of critical learning outcomes. The DMC “MinComps” (minimal competency) subcommittee worked by snail mail and annual meetings to identify the arithmetic skills that all students should possess. Although MinComps never achieved their goal of writing a position statement on this content, the group did have an impact on our courses and the textbooks used in those courses.

Never was our response to ask “What are the mathematical abilities which students need for college success and life success?” The response was ‘what outcomes should be in this course?’. There was a trend, especially during this time period, to have our textbooks converge to a common list of content topics and outcomes (very skill based). Workbooks were very popular in this period, often consisting of ‘name topic, state property, show example, give practice’. In some ways, the ‘programmed learning’ textbooks of a decade earlier were more supportive of student learning.

The content became the thing. When students did not succeed, we looked to identify a student learning problem. In some cases, we even tried to provide support to ‘overcome’ a student learning problem. Our efforts were directed at improving course pass rates … at the expense, frequently, of the sequence pass rate. Our friend ‘exponential attrition’ is very powerful … a sequence of 5 courses will always be worse than a sequence of 3 courses, unless we can realize close a 50% improvement in course pass rate. Going from 45% pass in all 3 courses to 67% pass rate in all 5 courses is not likely; if it has ever happened, you can be pretty sure that this improvement was temporary.

Since we were relatively ignorant of the sequence and attrition issues, we were pleased with longer sequences which reinforced the defective content we had inherited and then had normalized.

My younger colleagues will have a difficult time understanding the technological context for this work. When we had the “hand held calculator” subcommittee in the DMC, we were not talking about graphing calculators — the work was focused on basic calculators, with a recognition that scientific calculators were available. Our offices had computers (very slow) with no networking; I had a dial-up modem to connect to a nearby mainframe, but that was quite unusual. We often hand-wrote our tests (and it’s a miracle that any student could pass such tests!). Later in this period, we had the initial efforts to provide students with access to computers — often done in a separate computer classroom, not related to any math course. Homework, like our tests, were a hand written affair.

This technology did not cause any change in the content or delivery of instruction. If anything, the status of the technology was part of the set of forces which led to the normalization of the defective content in college mathematics. Our motto seemed to be “We don’t know if this stuff is really worth much, but at least we generally agree that it is what we should be doing because we are all doing roughly the same thing.” Many math faculty today continue to look at curriculum primarily from this lens.

The trend in this period to normalize the defective content contributed to our response in the next period (the early 1990s) when the NCTM standards suggested that such content was, indeed, defective. We had set up conditions which made us essentially immune to the valid critiques. That is where the next post will look at our history.

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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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