Data on Co-requisite Statistics (‘mainstreaming’)

Should students who appear to need beginning algebra be placed directly in a college statistics course?  For some people, this is no longer a question — they have concluded that the answer is an unqualified ‘yes’.  A recent research study appears to provide evidence; however, the study measured properties outside of what they intended and does not answer a basic question.

So, the study is “Should Students Assessed as Needing Remedial Mathematics Take College-Level Quantitative Courses Instead? A Randomized Controlled Trial” by Logue et al.  You can read they report at http://epa.sagepub.com/content/early/2016/05/24/0162373716649056.full.pdf

The design is reasonably good.  About 2000 students who had been placed into beginning algebra at a CUNY community college were invited to participate in the experiment.  Of those who agreed (about 900), participants were randomly assigned in to one of 3 treatments:

1. Elementary Algebra regular    39% passed
2. Elementary Algebra with weekly workshops   45% passed
3. College Statistics with weekly workshops    56% passed

At these colleges, the typical pass rate for elementary algebra was 37% while statistics had a normal pass rate of 69%.

The first question about this study should be … Why is the normal pass rate in elementary algebra so appallingly low?  I suspect that the CUNY community colleges are not isolated in having such a low pass rate, but that does not change the fact that the rate is unacceptable.

The second question about the study should be … Would we expect a strong connection between completing remediation (or not) with performance in elementary statistics?   The authors of this study make the following statement:

it has been proposed that students can pass college-level statistics more easily than remedial algebra because the former is less abstract and ses everyday examples

In other words, statistics is not abstract … not mathematics at the college level.  The fact that statistics focuses on ‘real world’ data is not the problem; the fact that the study of statistics does not involve properties and relationships within a mathematical system IS a problem.  I’ve written on that previously (see “Plus Four: The Role of Statistics in Mathematics Education at https://www.devmathrevival.net/?p=976)

The study uses ‘mainstreaming’ in their descriptions of the statistics sections in their experiment; I find that an interesting and perhaps better phrase than ‘co-requisite’.  It’s unlikely that the policy makers will move to a different phrase.

The authors of this study conclude that many students who place into elementary algebra could take college-level math (represented by statistics in their study) with additional support.  The problem is that they never dealt with the connection question:  How much algebra does a student need to know in order to succeed in basic statistics?  The analysis I am aware of is “not much”; in the Statway (™) program, most of the remediation is in the domains of numeracy and proportional reasoning … very limited algebra.

This is the basic problem posed in all of the ‘research’ on co-requisite remediation:  students are placed into low-algebra courses (statistics, liberal arts math), and … when they generally succeed .. the proclamation is the ‘co-requisite remediation works!’.  That’s not what is happening at all.  Mostly what the research is ‘proving’ is that those particular college ‘math’ courses had an inappropriate prerequisite of algebra (beginning or intermediate).

Part of our responsibility is to explain to non-math experts what the relationships are between various math courses, using language and concepts that they can understand while preserving fidelity with our own work.  We need to make sure that policy makers understand that it is not an issue of us ‘not wanting to change’ … the issue is that we have a different understanding of the problem and potential solutions.  In many colleges, the math department is already ahead of where the policy makers want us to ‘go’.

I encourage you to read this study thoroughly;  Because it using a ‘control’ and ‘random assignment’ design, this study is likely to become a star for policy makers.  We need to understand the study and provide a better interpretation.

 
Join Dev Math Revival on Facebook:

Dev Math: Where Dreams go to Thrive

In response to data showing the exponential attrition of long sequences of developmental mathematics courses, some people are using the quote “developmental mathematics is where dreams go to die”.  This phrase has been one of the most influential statements in our field over the past 5 years — not because it is true but because people (especially policy makers) believe that it is true.

This is a normal political strategy: frame an argument in a way that there is only one answer (the one that ‘you’ want).  I’ve seen leaders at my own college use this method, often successfully. … and I imagine that you’ve encountered it as well.  As teachers at heart, this style of communication is not natural for us; we respond by reasoned arguments and academic research with a goal of getting everybody to understand the problem.

The difficulty is that leaders who use the “where dreams go to die” phrase have little interest in understanding the problem.  Their goal is to remove developmental mathematics as a barrier to student success.  The next phrase after “where dreams go to die” is often “co-requisite remediation”, with claims that this solution is a proven success because of all of the data.  Of course, our view of this data is a bit more restrained than the leaders and policy makers; this is not a problem for them, as they have the answer in mind — all we have to do is agree with it.

We must do two basic things so that we can really help our students succeed:

1. Shorten and modernize our mathematics curriculum, both developmental and college level.
2. Consistently use our narrative:  “Developmental mathematics is where dreams go to thrive!”

Much of the material on this blog, as well as the wiki (dm-live.wikispaces.com)is meant to help faculty with the first goal.  The new courses, Mathematical Literacy and Algebraic Literacy, allow us to provide great preparation for college level courses within an efficient structure which minimizes exponential attrition.

“Developmental mathematics is where dreams go to thrive”:  We need to articulate this accurate view of our work, which is valid even within the old-fashioned traditional curriculum with too many courses.  I’ve posted about some of the research with a ‘thrive’ conclusion:

• The Case for Remediation  (https://www.devmathrevival.net/?p=2461)
• Research Trends in Developmental Mathematics  (https://www.devmathrevival.net/?p=1176)

Also, a great project at CUNY called “ASAP” gets a glowing external evaluation:  http://www.mdrc.org/project/evaluation-accelerated-study-associate-programs-asap-developmental-education-students#overview  The ASAP model is currently being validated at other institutions.  Please let me know of other research showing that dreams thrive in developmental mathematics.

We should add our own ‘thrive’ stories and data.  For example, at my institution, we had 6 students start in pre-algebra and the proceed up to Calculus I in a four year period … 5 of them passed Calculus I on their first attempt.  If we believe the ‘die’ narrative, you would expect zero or 1 of these to exist; I am sure that most institutions have similar results to mine where the data shows more of a ‘thrive’ result.

Our traditional courses must go; we must do the exciting work of renewing the curriculum based on modern thinking about mathematics combined with more sophisticated approaches to instruction and learning.

However, that work will generally be wasted unless we establish a ‘thrive’ attitude.    The two conditions existing together create a new system that serves students well.  Developmental mathematics is where all dreams go to thrive.

Join Dev Math Revival on Facebook:

Student Success & Retention: Key Ideas

I’m working on a project which involves a search for strong research articles and summaries, and that included some work on ‘retention in STEM’.  I have some references on that, later; however, I wanted to present some key ideas about how to keep students in class so they succeed and how to retain them across semesters.

Rather than look at certain teaching methods as ‘the answer’, let’s look at some key ideas with surface validity and examine their implications for teaching.

• Students need to be working with the content over an extended period in order to be successful.

We know that learning is the result of effort, usually intentional.  Attendance is easily measured, but is not sufficient by itself.  The class needs to establish environments where students want to work with the material, and we know that grades are insufficient motivation for many students.

• Non-trivial ‘success’ (positive feedback) based on effort is strong motivation for most people.

If success seems impossible regardless of effort, it is easy to see why students would stop working.  However, success regardless of effort is also likely to result in drastic reductions in effort.  As in most human endeavors, people need to see a connection between effort and reward.

• A teacher’s attitudes are more important than specific methods.

A few years ago, I was trying some very different things in a class; in fact, I was not very proficient with some key parts of that plan.  However, my students responding to my attitude more than those methods.  As one student said, “Mr. Rotman would not give up on me!”  An honest belief that almost all students are able to succeed is strong motivation.

We need to see our classes as a human system, a community with a shared purpose.  Most people need relationships with a purpose … connections that help them deal with challenges.  I am not trying to be a friend to my students, but we do form a community which can support all members.

• Every student contributes to the success of the class.

Not all students will pass a math class.  Some of those who do not pass are able to provide help to those who do pass.  This past semester, I had a student who did very poorly on written assessments who routinely helped the class understand concepts and procedures.  The contributions of a student are valued independently of their grade, and independently of any other measure or category (ethnicity, social standing, mastery of formal language, etc).

I have not mentioned any teaching methods; pedagogy does matter … but the pedagogy follows from other ideas.  I can not use the key ideas above if all I do is ‘lecture’ (though I do a fair amount of that).  My class must provide a variety of interactions in order for my attitudes to be clear … and for all students to have opportunities to contribute.  Establishing a community is social navigation, so students need times to talk with each other in smaller groups as well as the entire class.

Here are some good articles and summaries of retention in mathematics and other STEM fields; these studies focus on retention in programs as opposed to courses … though there are obvious connections between the two.

1. Teaching For Retention In Science, Engineering, and Math Disciplines: A Guide For Faculty http://www.crlt.umich.edu/op25
2. Increasing Persistence of College Students in STEM  http://www.fgcu.edu/STEM/files/Increasing_Persistence_of_College_Students_in_STEM.pdf
3. Retaining Students in Science,Technology, Engineering, and Mathematics (STEM) Majors
   http://mazur.harvard.edu/sentFiles/Mazur_399966.pdf
4. Should We Still be Talking About Leaving? A Comparative Examination of Social Inequality in Undergraduate Patterns of Switching Majors http://wcer-web.ad.education.wisc.edu/docs/working-papers/Working_Paper_No_2014_05.pdf
5. Gender and Belonging in Undergraduate Computer Science: A Comparative Case Study of Student Experiences in Gateway Courses http://wcer-web.ad.education.wisc.edu/docs/working-papers/Working_Paper_No_2016_02.pdf

Success and retention starts with us, and depends upon both our attitudes and our professional knowledge.

 Join Dev Math Revival on Facebook:

Using Mathematics: It’s Not Always About ME !!

In the traditional college mathematics curriculum, mathematics is used to solve problems which students do not care about.  Some reform curricula involve mathematics only for problems which most students care about.  Is one of these extremes naturally superior to the other?

Perhaps some researchers are already working on experiments to test that hypotheses.  My own conjecture on this might surprise a few people:

The net gain for students is higher in a curriculum which solves problems which students do not care about, compared to a curriculum focusing on problems students do care about.

The traditional curriculum normally focuses on individual students creating a symbolic statement (equation or function) for the problem, and then using this symbolic statement to determine all answers.  The reform curricula often engage students with informal group work around a context, looking for alternative strategies to find the answer; symbolic work comes later (often on a different class day).

Most reformers will assert that the group work in a context provides definite advantages in student learning.  The etymology of this assertion often has its roots in a constructivist point of view; the original researchers in this area were more interested in the social context and juvenile development.  We often conflate the issue by speaking of a ‘constructivist theory’ — there is no constructivist theory (since a theory provides predictions that can be tested with either positive or negative results); I’ve never seen research supporting constructivism in learning mathematics with adults.

However, there is a non-trivial advantage to the reform work with work on problems which students care about:

Students having the novel experience of working on problems they care about is exciting and motivating.

Seeing that process in class is exciting for instructors; sometimes, we become addicted to this experience to the point that we think students have to be dealt with in this manner all of the time.

Is a math class all about ME?? (a student)

Of course it isn’t.  Students are in college to either get an education or training (or both).  Getting an education is all about “not me” — understanding other points of view, analyzing problems, and solving … often with the person deliberately left out (objective point of view).  We might think that ‘training’ should deal with just problems which students care about … this view has two fatal flaws.  First, let’s assume that training exists to get a job (employment); how much of any job is something that the student personally cares about?  Sure, the student picks a program that they care about in general — but their job is going to involve a large portion of specifics which they don’t care about.

The second fatal flaw in the training point of view is ‘stability’ (or lack there of).  How many workers deal with the same types of problems for years at a time?  We are hearing from business and industry that they need a flexible work force — not one constrained by ‘it’s important to me’.

When I teach our traditional algebra courses (beginning & intermediate) I almost always make a statement such as the following:

Passing this math course means that you can apply mathematics to problems which you don’t care about, but you did so because somebody else said they were important.

The main downfall of the traditional curriculum is that it does not modify the pre-existing negative attitudes about mathematics [though I try 🙂 ],  Students have a negative attitude about mathematics and especially about ‘word problems.  Using problems which students care about can provide some scaffolding to get students out of their negative attitudes.

We can’t stop there.  For each problem students care about, we should have them deal with 2 or 3 which they don’t care about.  We need to make the connections between the processing done on the ‘care about’ problems and the symbolic tools of the trade (expressions; functions; known relationships [such as D=rt]).

At the developmental level, students will be proceeding to college courses.  College courses have a general expectation of dealing with symbolic statements.  Being able to determine solution to a specific problem is often a trivial exercise in itself.  Students need to see quantitative relationships and use appropriate symbolism to state that relationship.  We have no confidence that the majority of these situations will be innately important to the student; we do them a diservice to imply that the only mathematics they need is to find solutions to problems they care about.

We need to get rid of the traditional curriculum, recognizing that we achieved some good results within that.  We also need to moderate our use of ‘problems students care about’, and we need to make sure that we always keep the focus on the tools of the trade (relationships, symbolic statements, representations).

 
Join Dev Math Revival on Facebook: