Dr. Paul Nolting's Academic Success Press Blog: A Publication Dedicated to Math Success
Dr. Paul Nolting's Academic Success Press Blog: A Publication Dedicated to Math Success
Hello readers! We are hard at work transcribing and editing a number of exciting interviews for the upcoming weeks (including a few with future AMATYC speakers)!
In the meantime, we thought we'd link to a NY Times article from 2014, which describes in detail America's history with math reform at the grade school level. While the whole article is worth reading, by far the most provocative aspect of the piece is its assertion that American educators are incredibly skilled at deducing problems in pedagogy, even better at coming up with possible solutions for these problems, yet entirely inadequate at actually applying these solutions. Whether one agrees with this core argument or not, the article is a fascinating look at America's decades-long journey to improve math performance. Please read, discuss, and come back Monday for another featured post!
"Why Do Americans Stink at Math?"
ASP Blog: To get us started, can you briefly describe your background in helping colleges and universities increase success in math?
Getz: I taught high school and college math for twenty years before coming to the Dana Center. At the college level, I was the department chair of a department that was sort of unusual because it involved developmental and gateway math courses. We didn’t teach the higher levels of math, but we were in charge of all of the students coming in in their first math courses. In that role, our department was actually created to address high failure rates, and we were able to significantly increase student success. We implemented a lot of the practices that are now common at the Dana Center: integrated support, active learning in the classroom, revamping content and curriculum, etc. I’ve been at the Dana Center for a little over four years now, and I started working with the Carnegie Foundation to develop the curriculum for Pathways (of which I am the main author). After we completed that work, we started strategizing how to promote the same principles that we worked with at Carnegie around Math Pathways, and we created the new Mathways project to implement them in a systemic way from the state level down to the classroom. Now, I’m working a little more at the national level, along with multiple states.
ASP Blog: Can you describe for me the basic mission statement for the Dana Center?
Getz: Sure! We are an organized research center at the University of Texas at Austin, and our mission is to increase equity and access to education, primarily through math and science. We work with K-12 and higher education, and we work across the country. The center is actually much bigger than the higher education world. Sometimes people think if we are talking about higher education that there is just this small team at the Dana Center, but the organization itself is actually fairly large, and it is all under the direction of Uri Treisman, who is a very well-known and well-recognized figure in math education.
ASP Blog: What is your stance on the math redesign movement? In your eyes, what is it meant to accomplish, particularly for developmental education?
Getz: We really stress that the issue is much more systemic than just changing developmental education. The bigger issue is that we know that the completion of college-level math is a major obstacle for many students—when I say many, I mean hundreds of thousands of students, particularly at the community college level, but also at the four-year level. Really, this movement started with a focus on developmental education, because we started seeing data come out that tracked student progression across courses, and there was a raising of consciousness about the fact that very few students starting in developmental mathematics were able to get through a college-level math course.
[Now] we are seeing data that shows that even students who come in college-ready often don’t complete college-level math courses. There are very high failure rates in many college-level courses as well as at the Gateway level. As you get into more advanced students, the success rates increase. So we really try to emphasize that this work needs to look at entire math pathways. You can’t just separate one course out or two courses out, or a portion of that pathway, you really need to look at the whole pathway.
We don’t really talk about redesigning courses. We talk about redesigning pathways. We do this because it affects not just the system of an institution but entire states. It varies, of course, from state to state, so there are often state policies that become obstacles to implementing math pathways. There are issues around transfer and applicability. So, there is this systemic work that sits at the very core of math pathways.
ASP Blog: So are students today—particularly those who might not take on math-heavy majors—struggling more than similar students in the recent past? Or is it a matter of this problem has always been there, but we just haven’t been paying attention to it?
Getz: A little bit of both. It depends on how far back you want to go. But if you look historically at what has happened with requirements for mathematics in colleges, even a decade ago, it wasn’t all that uncommon for someone to be able to get a college degree without a college-level math course. There has been an increased emphasis on requiring everyone to take a college-level math course. As a math teacher, I think this is a good thing. I’m not suggesting that we pull this back. The problem was, however, that the math courses we had in place were all focused on getting students through calculus. I haven’t looked at historical data on success rates in this regard—but we do know that more students over the last couple of decades have had to take college-level math. So it makes sense that now that we have a more diverse population—diverse in the sense that they have very different educational goals—and that we have put them all into one slot, it is not surprising that this slot doesn’t necessarily meet all of their needs.
So one of the things that I always stress is that obviously student success is the big issue, and we always want to look at data, but from a math faculty perspective, it is also about students having the opportunity to learn math that will be very valuable to them. For the math faculty, it breaks my heart to see students learning algebraic manipulation skills that they are never going to use, when they could be learning really valuable mathematic concepts and skills that they really will use, and that will really improve their understanding of their world and help them become better consumers and better workers—help them better understand data-laden information that we receive all the time through work. So, I do like to stress both sides to this, because sometimes I worry a little bit about firm strategies that are just focused on getting students through math. What is really important is that these students learn something that is actually of value to them.
ASP Blog: What do you make of accelerated math courses? Paul often talks about how modern students have to learn new types of learning skills in order to keep up with faster, computer-based courses. Do you believe students must change their behavior to accommodate these courses?
Getz: It is an interesting idea that we would want to change human behavior to match the system we put into place. I understand what Paul is saying in that in some places this movement to do modularization might require changes in how human beings act and learn.
I find that questionable. I do believe what we can do is to support students to be more intentional and independent learners. I think that is a very important thing to do, whether they are in a classroom or sitting in front of a computer. But, I think what we really need to be careful about is understanding that there is isn’t a single strategy that will fit all students. Modularization and self-paced programs definitely benefit some students—students who are more motivated and more mature often do well in these programs. But a lot of places are backing off of modularization because they are realizing that all students don’t do well in the system. Research shows that those students who are at the greatest risk—those students who come in the least prepared, the least connected to their institutions—need strong engagement to their institution, to their faculty, to their peers. So, if those students are being put into individualized programs, then we need to pay real attention to the needs that these students still have. We can’t just say that we can change these students so that they no longer have these needs. I know that Paul has worked on how to help colleges figure out how to do this. How do you get these students to engage with their institution, faculty, peers, when they are sat alone in front of a computer? So those are the big issues here. I don’t think we can expect students to suddenly behave differently than human beings have ever behaved in the past. What we can do is build structures that build in the types of support that we know will help people become better learners.
ASP Blog: You have already described the Dana Center a little bit in earlier responses, but I am curious how, exactly, your organization is engaging in math redesigns? You mentioned earlier that you are focused more on systemic issues than just issues with individual courses. Can you talk a little bit more about that?
Getz: We are working at the state level to address policy—to identify and address policy obstacles. We try to empower faculty to have a voice in that—helping to set the vision for what Math Pathways should be in a state. We have a variety of students we do this through. And then, we work across two and four year institutions to identify and address obstacles in transfer and applicability. We work at the institutional level by providing tools and services that help colleges see what it will take to implement Math Pathways in a systemic way.
You may be picking up that I use the word systemic, systemic, systemic. Where we see people fail is when they think they can go to math faculty and ask them to simply implement a redesigned course. This doesn’t get deep enough. It is like tweaking around the edges. At the classroom level, we have developed curriculum for courses that are based upon this Pathways model, and also support major courses that are designed to be used in a classroom that are based around active learning pedagogy to increase engagement with students. Then we provide training both directly related to teaching these courses, and generally around active learning pedagogy.
ASP Blog: Can you explain the Pathways program, maybe in simple terms—what it entails, and what you think it can accomplish?
Getz: The model is based on four principles. The first principle is that all students should have access to pathways that are aligned to their program of study. The second is that these pathways should be accelerated so that most students can complete a college-level course in one year or less. The third is that there should be strategic integration in alignment with student success strategies in math courses. And the fourth is to use evidence-based curriculum, design, and pedagogy.
For the courses themselves, we develop tools and applications for institutions to apply these principles. So we offer a toolkit from which a college can choose which resources they use. Our course materials are part of the resources. The reason I have to make this distinction is because in Texas they have a statewide implementation of the NMP principles—that does not mean that every college is teaching the courses we developed. Some are doing their own versions; some are using other materials from other sources. So we talk about this as “coherence to principles without uniformity in practice.”
In the courses we design, there are three pathways: quantitative reasoning, statistics, and then what we call the STEM-Prep pathway, which is the pathway that leads to calculus. Within these pathways, there are individual courses. The reason we chose these pathways is that they seem to be the broadest paths that meet the greatest needs. Some colleges have a need for a technical math pathway. In some systems, we see people have a different pathway for business. So it is not like we are saying that these are the only pathways that ever make sense: it is just that these three are the ones that we created courses around. We see it as a starting point for discussion.
We think it is really important that colleges and systems evaluate what pathways they need based upon their student needs, which is kind of getting down to what programs do you offer, which pathways match those programs the best. One thing that can happen, and is of a little concern, is that you don’t want too many pathways. The other side of this, is the growing understanding—which comes out of behavioral economics—that too many choices is not good. People have less satisfaction in general when they have too many choices. You may have heard this in talk about 401k plans. When speaking to colleges about guided pathways, it is best to have two to five. This is a good range of choices that are broad and general so that students do not have to make decisions based solely on their major, but rather the selection of programs they are interested in.
One of the concerns about pathways is that students often change their minds. They move between majors. So if you make them make a choice too early, they might lose credit. What we are seeing is that students can generally make a choice like, “You know, I’m kind of interesting in social sciences or liberal arts” versus “I’m interested in a hard science field.” People don’t often bounce around between these types of choices. So by setting up guided pathways, you can have a small number of choices that make it easier for students to navigate.
ASP Blog: There seems to be a fine line here: you want students to have options, but you can’t inundate them with choices either. It sounds like you are really trying to strike a balance.
Getz: Right. Another thing that is important here is “opt-in” and “opt-out.” By having guided pathways, it establishes a default. This helps students say: “I walked in, I don’t know much about college—my family has never been in college—and I talked to an advisor, and I defined my general interests, and he or she helped me by giving me this default policy.” But you always want an opt-out policy. If students have a good reason to make a change, they should have the flexibility to envision a different pathway for themselves. We don’t want students to get into pathways that are so rigid that they can never get out—but you want something that is well-defined and easy to navigate. Then if students need to opt-out and can make a good case for it, they have that opportunity.
ASP Blog: So where do you see the redesign movement ultimately going?
Getz: I see that there is a growing trend to accept math pathways. It is very interesting to me how when I speak publicly, the difference in questions I get now versus four years ago. There is real legitimization happening in the math education world as national leadership and professional associations continue to come together. We are definitely seeing that leadership from math professionals are advocating and supporting math pathways. That is huge because there was a concern from math faculty about increasing standards and rigor. It has just taken awhile to come to accept that, no, we are not lowering standards—we are creating greater opportunities for students to learn meaningful mathematics. So I think this trend is going to keep moving forward. I think we are going to continue to see a variety of strategies regarding implementation. I think we will continue to see things like modularization and distance learning, and there will continue to be strong classroom-based programs.
That’s the good side. I’ll also tell you the bad side. We have a real trend toward more courses being taught by adjuncts, who tend to be underpaid and underprepared. It is certainly my hope that we will reverse that trend in the sense that at least if there are adjuncts, they are getting better support and that they have access to more training and have more of a voice in the courses that they teach. Given the economics of education, I’m not sure this will just go away. So I think we need to think about how to support faculty who are in that position, who are hired two days before classes start. We really have to think deeply about what help these faculty members need to be successful with students.
And that just about wraps it up! Please check back Wednesday for a new post.
Hello all! Today, we thought we'd do a little housekeeping by letting you know what to expect in terms of upcoming blog posts!
First, we will post our interview with Amy Getz from the Dana Center on Monday, Oct. 26. Our conversation revolves around various pathways for modern math students and provides a great summary of the Dana Center's foundational ethos.
In the coming weeks, we will also feature an interview with Rachel Beattie from the Carnegie Foundation, as well as a few from instructors who are dealing with math redesigns on the front lines of the movement. For more information about upcoming interviews, please see the "Upcoming Features" section on the right-hand side of the blog.
We also wanted to take this opportunity to provide a link to a USA Today article, which, while published in 2013, provides a perfect example of what developmental educators remain up against. The article demonstrates the basic narrative that continues to dominate the national discourse on developmental education—a notion of particular note as it is very much in line with the views of various national organizations, including many that are in charge of setting nation-wide policy. Click on the link below to find out more:
Of the many topics Paul regularly covers in his books and speeches, one of the most prominent involves early childhood experiences and their lifelong affect on students' attitudes toward math. When instructors, teachers, and Supplemental Instruction staff work with an anxious student to reduce or assuage his or her stress, they are in essence dealing with a lifetime of conditioning and the involuntary responses it causes. These responses not only affect mood, but also basic brain function.
With all of this in mind, we recently stumbled upon a great article on this topic in the Journal of Cognition and Development. Written by Gunderson, Levine and Block, "Math Anxiety, Working Memory and Math Achievement in Early Elementary School" does a magnificent job summarizing both the chemical and attitudinal responses elementary school students often have toward math.
The article explores the relationship between math anxiety and working memory in elementary school students. Though it focuses on young children, the implications of the article’s findings are highly relevant to college math departments, as they demonstrate not only the origins of students’ math anxiety, but also what type of student, exactly, tends to struggle with the issue. Intriguingly, the study shows that students with the highest levels of working memory suffered more acutely from math anxiety than anxious students with lower levels of working memory, as these students “tend to rely on WM-intensive solution strategies and these strategies are likely disrupted when WM capacity is co-opted by math anxiety.”
For their study, the authors of the article administered math achievement and working memory assessments to 154 first- and second-grade students. Days later, the authors used a new scale they’d developed to assess the same students’ anxiety levels. In the end, the authors found that “children who are higher in WM may be most susceptible to the deleterious effects of math anxiety.” This is particularly worrisome, they argue, because “these students arguably have the greatest potential for high achievement in math.” Anxiety sometimes causes these students to openly avoid taking math courses, which not only affects their own respective futures, but also saps college math departments of capable students who might boost university-wide performance statistics.
For more information, please seek out:
Ramirez, G. Gunderson, E., Levine, S., Beilock, S.L. “Math Anxiety, Working Memory and Math Achievement in Early Elementary School.” Journal of Cognition and Development. January, 2012.
Hello! Happy Wednesday! As our regular readers know, we typically use this day's post to bring attention to various research and field studies published in major developmental learning journals roughly during the past five years. Today, we have chosen to focus on "Instructional Delivery in Developmental Mathematics" by C.A. Zavarella and J.M. Ignash (published in The Journal of Developmental Education in 2009).
In this extremely fascinating article, Zavarella and Ignash present a quantitative study, which aims to measure the probability of student withdrawal from computer-based developmental math courses in comparison to that of traditional lecture-based courses. According to the study’s authors, students tested were more likely to withdraw from computer-based courses than traditional courses, usually after citing “personal reasons” on exit exams.
The authors are out to answer a number of questions with this study. First, they want to know whether a relationship exists between students’ learning styles and their completion or withdrawal from developmental math courses. Second, they want to determine whether the motivations for taking a particular course in a particular format play a significant role in the eventual withdrawal process. Third, they want to explore the relationship between College Placement Test scores and withdrawal rates.
The study followed three groups of students: a, 69 students enrolled in three sections of traditional lecture courses; b, 67 students enrolled in hybrid courses; and c, 56 students enrolled in three sections of distance learning courses. The authors collected data from a learning styles inventory each of these students took, as well as from an institutionally developed survey, which asked students for the reasons they decided to take certain courses. Finally, they tapped into their test institution’s CPT database for information on placement scores.
Ultimately, the study showed dropout rates were much higher for hybrid and distance learning students. Approximately 42% of the test subjects dropped hybrid courses, while 39% dropped an online course. Only 20% dropped their lecture course. This happened, the authors argue, because many of these courses “presented challenges [students] did not expect.” More than 50% of the students who dropped a computer-based course implied that they did not fully understand “what it takes to learn mathematics in a computer-based format.”
Our own thoughts on this: This particular study is intriguing, as it largely corroborates our own research on the topic. More often than not, when students drop online courses, they say something along the lines of “I thought it would be easier and less time consuming.” With this in mind, we recommend that institutions create a two-way channel of communication between themselves and their students. Students must understand the unique challenges of online courses.
For more, please see: Zavarella, C.A., Ignash, J.M. “Instructional Delivery in Developmental Mathematics: Impact on Retention.” Journal of Developmental Education, Volume 32, Issue 3, Spring 2009. Pages 2-13.
As promised, here is Part Two of our interview with Dr. Hunter R. Boylan! This segment of our conversation focuses predominately on the relationship between the government, educational think tanks, universities, and teachers. Once again, we'd like to thank Hunter for agreeing to this interview. We'd also like to thank our readers for their continued support. Be sure to check back on Wednesday for a new post.
ASP Blog: So you’ve touched on this a little already, but I want to get your thoughts on what, exactly universities and community colleges can do to improve developmental math given certain budgetary constraints…
Boylan: Universities tend to have much more money and flexibility than community colleges. So it is quite possible that universities will do whatever they want to do regardless of what the legislature or the state higher education executive body thinks. Universities probably have a little more leeway in how they implement these things, and some will just pick up the current instruction sheet and simply do what it says. Some will look at the instruction sheet and say, “We can modify this, and modify that, and still say we are doing it in spirit, and still get more of our students through.” And some will probably say, “This isn’t going to work. We’re going to keep on doing what we are doing.”
What state do you live in?
ASP Blog: I live in New York.
Boylan: Well, I don’t know what it is like in New York, but if you live in say, North Carolina or Ohio, schools like UNC or Ohio State are going to do pretty much what they want. In any event, what universities typically do is invest a lot more time and energy and money in the advising, placement, counseling, academic coaching and tutoring side. Rather than putting all of their energy into remedial courses, they put their energy into support services. They tend to have strong learning centers, they tend to have well-organized tutoring operations, they tend to do more intensive academic advising. Right now, this is typically the university model—to approach whatever academic shortcomings students might have through all the things I just mentioned.
Community colleges on the other hand don’t have those resources. While they’d like to focus more on intensive academic coaching, they can’t afford to pay for it. That is one of the reasons why community colleges are more likely to go with a course-based model. Now, many of them are revising their intake assessment processes. They are requiring less assessment, which enables more students to go on to college-level courses, but they are not putting the support directly into the courses like they probably should. Community colleges in America like the idea of embedded course services. They try to put more support services into classes, which is kind of labor intensive.
It is interesting. There are two trends in how community colleges are approaching this. On the one end, they are saying, “We need more time in class, so we are going to give you three hours in class, and if you scored lower on an assessment test, we are going to provide an hour or two of extra labs connected to the class.” So you’re putting more time in on class. On the other end, some community colleges are saying, “Ok, well you really don’t need to know everything a 16-week course will teach you, so we’re going to condense it all into 8 weeks, and you are going to work harder and longer.” So I find it interesting that some colleges are reacting by contracting the amount of time in class, while others are extending the amount of time spent in class.
Now, theoretically, a highly motivated student in either class will spend a lot of time studying and going over material. That’s probably true. So, well-motivated students will get what they need in eight weeks, because they’ll put in two hours a week in class, and spend another eight hours studying. So, for good students, both systems work. And by good students I mean those people who have study skills and motivation. For those students who don’t—it won’t work either way.
ASP Blog: There doesn’t seem to be much of an effort to turn students into these types of motivated students that you are talking about; we seem to sometimes assume that a student is just the way he or she is, and that there is no real room for growth or change. Paul has focused on this quite a bit: how do we make students better learners, how do we get them to take on the type of affective characteristics that might help them find success? Do you think that maybe some community colleges are ignoring this goal when they focus solely on trying to expedite the process itself rather than making sure the process actually works?
Boylan: Well, I think some states, like Virginia and Florida, have plans in place to measure the outcomes of what is going on (and hopefully to revise things accordingly). Florida State University got a multi-million dollar grant from the Gates Foundation to study the impact of all of these reforms—what is happening even now, is that the street bureaucrats there are releasing data that is saying that reforms are causing more students to fail college algebra, which is probably true.
With this in mind, I have hope that people on the ground will do one of a couple things. They’ll take the reforms and they’ll fit them into more efficacious patterns and, hopefully, put more energy into teaching those skills leading to achievement motivation. They’ll teach modularized math courses, but they’ll also develop videos for the students that teach them how to take a modular course on a computer. They’ll also provide a lot of personal consulting with the students to help them work their way through a modularized math course on a computer. So they’ll do what the state tells them to do, but they’ll also take what they know how to do and try to make the system that was imposed on them work. And they might be successful.
ASP Blog: So you are saying, if you are working at a school, and you are overseeing a developmental education program, and you have very little agency in the conversation about state mandates, and little choice but to follow them, then you might take a grassroots approach and implement your own support systems within what has been forced upon you?
Boylan: People are already doing that. The other thing that they are doing, is leaking damaging data to the press. They aren’t supposed to do this. I assume that someone at the system level will come down and ask these colleges “who released this data?” But the data was released because many people did not trust politicians to either release it at all or to release it without putting political “spin” on it.
ASP Blog: And you think that this may ultimately be these whistleblowers' only channel through which to enact any change? To make people in the general public aware of what is really going on?
Boylan: Yes. At least right now, channels of dissent are being stifled. I also think the important thing to remember about the reform movement, is that, in spite of its shortcomings, it still includes some good ideas. It is not entirely bogus. The people who aspire to lead the reform movement—Complete College America, Gates and llumina, etc— have some good ideas but few of those organizations have any actual experience or expertise in developmental education. This lack of experience and expertise makes it difficult for them to understand the context into which they want to insert reform. These organizations are coming up with some very good ideas and some very bad ones, but it’s difficult for them to know which is which. The bad ideas will probably have to be exposed by those you refer to as “whistle blowers.” They are the ones who can see what’s happening on the ground rather than looking at the situation from 30,000 feet.
Perhaps acknowledging their lack of expertise and experience, the reformers didn’t sit back in their offices and think something up based upon their own cogitation. They looked to community colleges for things that might work. They identified models that were successful in some settings and gathered data on them; then they took things they thought might work and promoted them. They have highlighted and promoted integrating reading and English, which I think, might be a pretty good idea. They’ve talked about embedded support services in developmental English courses. I think that’s a good idea. The Carnegie Foundation and the Dana Center, with their Statway and Mathway projects actually do represent something new and original—these are all good ideas. But what these organizations have done is to find existing models. With the exception of Statway and Mathway, they didn’t create anything new. They identified successful innovations that have at least worked in some places, and they are out promoting these ideas in various other places. On the other hand, given the legislation that has resulted from the reform movement, it’s hard to tell what innovations were originally proposed.
The problem is that doing these innovations right requires money, time, and training. And most institutions and/or legislators are not investing the money, time, and training into making these innovations work. Those that have should do well.
ASP Blog: It seems that many institutions have stumbled into a paradox: a lot of these changes are enacted to save money, yet, at least ostensibly, to make them work one has to invest more heavily into them and make sure they have all of the resources they need to be successful. You can see why people are waffling a bit as they are trying to do this….
Boylan: Yes. So the cheapest reforms—like “lets get rid of remedial courses”— are very popular because they don’t take time or money. Now they don’t work, either. But that seems to be beside the point. Again, I don’t want to condemn the reform movement. I’m just saying that because the people behind it have not been in the field or read about the history and research in developmental education, they were unable to create many new models. We have few really intelligent new workable models that anybody has presented. What we have are retreaded old models or individual cases where something has worked. For example, modularized math is simply mastery learning from the 1960s with computers added. The Accelerated Learning Program looks a lot like Supplemental Instruction from the 1970s only with mandatory attendance at enrichment sessions. The integration of courses and support services is something that developmental educators have been advocating since the mid-1970s.
Remember, the original definition of developmental education was the integration of courses and services guided by the principles of adult learning and development. The modern reform movement has at least emphasized the first part of that definition, the integration of courses and services. We’re still waiting for a pedagogy to catch up with the integration.
And that just about wraps it up! Pretty heady stuff, no? And we are just getting started! We have spoken to numerous national experts about the reform movement and its many implications. Check back every Monday for more posts and more conversations!
Looking Back to The Beginning of the Redesign Movement: A Discussion of B.S. Bonham and H.R. Boylan's 2012 Article "Developmental Mathematics: Challenges, Practices, and Recent Initiatives."
For the foreseeable future, the ASP Blog plans to use Wednesdays to bring attention to various research and field studies published in major developmental learning journals roughly during the past five years. Given that we are running the first of these articles between Part One and Part Two of our interview with Hunter R. Boylan, we thought we'd start by revisiting an important article Boylan published with B.S. Bonham in the Winter 2012 edition of the Journal of Developmental Education.
This article is particularly important, as it shows just how little things have changed in the post-redesign world. Written in 2012, it describes what was then “the current state" of developmental education. It also "discusses major initiatives designed to reform and improve success rates, and identifies research-based teaching practices associated with improved student performance in developmental mathematics courses.” Bonham and Boylan describe in detail how developmental education came to enter the very center of the national debate over higher education, especially with regards to efficacy and budget concerns.
Throughout the study, the authors explore the debate over developmental mathematics, chiefly the mainstream contention that developmental math courses often serve as “frightening obstacles” for underprepared students, many of whom have to take and retake these courses, which ultimately lengthens their time in college. According to this argument, many of these students ultimately withdraw from school. While the authors concede that this phenomenon does exist for certain students, they also point out that those students who pass their developmental mathematics course requirements “[are] just as successful in subsequent mathematic courses as those who were not required to take a developmental math course.”
The authors go on to contend that successful developmental programs utilize “multiple teaching and learning strategies.” This includes a greater focus on technology, math labs, project-based instruction, academic counseling, and proper placement policies. They also discuss at length the “math redesign model,” which first came into use during this period: chiefly, emporium, online, buffet, replacement, and linked workshops. The most effective of these “redesigns” employ research-based practices built upon “multiple teaching approaches rather than a single method.” As an example, the authors point to programs at Virginia Tech and the University of Alabama, which use technology when appropriate (i.e. for tests, quizzes, homework), but also provide supplemented instruction by small groups of teachers and tutors. “This approach,” they argue, “fosters greater student engagement with the material.”
Finally, the authors champion an industry-wide focus on affective characteristics. Research indicates, they say, that affective factors such as low self-efficacy and anxiety “can have a ‘negative and inhibitory impact on learning and performance in mathematics’” (De Corte, Verschaffel, Depaepe, 2008, p.25). This means that developmental educators must employ strategies to “help alleviate mathematics anxiety, build self-confidence, and maximize student learning.” One of these strategies, according to the authors, is to focus on study skills. Citing our own Dr. Paul Nolting’s Winning at Math text, the group explains that helping students develop these skills increases the odds that they will persist through (and not avoid) their math courses.
For more, please search for the full article at one of many article aggregators or library websites.
Bonham, B.S., Boylan, H.R. “Developmental Mathematics: Challenges, Practices, and Recent Initiatives.” Journal of Developmental Education, Volume 36, Issue 6, Winter 2012.
The State of Affairs: Part One of a Two-Part Interview with Dr. Hunter Boylan about Developmental Learning and the National Redesign Movement
Hello! Welcome to the official relaunch of the Academic Success Press blog! To set the stage for our upcoming posts—many of which involve conversations with experts in the field of developmental education—we thought we'd address the current state of affairs for our community, which, as we all know, is in a period of extreme (and at times tempestuous) transition. Who better to get things started, then, than the renowned Dr. Hunter R. Boylan!
Few proponents of developmental learning have been more influential the past few years than Boylan, longtime Director of the National Center for Developmental Education at Appalachian State University. His decades of experience in the field have made him a leading man for the cause, as he has seen and helped navigate the developmental learning community through numerous shifts in pedagogy and public understanding in recent years.
The following interview covers a great many subjects, including but not limited to: the efficacy of math redesigns, the general public view toward developmental learning, and the benefits and dangers of online learning. Due to length concerns, we have broken the interview into two parts. Please check back next Monday morning for Part Two.
ASP Blog: Two years ago, you did an interview with USA Today, where you spoke with a journalist about a national shift away from (or reform of) remedial and developmental mathematics. In it, you implied that many of these new approaches were failing to meet their goals. Do you still feel this way?
Boylan: Yes. We are still addressing the problems with a rather substantial variety of alleged solutions, ranging from the potentially good, to the potentially ugly.
ASP Blog: Many of the “solutions” promoted in math redesigns over the past year haven’t addressed the true roots of the problem in that many of these students have been underserved since elementary school. They’re coming into college drastically unprepared. Do you still believe this is the case?
Boylan: I wrote an Op-Ed for an academic journal last year. My contention in that was that we have made a lot of structural changes: we have changed the placement process for remedial courses, we are putting more people directly into college level courses, we are using more computers, and we’re accelerating developmental courses, we are providing embedded support services. When you look at all of these things, what they are actually doing is changing the structure of our delivery system. They are not changing the quality of the teaching that goes on. Nor are they addressing any of the characteristics of students that cause them to be underprepared in the first place and cause them to become attrition statistics.
For instance, ethnic minorities still have lower pass rates and completion rates than anybody else. First generation college students have lower pass rates and completion rates. The poor have lower pass rates and completion rates. But in all of our reform of developmental education, we are not addressing any of those issues. We are not asking ourselves “why is it that minorities have lower pass rates than majority students and what can we do about that?” We are not asking “so why do first generation students have high casualty rates?” We are basically just saying, “If we put them into this delivery system then they’ll do better.” Well they are going to maintain the same characteristics in the new delivery system that caused them to drop out in the old delivery system. That’s my view of the situation.
ASP Blog: That is what is interesting about this. The argument against developmental education is kind of myopic to me. Those who do not believe in developmental education are blaming the whole system writ large almost as if developmental courses merely add extra hurdles for students to clear. In reality, this is only true of poorly designed developmental courses. Paul likes to point out that one of the main keys to fixing a college’s developmental math platform is to improve classroom and supplemental learning through better teacher and tutor training. Do you agree?
Boylan: That is part of the answer. One of the things that needs to be taken into account is that we are doing a much better job integrating courses and services, but we still aren’t integrating those based upon adult development and learning theory. If you are going to teach a class, most people agree that it would be a good idea if you had some knowledge of how people learn—if you maybe understood learning theory and could organize and deliver your class according to the principles of at least some theories about learning. People don’t do that in remedial courses. And that’s the reason why we much prefer developmental education to remediation—because there is a body of theory called developmental psychology or adult development—however you want to refer to it—that discusses how we should teach the students. That is what is lacking. We are not using what we know about adult learning and development to deliver our courses. We are simply changing the structure of how courses are delivered without changing the pedagogy.
ASP Blog: What are the states that are mandating changes to developmental education actually putting into effect right now?
Boylan: The most popular change seems to be to allow more students to bypass remedial courses, usually by modifying the assessment process in some way. That is probably the number one change. I can see why legislators like this, because it doesn’t cost anything and it creates the illusion that they are actually addressing the problem. The second biggest one is to change the delivery system. This involves various types of modularized courses that are frequently computer based. What they are often doing is a discount version of the Emporium Model.
The Emporium Model can actually be labor intensive. One of the reasons it worked in the first place was that students got instant feedback right when they were having a problem. Now, the tendency is for colleges to put one faculty member in a room with 25 students at computers and let the students go to work. The one faculty member can’t get around to give personalized service to all of the students. So basically they have taken the Emporium Model and understaffed it, and said, “We have the Emporium Model.”
ASP Blog: I assume people have been collecting statistics on whether these classes are working, right? The same with online courses?
Boylan: All of the data we have on this matter shows that online developmental education does not work. Early results show that the major consequence of allowing students to bypass remediation is that more students are failing college level courses. In fact, I just got an email today from somebody who teaches at a community college. It basically said, “Our weakest students are being funneled into these short, technology based modules, or into a short eight week section. Consequently our standards are being lowered even further, so that we can prove that the techniques are successful.” What she was implying is that there is pressure on teachers not to fail too many students, because then the innovation looks bad.
ASP Blog: Right, the innovation that just happens to be cheaper.
Boylan: Right. Now, I don’t know how widespread this is, but there is no doubt that some teachers are feeling pressure to make sure these systems work. On the other hand, even with whatever pressure exists, the major result is that more people are failing college level courses. I talked to a reporter the other day, and she said something like this: “Well what about the stigma of being put in a remedial course?” And I said, “Well it is choice of which stigma do you want? Do you want the stigma of being placed in a remedial course, or do you want the stigma of failing college English?”
Update: Here is a direct link to Part Two.
Dr. Nolting is a national expert in assessing math learning problems, developing effective student learning strategies, assessing institutional variables that affect math success and math study skills. He is also an expert in helping students with disabilities and Wounded Warriors become successful in math. He now assists colleges and universities in redesigning their math courses to meet new curriculum requirements. He is the author of two math study skills texts: Winning at Math and My Math Success Plan.
American Mathematical Association of Two-Year Colleges presenter, Senior Lecturer-Modular