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! Today we present a brief interview with Dr. Rochelle Beatty. Beatty, who has worked for years both in the academic and publishing worlds, is currently teaching a few math courses at a community college in Kansas. Because we have spoken with so many administrators and researchers in recent weeks, we thought we'd mix things up a bit and try to capture the teachers' perspective on study skills and math redesigns. Enjoy! ASP Blog: I want to start by asking you about the importance of math-specific study skills, specifically for first-year students or students in developmental mathematics. How important is it that students learn and use these skills in their first college-level math courses?
Beatty: Very important. If students come into college unprepared, then they need not only instruction on the content of a class, but also on how to study—because this is usually one of the main reasons they are unprepared: they've just never had a grasp on study skills. This includes simple things like knowing how to take notes or understanding the importance of being in class. The easiest thing you can do to ensure a good grade is to show up. It seems like sometimes this is the biggest challenge with our developmental math students—their lives just keep getting in the way. All of this falls under study strategies: knowing how to manage your time, knowing how to prioritize school so that your studies are always at the forefront of your life. I really think that—with a lot of redesign models moving to computer-based modes of instruction—study skills become even a bigger part of the picture. Students need to be able to archive their work on paper, so that they can go back and reflect upon what they’ve done and not only on what they’ve seen. ASP Blog: On that topic, what specific skills do online or emporium model students need? Beatty: Again, time management is particularly important in this setting. Students are not going to make it through a course if they think that their computer lab time is the only time they need to be engaged with class content. It still holds that students need to study three hours outside of class for every one hour in class. In fact, I just told my students yesterday: “Don’t just think that those three hours are going to happen on their own. You have to set a schedule, and it probably isn’t a good idea to devote these three hours to the night before class in a single chunk, because your mind is easily fatigued. So you have to make sure you have one hour somewhere during the day to go back and study your math and keep progressing on it.” The other thing I tell students is that the Internet they find on campus might be some of the best Internet around in terms of speed and having instructional and technical support. So they should always make sure they schedule at least one additional hour of computer time between classes somewhere on campus. ASP Blog: In terms of computer skills: one would assume that modern students would have grown up with computers and therefore have a basic grasp on how to use them. But this isn’t always the case, correct? Beatty: Sadly, although our students are extremely connected to their gadgets—and have anxiety when they are without these gadgets—this does not mean that knowing how to use those things for everyday life is equivalent to knowing how to use those devices for educational or instructional usage. You really do need to know where your students are [in this regard] and make sure you can provide them keyboarding skills and other traditional computer skills they might not have. Not only do you need to teach math, but you need to teach computer proficiency. Sometimes these skills are not always intuitive—even with something simple like printing documents. There are so many other things that come into play also. With their phones and gadgets students aren’t having to save files or take screenshots. If you are teaching an online or emporium model course, you really need to be hands on in the classroom. ASP Blog: How important is it that teachers read up on new pedagogy—new ideas, new discourse, being published in academic journals? Beatty: I think it is huge. For instance, I think that if teachers don’t understand the difference between how a developmental math student processes information versus how a college-level student processes information, they can’t properly serve either group. The same is true if you don’t understand adult students and their learning preferences versus traditional students and their learning preferences. There is a lot of theory out there that I think instructors should not only be aware of, but also incorporate into practice. ASP Blog: You wrote your dissertation on cognitive development and vocabulary. Do you use this research in your classroom? Beatty: Yes. Specifically vocabulary. In mathematics, understanding what certain words mean and understanding how one set of directions differs from another set of directions can really be a make it or break it situation for students. Students must make vocabulary a priority, which once again goes back to study skills. Cognitive development is also important. Students have to grow from a perspective that math is dualistic—right/wrong, black/white, true/false—to a perspective that math is multiplistic—that there is not just one way to solve a problem, one way to pose an answer. Students should not erase their work just because their path is different from one of their classmate's. Students need to know how to let that point of confusion be an easy thing to accept while one waits for the inevitable “Aha!" moment—when they realize, "we both got the same answer, we just went about it differently.” I think this is another place where developmental students often struggle—often because past high school instructors insisted that work only be completed by using a very uniform approach, and now their college instructor uses an entirely different method. In the classroom, we need to not only focus on the content, but also make sure that our students embrace this notion that math doesn’t always have to start the same way—that you have to look at a problem and decide between all of the different methods you have at your disposal.
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Welcome back! Today we present the final section of our talk with the Carnegie Foundation's Director of Productive Persistence: Rachel Beattie! This particular portion of our conversation centers on the testing and application of new strategies in the classroom. The Carnegie Foundation, one of our nation's most prominent educational research centers, has developed a fascinating model for applied research, and Rachel does an amazing job here breaking down exactly what teachers should and should not do when conducting research or applying new strategies in class. Enjoy! ASP Blog: Moving on to the next topic, will you talk a little bit about the non-cognitive factors that affect students while they are learning math? Beattie: Sure! This could easily turn into quite the list, as it really is a complex landscape—all of the different factors that affect math learning. Once again, the knowledge that intelligence is malleable and not fixed is really important. When talking with students, I often hear them talk as if there are two races of people: math people and non-math people. We want students to see that this isn’t really the case. This is usually an uphill battle. Over two-thirds of our students answer this way. For students in developmental mathematics, you can probably guess which group they think they are in. That is why we make sure our pathways address productive persistence—to make sure students think about creating new mindsets. But we also believe that many other non-cognitive factors are important: belonging being one of the biggest. The sense that one belongs in a math course is incredibly predictive of math success. It is really a problem in math because of all of the negative stigmas and stereotypes attached to mathematics learning—that girls, for instance, can’t learn math. Even positive stereotypes present problems. The point is that if you believe that others are judging you, or that stereotypes dictate that your classmates don’t think highly of you, this can drastically change your feelings about your ability to succeed in a particular setting. You might constantly question whether or not you belong—especially if something negative happens [in class]. Emotional regulation is another main non-cognitive factor. What is really bad here is how we sometimes mistake stress—sometimes your body has the same physiological reaction to things you want to approach as it does to things you want to run away from: heart-beating, sweaty palms, intake of oxygen, all of these are related to both of these reactions. So what we do is have students replay these physiological reactions and test their bodies’ ability to get ready for stress. We have seen that this significantly improves performance on exams—it doesn’t help students develop better study strategies—but it does reduce anxiety enough to help students perform better on exams. The last factor I’ll bring up is homework systems. We want students to become self-regulated learners. We actually build in opportunities for students to practice these self-regulating skills directly within their homework. This helps students increase confidence in their knowledge of how to accomplish the task at hand. We also make sure that homework assignments always build in complexity and are applied in different situations. This is really essential to students becoming experts. It also helps students keep engaged. Reflection is another major part of self-regulated learning—so we also include a phase after each homework assignment for students to reflect on the strategies they used and any next steps they want to take. Many of our students, in the past, have only learned shallow study and homework strategies. We want to create an environment in which they can flesh out their meta-cognitive skills. ASP Blog: It seems like you are very much in the business of applied psychology. You use whatever you can figure out about the way people think and learn and apply this knowledge directly into the classroom. What is interesting about this to me is that one both learns and applies information in the same exact setting: the classroom. How can universities use the classroom as a test case, while still not losing focus on the main function of the class itself: teaching math? Beattie: That is a great question. Our goal is to never interfere with the teaching of mathematics. For this reason, we use a methodology called “improvement science.” This involves small paths of change, not huge overhauls. The goal is to conduct tests that do not take more than ten minutes or so from a class. It is based upon six different principles. 1. You should be user-centered and focused. You really listen to students’ questions and concerns, and you are extremely focused in on a direct problem. 2. Next, you really need to attend to students’ abilities. We want to understand what works for whom, and under what conditions. Across our pathways, there has never been this “one-size-fits-all” mentality. There are adaptations that people need to make, in terms of setting, for something to work. 3. It is really important that if you do make a change, you figure out how this change interacts with everything else in your particular setting—otherwise whatever you are trying to apply might become overwhelming. 4. We also document what we learn. What are my hypotheses, what are my learning questions? What is my data? This helps you to reflect on an action afterwards and prepare for the next test. We can’t improve what we can’t measure. 5. You don’t just want to look at test scores. You want to take note of the everyday behavior in the classroom: are students turning in their homework, are they asking questions, how are groups working? In order to improve a classroom, you really need to understand what is happening there every day. 6. We help create what we call Network Improvement Communities to make sure faculty, teachers and students are working together. Creating a networked community keeps you from having to do everything yourself. If everybody is working together, then someone might have already tried something that will work well in your particular setting—they have already tested it out, and it just needs to be adapted a bit. All of this helps to really reduce the load of testing so that it doesn’t seem too unwieldy. ASP Blog: Can you talk a little bit specifically about how to properly measure strategy results within a classroom? Beattie: Outcome measures are always really important, so I don’t want to say never measure your outcomes—but you do want to look at the larger goals and aims of your project. If your goal is to improve success in one math classroom, then you definitely want to look at grades, as well as the credits students get in mathematics after that class. At the whole college level, you want to look across your whole department: grades, credits, transfer rates, etc. With outcome data, you want to make sure it closely mirrors your aims: why you are doing this work in the first place? What is really important for our work is what we call “process measures.” These actually measure the process of improvement, the daily processes in class. For us, attendance is a big one. We have developed a couple processes that we know work because we measure them daily. We were able to meet semester long attendance rates between 85 percent and 93.3 percent with just one small change that we tried out. So it is really powerful to put these day-to-day measures to work. Another one we look at is group functioning. Are students being supported in their groups, do they feel like they are being productive and that everyone is contributing? That is really important to form a community. You also want to look at “balancing measures.” Sometimes changes unintentionally affect classroom learning—I love that you already brought up time, that new strategies take up a lot of faculty members’ time and keeps them from doing other things that were already affective. This means that it is important to think about “if I do this change, what might be affected in my classroom either short term or long term and how can I measure that?” Finally, another part of our data collection system is what we call “practical measures.” It is hard to measure a student’s mindset in three minutes. If you are familiar with psychological research, we aren’t big on short test batteries. Questionnaires and interviews are always LONG, because you really want to explore the contextual frameworks, you want to understand students’ beliefs on multiple levels. However, with a practical measure, you have to cut it down drastically and really focus in on the variables that are causally related to student success. With practical measures, we measure students at week one and week four, only because we do a lot of intervention and we are setting up a lot of classroom norms and expectations—this allows us to measure a before and an after. It is really wonderful to see [this dynamic] in our data system, because it helps us understand the different elements that lead to student success. This is true from our point of view, but also our faculty’s. We actually give each of our faculty members a report about their classrooms and about productive persistence. This gives them classroom aggregated data on individual and group mindsets—on how well students are transitioning. And that' wraps it up! Once again, we want to thank Rachel Beattie and the Carnegie Foundation for their participation. Tune in next Monday for another exciting post! Productive Persistence: Part One of Our Interview with the Carnegie Foundation's Rachel Beattie11/9/2015
ASP Blog: Do you want to tell us a little about your background? Beattie: Sure! My background is in psychology. When studying for my Ph.D., I specifically focused on the etiology of learning differences in mathematics [with regards to] reading and language—with a heavy focus on dyslexia and specific language impairments. I wanted to understand why these learning differences came to be and what the actual differences were between typical and atypical reading and language processing in mathematics. While I was doing that, I was also an adjunct professor at Occidental College and USC. After I finished my Ph.D., I taught research methods, statistics, learning and memory courses, and I helped TA a course on the science of happiness. I then went to Ohio State University where I did my postdoctoral fellowship in neuroscience, which involved conducting neuroimaging on children and adults related to their mathematics reading and language processes. This gave us great insight into the development of these differences. After my postdoc, what I really wanted to do was get away from research about the basic processes, and get more into applied research—actually helping students and teachers in their classrooms during the school year. So, I started working at the Carnegie Foundation. I’ve been here for a year and a half now, and it has been really wonderful to actually make a practical difference on a daily basis. ASP Blog: Can you talk a little bit about the variables that predict math success? Beattie: Sure. I’ll speak mostly on developmental mathematics because that is the data I am working with right now. Obviously, one of the biggest variables is the foundational mathematics skills that students come to a course with—we actually measure these when students come in with a conceptual knowledge quiz. This is a pretty strong predictor, though it is not necessarily deterministic. There are other factors that we see that are really important as well. We see that students’ mindsets about their ability to perform and learn in a classroom are also predictive. We also often see that a student’s certainty of his or her belonging in the classroom is important. If he or she has high learning uncertainties, then we see that they are much more likely to withdraw—and if these same students finish a course, they usually have a lower score at the end. Anxiety is another interesting variable in the data. Research is showing us more and more that very low and very high anxiety are maladaptive. Very low anxiety is actually negatively predictive of success. It is very linear too, as we see that high anxiety is actually a predictor of success—we think this is because these students are putting in more effort outside of the classroom. That is our current working theory, though we are still puzzled a bit about that. Also, in the pathways, we do a lot of intervention around students mindsets and beliefs. Intriguingly, we see that their week one beliefs are no longer predictive of course outcomes. When we started we saw that, yes, they were very predictive to these mindsets, uncertainties, stereotypes, and anxiety. However, now we see that week four is much more predictive of success than week one. This suggests that we have shifted students’ mindsets. It is really nice to see. We always want to create a learning environment, a culture, where your belief sets at the beginning are irrelevant. It is how you perform throughout the class that is what is ultimately important to your success. ASP Blog: Interesting! How much of this is the result of students better understanding what is expected in a class and having a better grasp on whether or not they have what it takes to find success in the course? Beattie: I’m sure that is part of it. We see that students are more comfortable asking questions by [week four]. A lot of it, though, is the actual interventions we conduct to help students see themselves as capable mathematics learners. It is important to shift student thinking and self-perceptions in that way. ASP Blog: Which is a perfect segue into your personal expertise: productive persistence—the ability for a student to persevere through difficult times or even learn how to handle success. Do you want to talk a little bit about this behavior? Beattie: Of course! My favorite subject! People always ask me what “productive persistence” means. We think of it as how students continue to put forth effort during challenges. When they do so we hope they are using affective strategies. We focus on productive persistence because in our data we are seeing a lot of students being unproductively persistent. We don’t want students coming back to the same courses over and over again. They know the course is important and that they need it in order to pursue their dreams. But they aren’t succeeding; they aren’t being consistently productive. We want to help create environments that allow students to be productively persistent in mathematics. When we develop frameworks, we introduce students to faculty, we consult with psychological literature, as well as with general education reform literature, and we form a network of faculty members and researchers to create frameworks based on all of these sources of information. [During this process] we came up with nearly `100 possible constructs that might contribute to productive persistence, and we narrowed these down to five high-leverage factors. If we make real movement on these five, we will help students become more productively persistent. While there are many things that affect productive persistence, we focused on the following five because they are within our locus of control: 1. That students believe they are capable of learning. They believe it is possible to succeed in a course. 2. It is really important for students to develop social ties to peers, faculty, and the course. If anything happens that makes students wonder if they belong in a classroom setting, they often take this on as their identity within the classroom. 3. That students see a course has value. When we talk about value, we mean that students are able to relate material to their short-term and long-term interests. 4. We want students to know how to succeed in a college setting. This involves traditional study skills, cognitive study skills, but also emotional recognition skills and general college-know-how skills: how to navigate a syllabus, knowing how to navigate course progression, etc. 5. We want to help support faculty to help students to develop these mindsets and skills. We believe that we are in the business of shifting student perceptions, but also that it is important to change the learning environment. There needs to be a congruency between the mindsets we are helping students develop and the environment in which they are learning. We also want to create an effective pathway through college math. We actually created a curriculum that engages students in math that matters—so it involves real life problems, so that students can see the relevance of mathematics in their lives. To support all of that, we have a lot of support for faculty built into the classrooms, we have faculty mentorship, we have online resources, and a lot of this focuses on productive persistence. The pedagogy again supports productive persistence because it promotes collaborative learning. We focus on activities that involve students working with one another to better understand the concepts of mathematics. We don’t just want them to have the procedural skills; we want them to have the conceptual knowledge too. I think productive persistence works really well as a part of this whole structure. We want the whole environment, the pathways of developmental mathematics, to support students to develop the right mindsets and skills. That wraps up Part One! Part Two continued, here.
On July 26, the Washington Post published an interesting article regarding entrance exams and remediation. Given the tenor of our last post, which recapitulated an article in the Journal of Developmental Education that advocated the reform not replacement of assessment tests, we thought we'd pass along information on a different approach being taken by Montgomery College in Maryland. The entire article is interesting—though we may quibble a bit with a few of its major points. While well-intentioned, the educators interviewed in the piece make the same basic argument leveled by comparably ardent anti-remedial forces. Rather than recognizing and fixing flaws within the developmental education system, they are putting more of an emphasis on avoidance, as evidenced in the quote below: Instead of relying on standardized test results, the pilot program also looks at high school transcripts. If students earn an A or B in Algebra 2, for example, they might be allowed to move into college-level math. If students earn similar grades in advanced placement or honors English and world history, they might be able to go into college-level English. This in itself is not necessarily a bad idea. Still, one has to wonder, how are these students going to perform when placed directly into college-level math courses? Let's say these same students who got an A or B in Algebra 2 took said course their junior year of high-school. After not taking a math course for more than a year, are they still prepared to take the hardest math course in which they've ever enrolled?
The answer to this question certainly remains up for debate. Hello readers! Happy Monday! For our first post this week, we want to turn your attention to an interesting article, which ran in the Winter 2014 edition of the Journal of Developmental Education. Written by D.P. Saxon and E.A. Morante, "Effective Student Assessment and Placement Challenges and Recommendations" explores the challenges of student assessment and placement methods within the greater structure of modern developmental education redesign movements. It also provides a few recommendations for what its authors deem “common inadequacies in college assessment and placement processes.”
The authors begin by arguing that placement exams are extremely important to first-year college students. They state plainly that making sure students wind up in the correct courses is crucial to their future success. Citing a study by Hunter Boylan, they contend that research proves mandatory assessment and placement exams are effective, assuming institutions have already established evidence that their developmental courses and instruction are “quality” attributes. With this in mind, many challenges remain. To begin with, the authors say, “No test gives an absolutely exact measure of skills or any other variable.” Worse, many of these tests fail to include “other measures.” This is particularly true of affective characteristics, which the authors point out account for nearly 41% of a student’s grade. These characteristics—which included prior employment, confidence levels, anxiety, attitude, etc.—typically fall into the realm where “life and college” intersect. This means that affective characteristics tend to place math within the greater context of a student’s life and thereby become very important for their future success (particularly for first-year college students taking their first college-level math course). The authors also point out that many institutions suffer from inadequate and low-performing advising systems, while others often fail to enforce mandatory placement policies. In the end, they suggest that institutions—particularly those in the middle of large-scale redesigns—should take a series of steps to ensure success. Colleges should help students transition from high school to college, require mandatory assessment and advising for all incoming students, coordinate assessment services, and modify placement tests to directly address skills deficiencies. They should also strengthen bridge programs, use more effective test cut score ranges, and learn to evaluate the placement process systematically. For more please see: Saxon, D.P., Morante, E.A. “Effective Student Assessment and Placement Challenges and Recommendations.” Journal of Developmental Education, Volume 37, Issue 3, Spring 2014. Pages 24-31. 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: Link 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. Thoughts on "Instructional Delivery in Developmental Mathematics" by C.A. Zavarella and J.M Ignash10/14/2015 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. |
AuthorDr. 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. Blog HighlightsAmerican Mathematical Association of Two-Year Colleges presenter, Senior Lecturer-Modular Reader Contributions
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