Nolting: I know a lot about your background, having worked with you on different projects
and seeing you at conferences, but for our readers, why don’t you tell us a little bit about your mathematics background and your current position.
Rineck: I currently have a master’s degree in mathematics. I’ve been teaching math for eleven years at [The University of Wisconsin-Milwaukee], and I am currently also working on my Ph.D. in math education. At UW-M, I teach and coordinate Math 94—Foundations of Elementary Mathematics. We start with students who have an ACT level of less than 16, and we go from basic math all the way up to beginning Algebra.
Nolting: I know you have attended and presented at AMATYC and NADE conferences. Can you describe what you spoke about?
Rineck: I have talked quite a bit about the course I teach and coordinate. It is a unique course in that it is a vertical redesign—so we don’t teach material in the same order we would normally teach math in. We teach it in a modular design, where we talk about definitions of all the items we are using, then we do operations, then we do solving—we solve inequalities and equations together—then we do applications. I have also talked about how to incorporate manipulatives and formulated assessments into courses. Manipulatives are not just for elementary and middle school students, they help conceptual understanding for adult students also. I have had a number of students really enjoy [manipulatives], as they can finally understand why integer operations work the way they do.
Nolting: Yes. I have had the same experience with manipulatives. You started talking about the design of your course. Can you go into a little more detail—specifically the types of students who are taking your class?
Rineck: The math course is a six-credit course. It is all developmental mathematics, so it is six-credits for financial aid and payment, and it is zero credit toward graduation. It is accelerated, so students do two or sometimes three classes in one semester.
It is designed in a way that we define everything thing. So in the first module, we define what a number is, what types of numbers there are, how to plot things on number lines and coordinate graphs. But we also discuss complex numbers and how to plot them on complex grids; the properties of real numbers; exponents and exponent properties, even rational exponents. The second module is operation—with all these [same] topics. For instance, in our addition section, we add everything: integers, rational numbers, rational expressions, polynomials, complex numbers, and radical expressions—all at the same time. This way students actually see the connections with all of these topics. They have been taught so often “This is how you add a fraction” and “This is how you add a polynomial” and “this is how you add a rational expression” but they don’t see the continuity between those three things. We try to reinforce that continuity.
Nolting: So they take six-hours, but they can complete one or two courses during that time?
Rineck: Right. If they complete their online homework before the middle of the semester, we actually let them accelerate into a credit-bearing class. They stay in the same classroom and do the material we are working on, but we do have time built into the class for reviews and working with manipulatives, so that during those same class periods, the students who have accelerated work on their credit-bearing material.
Nolting: You teach at a university. I’m wondering how these courses play out with the types of students you have?
Rineck: It works really well. UW-M is virtually an open-access university. I think right now 85-90 percent of applicants are accepted. It is an urban university, so we have a lot of commuters and non-traditional students. About 35 percent of the students in my course are international. We have twenty percent students of color. Five percent are veterans. The course is designed for student success. We try our best to make sure all students succeed. To that end, we require that all students be eligible to take exams. We require students to do their homework to be eligible to take an exam. Some of them get upset, but when I explain, “Why do you want to take an exam you aren’t ready for? Then you don’t do well and hate math even more. Let’s do our homework, let’s be prepared,” then all of a sudden they start succeeding in mathematics.
Nolting: I visited your classroom a few years ago, and I know the curriculum has changed. How has the success rate changed between then and now?
Rineck: Before our redesign, we had below a fifty percent pass rate for our developmental sequences. Currently, my course has a seventy-five to eighty percent pass rate, depending on the semester. Typically Fall semester is better than Spring—because in the Spring semester, we have a lot of repeaters. Frankly, that is my next goal: trying to figure out how to help these repeaters.
Then we also have a quantitative literacy pathway that also has a 75 percent pass rate. I think currently our algebra pathway, which is right above where I start, has about a sixty-five to seventy percent pass rate. My course is doing very well because it is very comprehensive. Students are required to be there—so the more math you do the better you get at it.
Nolting: I know that some institutions are really struggling to increase pass rates in modular course designs. Yours is about the highest I’ve ever heard of. Getting seventy-five to eighty percent—that’s higher than regular classrooms. What I’d like to do, is go step-by-step to describe the changes you made to your courses. First, can you explain the unique challenges of the modular design?
Rineck: The modular design typically requires mastery at each module. That is a little bit different than just getting a “C.” With modular design, teachers aren’t used to requiring mastery at every level. The pushback from students, and from teachers for that matter, can be hard.
Nolting: What would you tell students about what is uniquely difficult about modular courses?
Rineck: They have to be aware that this is not how they’ve ever learned mathematics before. I would hope that they have the support they need. A lot of times, I find that students are missing just one or two components. Then, all of a sudden, when they understand these components, they just fly. But they have to understand that this is a little different from how they’ve learned before, and they have to be open-minded to that. That is one of my great struggles right now. I keep hearing: “Well that is not what I’ve been told before,” or, “That is not how I’ve learned it.” Sometimes you just want to say, “Well…that may not have worked for you in the past, so let’s see if this way works for you.” So that open-mindedness really helps, for a lot of reasons.
Nolting: Right, so you are building confidence among students in both you as a professor and the design of the course itself. I want to get back to the step-by-step design of your course. Can you explain the curriculum—particularly how you flip the classroom with study skills and other materials.
Rineck: Yes. So the entire classroom is actually flipped. For the math materials—not the study skills materials, but the math materials—I have created videos and a workbook that goes along with the videos. Students watch these videos outside of class and attempt their homework and workbook work. The workbook has multiple points of entry. For the most part it goes from pretty basic material to pretty challenging material. What I am looking for is that students have tried the material and attempted the work so that when they come to class we can discuss where their difficulties were. Instead of going through the simple procedures, I’d rather have them try it, then we can talk about, for instance, what the difference is between a negative number and a negative exponent (as well as their similarities).
Then, for the math study skills component, I have them watch some videos on growth mindset at the beginning of the semester before they come into class. Once the class starts, I have them read your Winning at Math textbook. This is part of their outside homework. They do the study skills assessment, the locus of control assessment, and also complete some questions about what they’ve read. I find that students typically don’t have a problem with this, as it isn’t a math textbook, and students do actually like reading the book versus actually doing their math homework.
So that’s how I flip the classroom. It takes a lot of time, a lot of prep-work. But I’ve found it is very successful for the students who really try. For the students who struggle, they are able to keep watching the videos and reading the book until they finally get what is going on—this versus us going really, really fast in class, where students are just copying what teachers are putting on the board.
Nolting: How does the math study skills evaluation help students?
Rineck: It helps the students because they get a report at the end of the evaluation that tells them where they have good study skills, and where they need some help. It identifies the chapters in the book, which they can go to to get the help they need. It also identifies some pretty good warning signs for me, so that if a student has consistent scores except for one, I can stop and talk to that student and say, “I am pretty concerned about your test-taking strategies. Let’s talk about this so that you understand how to prepare for a test, and let’s see if that helps you in the future.” Or, if it is their learning and memory scores, I can ask about what their challenges have been in the past, and figure out if there are things I can do to help them ensure success.
So the study skills assessment is something I really push students to do—actually it is one of the requirements for students to take the first exam. This way, I know where students are coming from, and they know where they are coming from and what they need to do to help themselves.
Nolting: It sounds like the evaluation pinpoints the areas students need help in. They learn some of those areas outside of the classroom, and you probably teach some of those areas within the classroom as well. But what I am picking up from you is that you are able to go up to a student and say, “Hey, it looks like you are good here, but you need help here.” That’s exactly what I wanted this evaluation to be—a math diagnostic. You can go right to the study skills—often just one or two areas—and fix those things so that students can be successful in math.
Rineck: Totally. It has been such a valuable tool for me to use. If the scores for a whole class are low in say test-taking strategies, then we can set aside time to talk about test-taking strategies. We can talk about what we can do to improve test-taking. If the scores are low in note-taking, then we can talk about note-taking.
I do have to tell you a little anecdote: One of my students from last spring came up to me. She was really excited at the beginning of the semester because I email students and call everybody, and before they come to class, they have to watch videos on the “growth mindset.”
When she came to class, she immediately said, “You get me!”
I said, “Thank you! I hope so!”
Then she started with the study skills book, and she comes in like two weeks later and she says, “You know…I’ve never taken notes in math class. I have taken notes in all my other classes, but never in math class. I started taking math notes like the way the book describes, and I’m really starting to get it!”
I looked at her and I said, “Huh! Do you think there is a correlation there?” And she laughed.
I don’t think students realize that there are specific things you have to do to be successful in math, and if you do them you can be successful.
Nolting: I have some instructors tell me that they don’t have time to teach study skills. It sounds like this student may not have passed your class without reading about them. What would you tell instructors who are reluctant to incorporate study skills into the classroom?
Rineck: In my experience, having taught a lot of things now, I’m starting to learn that if you go slow, you wind up going fast. Taking time at the beginning of the semester to teach study skills, to teach test-taking strategies, to teach how to reduce test anxiety, students build the base they need. I teach this material during the early part of the semester and by the second half of the semester, they actually start going faster because they have the tools they need to learn the material. So yeah, it does take time, but eventually, because they start doing what they are supposed to be doing, it takes less time in the end. You do actually make up the time.
As promised, here is Part Two of Dr. Nolting's conversation with David Arendale. In the previous installment, the pair discussed the history of developmental education and how it led to present practices. Part Two explores what developmental education might look like in the future. Enjoy!
Nolting: What do you think we have learned about developmental education in recent years?
Arendale: I think that developmental education was not very responsive to change, and I think it was in a bad position about ten years ago, when the debate began to change regarding its role, its cost, and whether or not we ought to have developmental courses offered at all institutions or limit them to two-year institutions. There was not a lot of widespread, innovative work going on in developmental education. We were really slow to respond to the demands of legislators and public advocacy foundations like the Gates Foundation, College Completion America, and all of the others. We didn’t have a lot of great research, and we didn’t have lots of models. The thing is, we were doing good work, but we weren’t doing a good job of publicizing it, and I think because of the storm of criticism we are doing much better now.
I think we now understand that everyone doesn’t need to be placed into a developmental education course. Somebody came up with an analogy of a three-layer cake (it’s not mine). It used to be that everyone inside the cake was required to take some level of developmental education. The top layer includes students that don’t really need to take a developmental-level class before they can take other classes. Students in the top layer can probably be successful if they have supplemental education that provides necessary support. Then you have the middle layer, which includes students who have deep needs because they have let their skills atrophy after they have perhaps been in the job force for a decade and have forgotten things. This layer does need developmental education. The bottom level of this cake—and this is the more controversial layer—includes students who, for lots of reasons, are low in their ability to do some of the basic competencies in the areas we would expect: reading, writing, and mathematics. If you have students who have deep needs in all three of these categories, it might not be possible to make up for twenty years’ worth of deficits in one or two semesters. Maybe they do need to think about other options like trade schools and certificate programs. Frankly, some of those programs might give students more employable skills than they’d get while going into deep debt for a liberal arts degree. This seems harsh…but [colleges] might not be able to take care of students who are in the bottom layer, which is really a small minority, only about ten percent.
Nolting: Yes. I did some research on this at my college a while ago. A lot of people in the math department believed that the students enrolled in our lowest level math course, pre-algebra, maybe had deficits in other areas and just weren’t going to be successful in college. I found out that about seventy-five percent of those students were in one or no developmental courses. Students who were in all three developmental classes—we found it very difficult to help them. Especially students who were reading at a third or fourth grade level. That was tough.
A lot of our students are now being placed directly into credited courses. Do you think that these new first-year credited courses are becoming the new face of developmental education?
Arendale: From what I have read, the main case study here is Florida. It seems that a number of teachers have had to change their first-level course into a hybrid developmental course. This has caused them to change curriculum and [scale back] the amount of content they present in order to meet the needs of the least prepared students. They are feeling pressure from high-level students, who believe they are being held back. The instructors feels like they are stuck in the middle of these groups, because they are forced to be bimodal. Some students can handle college-level material and others cannot.
Nolting: Right. I have seen that more colleges are asking for help in first-credit English, and particularly first-credit math courses. What are some of the strategies that can help all levels of students in these first-year courses—you talked a little bit about Supplemental Instruction, and you started PAL as well, correct?
Arendale: No. PAL is the University of Minnesota’s approach to offering peer cooperative learning support for very difficult classes. [At my school] we drew on Best Practices from Supplemental Instruction, as well as peer-led team learning from a national model out of the City University of New York, and the Emerging Scholars program. We built our own model, which has mandatory attendance for students in PAL. We found that the students who needed the most help were not going to the voluntary support sessions because they felt self-stigmatized, and they didn’t like admitting that they were “weak.” For us, for critical courses, particularly math sciences courses, everyone goes. That has been our approach. This was a departure from SI, which was built on voluntary attendance.
Nolting: So how do you envision the future of developmental education, especially accounting for these new first-level courses?
Arendale: I actually teach a first-year course—my global history course. I think the real future involves a Universal Design for Learning (UDL). There are lots of things I can do as a faculty member to increase the success of all students in the class rather than just figuring out from a deficit model who is sick and targeting all services on them. In a UDL model, you apply new approaches for every student in the class. There are probably fifty things I do in my class that help all my students regardless of what their issues are. It isn’t the same thing as a developmental model, and it isn’t a replacement, but my own personal opinion is that all of us who teach first-year courses can learn a lot from universal designs.
Let me give you a few examples of this. A lot of students have trouble keeping up with note-taking. They aren’t likely to raise their hands and say, “Excuse me professor, I can’t write fast enough.” This is difficult to do in front of fifty other people. So what do I do? I record all my class lectures. Everything I put up on the laptop screen—PowerPoint slides, video clips, etc.—is recorded and placed online. I also send them this material before the class begins. I knew an instructor who did this fifteen years ago for immigrant students who were having difficulty adjusting to a different style of classroom. What I have discovered is that about twenty-five percent of my students watch those lectures—some of them twice. This includes some of the best students. They see [this material] as an additional resource when they are not able to keep up for whatever reason.
Another one: I make an audio podcast where we actually review class sessions. I have students come in and provide summaries about a unit, and I provide upcoming exam questions. Probably about forty-percent of my students subscribe to it. This gives them academic resources that they would not be able to access any other way, because they have a difficult schedule, and they don’t have time to go to a tutoring center or they don’t know other students in class. What I have tried to do is make sure that I make resources for the class accessible for everybody.
Nolting: You seem to believe that UDL is the future of developmental education.
Arendale: Yes. I think that [in the years to come] we are going to be talking more about UDL than we are DE. I think that UDL is the overarching umbrella for lots of things. I think that developmental education fits beneath UDL.
Nolting: So how can universities integrate these strategies into college core curriculum?
Arendale: There was an organizational sociologist, Kurt Lewin, back in the 1950’s. He came up with a model for explaining how change occurs in an organization. There were certain stages. First, you have to be dissatisfied with the current state. If you aren’t dissatisfied, you aren’t going to make any changes. It’s like the flavor of the month. I can’t tell you how many times I have been at an opening meeting for faculty, and the college president came in and told us what the new initiative was for that year. Then, the next year, it would be something different. Well one of the local colleges up here, the president came in and presented data to the faculty regarding students who were dropping out, and he helped them to see how much revenue was being lost. Until faculty actually recognize that there is a problem, nothing will change.
Once you establish that a problem exists, then you have to present models that the faculty can adopt. This can be done through training materials, but frankly, I believe this should be done through personal interactions: teaching circles and workshops. These things are necessary for change to happen. Most faculty, with their heavy work load, aren’t going to make changes without human interaction.
The third part of this: you have to incentivize people to make changes. You have to pay them to participate in the teaching circles and workshops—even if you give them a very small stipend or you provide some money that goes into a professional development account. This also needs to show up on year-end appraisals. Sometimes, administrators say what they want everyone to do, but then they use the same criteria every year to decide whether you get a raise or not. Faculty need to see that there is a relationship between new behaviors and outcomes and some sort of economic incentive.
Finally, you need to have faculty refreeze themselves into the new pattern. This comes from long-term professional development programs that go on for years and years. I think that having a Teaching Learning Center at every college is essential—where you have an experienced faculty member who is running a center for workshops, which allow faculty to reflect, to observe, and to change their behaviors.
The Academic Success Press Blog is proud to present Part One of Dr. Nolting's conversation with David Arendale, former NADE president and current Professor of History and Higher Education at the University of Minnesota Twin Cities. In this chapter, Nolting and Arendale discuss history: first Arendale's personal history, then the history of developmental education. Enjoy!
Nolting: Can you tell me a little bit about your developmental education background and how you have helped students become more successful?
Arendale: I started off as a community college instructor in the late-1970's. I was teaching traditional courses. I had a mix of students with different academic preparation levels. I knew that I needed to reach out to meet the needs of some students who weren’t picking up the material as quickly as others. But I was kind of clueless how to deal with them. I had an opportunity to go to work with a Title III grant at my institution, and they needed someone to run a learning center. It looked interesting, but I told them that I didn’t have a formal education in that area. They said, “Well, do you understand how to teach a history class?” I told them, “Well yes.” And they said, “That’s a good start. You understand how to teach, but we need to set up a center with tutors and things like that to help students do better in classes.” So what my background was, was that I went around joining all of the professional associations that I could, in order to review publications and go to conferences and learn on the fly. I didn’t have any formal preparation for another decade. At that time, I went to and participated in the Kellogg Institute at Appalachian State, and that is where I received my formal preparations.
That was really the extent of my formal preparation for developmental education. I always felt kind of embarrassed about that until someone else in the field said, “Well, David, you are a content area specialist.” I answered, “What’s that?” And this person said, “You know history, so you understand how a student should learn history.” I responded, yes but not through a formal preparation. And he said, “There are a lot of people inside of our profession that are transplants from other academic areas.”
Nolting: What is your history with NADE? You were president once, or was it twice?
Arendale: I got involved with NADE because of the on-the-fly learning process I mentioned earlier. I was in Kansas for the first decade of my career, where I was involved with one of the local chapters of NADE. I went to chapter conferences and national conferences, and then I made the decision to go to the Kellogg Institute. When I was there at the conference, at the month-long workshop, a number of us were having lunch one day, and we were talking about our futures. They all nominated me to run for president of NADE. I told them that they would all have to be on my cabinet and my major national committees. We all made an agreement. I went back and became president of my local chapter of NADE, then eventually ran for office after serving as a co-chair for one of the national conferences that was held in Kansas City. Back in the mid-80's, a path to the NADE presidency was helping to host national conferences, and getting some national recognition.
It was a wonderful experience. I like to tell people that my presidency was the greatest personal and professional development activity you can ever do. After you finish up, you look back on it and wonder, how in the world did I keep my day job and still do all of the travelling and do all of the work of being on the board. People ask me, “Wouldn’t you like to do this again?” And I look at them with a funny expression on my face and go, “Are you out of your mind?” Then I smile and tell them that it was a wonderful experience and everyone should get a chance to do it.
Nolting: Can you give us a brief history of developmental education, where it started, where it was 100 years ago, and where it is now? If I remember correctly, this was your dissertation topic?
Arendale: It was one of them. It was what they call “chapter two” of dissertation research, when you are doing your background literature search. I became fascinated with the history part. What I found out was that developmental education has always been with us. If you went back to the very founding of the Ivy League, they all had tutors provided for every single student. All of them were in a developmental grading course. The reason was, there was no formal preparation, no public schools. Before, affluent families would ship their kids off to England for boarding school. So, at the very beginning, 100 percent of students were developmental. This went on for a couple of hundred years. Jump all the way up to the mid-1850's. The University of Wisconsin, which is considered a very prestigious research institution, ninety percent of their students were in what was essentially an academic preparation academy before they were even permitted to take any classes. Why was that? There was no free and mandatory public education at the time.
So this whole thing about how developmental education was created because of the G.I. Bill after World War II—well that isn’t true at all. We have always had these services. Even today, at Harvard University, they have about ten percent of their students in a developmental writing course. Now they don’t call it developmental education, but essentially, because they deem these students below the standard for Harvard-level classes, they require them to take this course. I always like to think about who was initially responsible for developmental education. It was Harvard. They had the very first developmental math and writing and reading courses. Part of the reason was that they were also the very first to offer elective courses. They quickly figured out that students needed these courses to meet the standards at Harvard. Now, the ten percent of students who have to take this course today, they would probably be honors students at my first community college.
Academic preparation is relative. It all comes down to what are the institutions' requirements. One of the things I find disappointing when I look at the history of developmental education is that privileged people have historically had all the advantages. They are now second, third, and fourth generation college students, and they go to well-funded private or suburban schools. Now, you have a new crop of students—students of color, the historically under-represented, the economically poor students—who do not have all of that social capital. So the things that they need are the same things that students needed back in the 1600's and 1700's and 1800's. But public officials say, “We don’t need to provide these services for you.”
Developmental education is a sad political fight that has gone on for a long time. I have written about how the language of developmental and remedial education has been politicized. I think it is really sad that we don’t hold to the concept that all students are developmental. That’s why you go to college. Think of the slogan for NADE: “Helping the under-prepared students prepare, the prepared students to advance, and the advanced students to excel.” Developmental education helps students move along a continuum line.
Nolting: What is one of the most surprising things our readers might not know about the history of developmental education? I remember you talking once about how developmental education was used during the Civil War because they didn’t have enough students to attend universities?
Arendale: Yes. That is correct. We like to use academically under-prepared students as a way to boost enrollment. There were two periods when this really occurred. One was during the Civil War. In fact, there were a number of universities across the nation that set up boarding schools and high schools to bring in enough students to keep the doors open. After the war was over and enrollment started picking back up, they started closing these schools. The same thing happened again during the 1970's and 1980's when there was a decrease in enrollment at a number of institutions. They opened up more access for students, not necessarily out of the kindness of their hearts, but rather for the economic gain they could obtain from those students.
The sad thing that I have seen in a couple of modern examples is that some community colleges think they need to set up an admissions test for students. If they don’t score high enough, they’ll deny them admission. That is a significant discussion. We’ve never talked about closing the door to higher education. We’ve always said that there is always an appropriate place for you to start at. Well now some community colleges are receiving less money from the state, but are being overwhelmed by enrollment because four-year institutions are eliminating students. So community colleges are between a rock and a hard place. They are not receiving the money they need to operate, and they are being overwhelmed by the number of students who want to take classes. So now they are talking about [entrance tests].
This isn’t widespread, but my philosophy is that whenever I look at history, ideas precede actions. You are hearing discussions about how we should limit access to higher education in America, and I think that this is particularly disturbing.
Thoughts on Weger, Hooper, Meirer, and Hopthrow: "Mindful Maths: Reducing the Impact of Stereotype Threat Through a Mindfulness Excercise"
Post Author: Kim Nolting
As part of an ongoing effort to aggregate and discuss outstanding scholarship published within the past few years on math and math learning, we thought we'd quickly highlight a fascinating article published in 2012 in Consciousness and Cognition.
Weger, Hooper, Meirer and Hopthrow explore effects of stereotype threat, the pressure resulting from social comparisons that are perceived as unfavorable, The authors focus on women performing math tasks in the academic setting, specifically on math assessments intended to measure gender differences. The study hypothesizes that a five-minute state mindfulness intervention would counteract the stereotype threat on the female participants, as demonstrated by higher performance of the participants receiving the intervention.
[Note: “Mindfulness is characterized by a nonjudgmental awareness and attention to moment-by-moment cognition, emotion, and sensation without fixation on thoughts of the past and future.” State mindfulness is a short-term mindfulness accomplished through a mindfulness intervention, while trait mindfulness is more stable over time. (Kiken, Garland, Bluth et.al., 2015). (Kiken, Garland, Bluth et.al., 2015). ]
These researchers support their investigation based on the following research. First, for more than a decade, research has established that individuals who perform within a context where they feel stereotype pressure underperform. Many individuals allow evoked emotions from this stereotype pressure to reside in them, turning the messages of the stereotype into their own self-assessment.
Second, the emotive energy used in reaction to stereotype threats comes from the same source in the brain as cognitive energy, specifically working memory. The experience of stereotype threat also steals energy away from the brain’s ability to attend to a task systematically and efficiently.
Third, Weger and et.al base their experiment on research, which has shown that working memory capacity mediates the effect of stereotype threat on a woman's performance in a math test.
Fourth, state mindfulness intervention has been established as a powerful tool to help individuals monitor and constrain negative emotions and thoughts during a specific task and use endogenous attentional control. State mindfulness is a psychological construct “in which individuals experience their environment by focusing on the present in an unbiased and non-judgmental way,” (Weger & et.al, 2012). A drawback to trait mindfulness interventions is the length of time it requires and the detailed logistics.
Thus, the researchers in this study set up a 2 (intervention: mindfulness vs. no mindfulness) x 2 (Stereotype threat: activated vs. not activated) design. Seventy-one female psychology students took part in the study. Researchers addressed several possible interfering variables in their design.
Researchers used a well-established five-minute state mindfulness task, using a pre-recorded audio file that guides students through the process of eating two raisins. The intervention is designed to encourage participants to strengthen awareness of the present and to “drop in” on their actual lived experience, and then sustain it as best they can.
All participants completed the first math test, then the intervention group completed the five-minute mindfulness intervention while the other participants simply ate two raisins. The stereotype group was told the second math test was to explore why males are better than females in math. Then all participants took the second math test, followed by the Toronto Mindfulness Scale test.
The group difference test scores (mindfulness vs control group) revealed a main effect of mindfulness. The mindfulness group performed better on the second test than the control group. The predicted interaction of mindfulness and stereotype threat was significant in that the participants in the threat group performed significantly better on the second test after the mindfulness intervention than the non-mindful control groups. Read the article for other findings.
In the discussion, researchers noted that the mindfulness intervention was just five minutes, something which can easily be completed in the classroom. Only the students’ willing to exercise control could influence the outcomes.
It appears that the mindfulness intervention allowed students to dissociate the threatening cues they receive from stereotype pressure and reinterpret the cues so they can have a more positive motivation to show their strengths. In addition, the mindfulness intervention allowed students to use more working memory since it no longer had to combat as many negative emotions from stereotype pressure.
We know that with practice, good behaviors can become habit. So many of our students have years of negative experiences due to bad habits only to become part of the vicious cycle of negative self-esteem, repeating bad habits and negative results. Even though we are instructors and not counselors, it does not take much time to participate in the training of state mindfulness interventions with the purpose of using them regularly with our students.
The interventions must be based in state mindfulness to work, as seen in a previous article.
We would like to hypothesize that helping students with state-mindfulness interventions that they can use on their own will encourage them to also use productive study skills, particularly when the math is challenging.
This intervention can benefit all students, avoiding singling out those who are struggling. In fact, some students may be familiar with mindfulness practice because it has been integrated into many other contexts such as athletics and competition.
Many people allow emotions and subsequent self-perceptions to define themselves. Pair this with actual external criticism and we hear many students say, “I’m just not good in math.” We do not have the time or expertise to counsel them, but we can help them minimize anxiety and increase focus when they are with us in the classroom.
Weger, U.W, Hooper, N., Meirer, B. & Hopthrow, T. (2012). Mindful maths: Reducing the impact of stereotype threat through a mindfulness exercise. Consciousness and Cognition 21 471-475.
Today, we at the Academic Success Press Blog launch a new feature, which we hope will keep our readers abreast of recent events in the world of mathematics education. Every two weeks, we will aggregate stories from around the nation, which we find either interesting, important, or even distressing. Today, we present several recent stories about the transition between high school and college math.
Chicago Tribune: “New math course would aim to boost students’ skills in Elmwood Park”
Here, Pioneer Press reports on the efforts of a Chicago-area high school to prepare struggling math students for college placement exams. The school now offers a “mathematical modeling and application” course, which it hopes will help students avoid developmental mathematics courses during their first year of college.
Daily Miner: “Mohave Community College launches math readiness program”
Here, Aaron Ricca describes how an Arizona community college plans to help outgoing high school students determine their ability to learn college mathematics.
KOSU: “Should Oklahoma Require More Math in High School?”
Here, Oklahoma Watch and Jennifer Palmer cover a recent debate in Oklahoma between public officials regarding the amount of math courses students should take in preparation for college.
The Atlantic: “The Common High-School Tool That’s Banned in College”
Here, William Pang discusses the reluctance of certain universities to allow the use of graphing calculators. It also provides a brief but enlightening history of calculator ownership between the late-1970's and modern times.
KOMO News: “Why Stem is the Secret to Success—For Washington and Its Youth”
Here, KOMO-TV discusses, among other topics, a general aversion to math among young students. It is one part of an ongoing investigation into job availability and the long-term career choices made by incoming college freshmen.
Academic Success Press is proud to present the third and final segment of Dr. Nolting's interview with Jane Tanner, president of AMATYC. Here they discuss active learning, motivation, placement exams, and study skills. Enjoy!
Nolting: Earlier we talked a little bit about the “active learning process.” What role does active learning play in new math redesigns?
Tanner: It involves a lot of group work—actually meeting and discussing and picking each other’s brains—rather than a teacher walking up to the board, putting a problem down, and then saying “alright, everyone try another problem just like this” then “alright what did you get for an answer.” [This old method] loses people. In active learning, the teacher can actually move around the room, make sure that students are all working towards the problem, and ask thought-provoking questions.
Nolting: It sounds like this calls more on cognitive and modality styles…
Tanner: Exactly. What we are trying to do is address issues that are barriers to success. Active learning might be the way to go.
Nolting: Many math redesigns haven’t addressed the true roots of some students’ problems. Many of them have been underserved since elementary school. Some come to college drastically underprepared, others well prepared. How can colleges make up for this difference?
Tanner: That is a hard question. I attended the International Congress on Mathematical Learning this summer in Germany, and one of the last sessions boiled down to, and I am sure you have heard this, that college teachers blame a lack of preparation on high school teachers, the high school teachers blame middle school teachers, middle school teachers blame it on the elementary teachers, and the elementary teachers blame it on parents.
I don’t want to answer that way: but we do need to address that somewhere along the line students aren’t being turned on to mathematics. That means that they are more likely to not listen, to not prepare, to struggle. What can be done? Well, there are summer bridge programs, for one. These are programs—which might be for economically disadvantaged students—that give students more of a chance, sometimes by including study skills as well as math skills. This gets [math] back into their memory, as they have now tackled it more recently [before beginning their first college semester].
But that is another big problem: not all states require four years of high school mathematics. If you don’t like the math, and you only need three years, what do you decide to do in your fourth year? You don’t take it. Then you come into college and you need math. So where do you place? Developmental math. Students should take some sort of math course during their senior year of high school. That would really help. Also, colleges need to have some sort of placement exam or something else to identify when students are struggling and to get them into the right courses. I know representatives from my college worked with you [Dr. Nolting] at the first math summit. We ended up having a college skills course using one of your books. I think they ultimately wound up teaching those skills and strategies in each of the individual developmental classes. Also, if you try different pathways, and if you can get students through an algebra course and into something more interesting, they care more about the stuff that they will actually use in their careers.
In my presentation in Germany, I had a slide, which was taken from a local newspaper from January , which stated that only 40 percent of students who graduate from high school in New York State were ready for college. This was a statistic released by the New York State Department of Education. [The researchers] featured an aspirational number, which meant that if your students scored at least a 75 on an English regent exam and 80 on a math regent exam, you were considered ready for college. Only 40 percent in New York were considered ready. Research from April 2016, suggests that only a third of U.S. high school students are ready for college-level math coursework and reading. The performance of the highest achieving students is improving, but the lowest achieving students are performing worse than ever. It is definitely a problem.
Nolting: Some states no longer require any placement tests in math, English, or reading. What are your thoughts on that?
Tanner: We had a mix up about a year ago, when we changed our instrument [of placement], and we had to create something like 26 sections of our basic math class based on this placement exam. We had to scramble to find enough teachers to teach the courses. We now only use a placement exam if a student has been out of high school, or if they transferred in from another college. At a department meeting, it was reported that this seems to be working—students seem to be getting into the correct class.
Nolting: Also, math departments work closely with learning resource centers and math labs. What role do they play in helping unprepared students?
Tanner: The math lab we use, generally students go to it to get help on problems from the classes in which they are currently enrolled. I don’t think this involves working on other skills. But we do have something else called a diagnostic center. If you take a placement exam or you don’t like your placement, you can go to the diagnostic center and they will give you additional testing and give you packets to work on so that you could get through a beginning algebra class or even an intermediate algebra class through diagnostics and not have to take it as a course. If you do this during the summer, the diagnostic center can give you some work to do, and you have to pass a final exam, but this could save you from having to take a semester course.
Nolting: Despite research to the contrary, an assumption still exists that students are locked into certain behaviors—one is the type of student that one is and nothing can change this. I bring this up because in the past I know we have talked about how to determine how motivated students are. Some people assume that students are inherently motivated or unmotivated. Students often buy into this philosophy, especially when they think they aren’t good at math. What role do you think motivation plays in college mathematics, and how can you convince students to prioritize math?
Tanner: I think there are two types of students: students who come out of high school and nontraditional students. I think nontraditional students have gone through so much to come back to college.
I really like working with mature female students who have been told in the past that they aren’t good at math and at some point started to believe it. They get to me five, ten, fifteen years after high school. When I still taught in the classroom, [some of these students] would come up to me and say, “Oh my God, I never understood this before, but with you I understand it. I wish I had had you in high school, you are such a great teacher.” When this happened, I would say, “Yes, thank you. I am a good teacher, but I can’t take all the credit.” These students are older now, they have goals. They see what they want to do. They more than likely have children, and they don’t want to let them down. They want to show them that they are worthy of an education, that they can accomplish goals too. It means a lot to them now, while it didn’t mean much fifteen years ago.
I think that motivation is there [for these students], and we need to figure out a way to motivate our students who are coming right out of high school in the same manner. They haven’t lived live life like nontraditional students. They come to college with the same bad habits they had in high school. If they didn’t do their homework in high school, then they aren’t going to do it in college. We need to get them motivated, so that they can become successful.
Some of these new courses we are working on, in terms of Pathways and emporium model, may just do that. Certainly study skills play a role in this. Again, if they didn’t know how to study in high school, they won’t know how to study in college. They need to be taught how to learn math if they don’t know how to do it.
Nolting: Right. As you said earlier, the answer might be to add study skills directly into math courses. Research has shown that dedicated study skills courses do improve success rates of students—but it is hard to get students into these courses.
Tanner: Right. We used to have an hour long workshop on math anxiety—a word you don’t hear too much anymore—and I’m not sure how many people ever took it. But I do believe that you need to put study skills into these courses, because students need to know how to study. Tell them what worked for you in school. Or let your class work out what works for them. Maybe it doesn’t necessarily have to come from teachers, but rather from their peers.
As promised, here is the second segment of Dr. Nolting's conversation with AMATYC president, Jane Tanner. Here, they discuss the state of the Math Pathway system. We will publish part three the week after Thanksgiving.
Nolting: I’d like to discuss the current status of the Pathway system. For those who don't know, maybe you can start by describing what "pathways" are?
Tanner: It describes different ways to get to your first credited math course. It is not [the traditional method] where you take college algebra, then intermediate algebra, then precalculus, and so on. Many of our students do not need calculus but they do want a math course that doesn’t involve the sort of heavy mathematics that students tend to dislike. So what has been worked on is a different type of course that will still apply algebraic constructs but make them more applicable to life, more hands on. Not like the old math of [household] finances and that sort of stuff, but rather [these courses] are designed to give students an “Aha!” moment, like "I might be able to use this sometime." I don’t know if you know this, but have your heard of the Seattle 15?
Tanner: Well I was one of the fifteen. I was in the right spot at the right time. It was amazing to be in a room with fourteen other people and a facilitator, and just brainstorm. We knew the status quo was no longer acceptable and that we needed to think outside of the box. We developed this way of thinking where you don’t need quadratic equations or whatever, but you could help students out and help them get through curriculum they are actually interested in. This led to another meeting a year later. We met at Carnegie and continued to develop some of these exercises. It was like watching the birth of a baby: it has grown and grown. I think at one point Carnegie and the Dana Center were working together, but they somehow split off. AMATYC has its own “New Life.” They are all encompassing the same things, but they are all a little bit different. We have a lot of authors out there who are buying into this, which is really helping us make our students become more successful.
There is always room for improvement. Earlier, you mentioned students who want to change majors. We do offer a course at my school [to address this] that is on the Quantway model. It is a credited course, so students can go from a non-credited course to a course similar to a beginning algebra placement. They can then go into a precalculus course afterward. But we can’t always make our decisions based on “what happens if students change their minds.” We can do our best to work with these students, but, like fifteen years ago, sometimes a major change results in a longer stay in college.
Another problem I see with the Pathway system is that our counselors and advisers do not understand it at all. They, at least at my school, used to have trouble placing students into the correct courses before pathways; now that we have introduced a few more liberal arts math classes, in addition to our pathways classes, it is really confusing. There needs to be an education system put in place for the people who advise our students into our courses.
Nolting: I totally agree. When I work with colleges, I get that question all the time. One of the responses is: even in the previous days when you went from intermediate algebra to a finite math class, and you were close to graduating with a liberal arts degree, then halfway through the finite math course you decided you wanted to make money so you changed your major to business, well at that time you had to go back and take college algebra through applied calculus. So it is kind of similar to what we are doing now, but it looks like your college has provided a different pathway, just in case a student changes his or her major.
Tanner: We have pathways similar to what other colleges are doing with Quantway, but we still [allow students to enter] a beginning algebra course and then get into one of two different liberal arts math classes, which are credit bearing. So if you don’t want to do the pathway, you can still take beginning algebra. But it is our hope that we can phase beginning algebra out, at least in the number of sections we offer. Of course, if you are going into a major that needs calculus, then you are going to need beginning algebra. But if you are not in that path, then go the other way.
Another thing to consider, with the new Pathway systems--maybe students are going to get turned on to the math they take. Maybe these systems will turn their dislike of math, or their thoughts about how they aren’t good at math into thoughts of “I can do well in math!”
Nolting: Right. I have had students who didn’t like math, got into the pathways, then took the liberal arts courses with Quantway. They made an “A” or a “B”, and all of a sudden they considered going back and trying to take intermediate algebra. If they previously wanted to be a pre-med major, but thought they couldn’t handle the math—they now feel confident enough to go back and try.
Tanner: I think it builds up their confidence, if they give it a chance. Because it is different and students aren’t used to it, some don’t like Pathways. More so for the ones, at least the ones I know, who go from pre-algebra into one of our two liberal arts classes. If they are not successful, they just say give me an “x.” At least I can cope with an “x," even if I don’t understand it. But in our other courses, we do other things like voting theory, circuits, and other topics. Some people aren’t comfortable with these things, so they go back and take traditional courses. But what I think is important is that we do offer choices so students can decide on their own.
Nolting: The key is, the more realistic choices we give students, the more likely they are to complete a math course. We also have students going into statistics, and they find out that they don’t hate math as much as they thought they did.
Tanner: Right. We also have a liberal arts statistics course at my college. It is not Statways. Nursing students take it, criminal justice majors take it. A course like that is good for anybody to have, not just students interested in math. In the common core, it seems that things are moving toward more of a statistical understanding—so that is how we address the problem at my college. But we are investigating whether or not we want to implement Statway. We do have somebody coming in November to a meeting we are going to send representatives to—and their school does offer both Statway and Quantway. We are going to send three or four people to go and listen. We are going to pick his brain to see if that is a good way for us too.
That concludes Part Two! Click here for Part Three.
Post Author: Kim Nolting
As with many psychological and social constructs, the construct of mindfulness is often described differently once it becomes operationalized into a specific context, in our case during the first five minutes of class into the learning and teaching process. Brown and Ryan provide an overview of mindfulness in their introduction which is detailed enough to understand and apply to teaching and learning. Their research design, on the other hand, was detailed with five different studies. If interested, spend a little time and read each one.
Brown, Warren K., and Ryan, Richard M. (2003). The benefits of being present: Mindfulness and its role in psychological well-being. Journal of Personality and Social Psychology 84 4 (822-848).
Nature of Mindfulness
The most common definition of Mindfulness is “the state of being attentive to and aware of what is taking place in the present" (Brown and Ryan, 2003). Awareness is the background “radar” that continually manages the inner and outer environments. We can be aware, however, without focusing intently on a single aspect of the environment. Attention is focusing on a specific aspect or piece of the present environment. Brown and Ryan describe it as follows, “attention continually pulls ‘figures’ out of the ‘ground’ of awareness, holding them focally for varying lengths of time” (Brown & Ryan, 2003). Mindfulness is enhanced attention during which a person is capable of disallowing other distractors to interfere with focus.
Brown and Ryan discuss several distractors which can turn mindfulness into mindlessness. First, rumination of past experiences and their emotions/thoughts can distract a person from focusing, attending to in a mindful manner. Second, anxieties or fantasies about the future also distract meaningful focus. Third, a person can have so many activities and tasks going on at one time that can detract from focus. Fourth, focus can be detracted when a person acts compulsively or automatically without thinking about the behavior. Fifth, sometimes a person refuses to attend and focus on the present environment because she wants to avoid any of the negative thoughts or emotions the present situation might evoke.
Brown and Ryan clarify Mindfulness by relating it to another construct: emotional intelligence. Emotional intelligence includes “the perceptual clarity about one’s emotional states,” (Brown and Ryan, 2003). Part of learning how to keep the above detractors from interrupting mindfulness is the willingness to be aware of them. Mindfulness involves perceiving the stimuli in the environment as they are, without detractors misinterpreting them. A person who uses mindfulness is able to identify when emotions or thoughts begin to detract focus on the present and then interact with the emotions or thoughts in a way to remove them from the present environment. Brown and Ryan also discussed how this component of mindfulness is important for another vital skill for success, self-regulation, which relies on a person’s ability to be insightful regarding their own emotions and thoughts in order to evaluate the benefits of a behavior and then adjust if necessary.
Among the many findings, Brown and Ryan were able to state that mindfulness, both trait and state, contribute to autonomy, defined here as “behavior that is fully endorsed by the self,” (2003). A person who is maturing in the art of mindfulness knows her values and interests and lives day-to-day based on these values; subsequently a person with identified values and interests can self-regulate behavior that meets personal goals.
Brown and Ryan refer to other mindfulness literature which emphasizes the important of a person being non-judgmental of his emotions or thoughts when interacting with them with the purpose of putting them aside in order to focus in the presence as it is.
Finally, Brown and Ryan state how mindfulness can be developed with practice, increasing the value of it.
Kim Nolting’s Response
While studying Brown and Ryan, I thought of past college students who constantly struggled. Their minds were their own worst enemies. For instance, rumination about negative experiences with math instructors, family criticism, self-criticism, embarrassment in front of peers, tunnel their way into their thoughts. These ruminations and worries about the future do not take place solely in the classroom or during tests. Students can ruminate and experience anxiety when they purchase their math books. The cashier can even evoke anxious thoughts when she tells math students not to write their names in the books in case they return them the next week. Students can get anxious when they receive an email from the instructor asking them to review the first chapter before classes begin because they should already know the information. During the first class, they can think destructively when they see that chapter one was just a review for most of the students but not for them. For some students, math anxiety creeps in by just opening the book to study.
These ruminations and worries about the future can also trigger another detractor Brown and Ryan mentioned--avoidance behavior like procrastination. Who likes feeling anxious?
Once a college counselor referred a seriously anxious student to me in order to help her with some assignments. She shook the entire time and struggled focusing because her anxiety was more than just an emotion. She had allowed it to become her state of being. We made some progress but not much since her anxiety was stealing energy from her working memory. Fortunately for her, our college had at least seven counselors and only about 700 students. A counselor was able to work with her throughout the semester.
What about students who do not have the option of counselors on campus?
What can we do as instructors who are not trained as counselors?
Jane Tanner, current president of AMATYC, was kind enough to speak with Dr. Nolting early last week and the ASP Blog is now proud to present the first segment of their lengthy conversation. For the sake of context, we have provided links throughout the text for particular documents discussed during the conversation.
We particularly encourage you to download and read the Common Vision report, which was a joint effort between AMATYC, AMS, ASA, MAA, and SIAM.
Also, please visit AMATYC's great Webinar website!
Nolting: Let me start by asking a question we like to ask to all of the national experts we interview for this blog: How do you see the current state of Developmental Mathematics at the national level?
Tanner: My opinion is that it is in a state of flux. That is my opinion, not necessarily that of AMATYC or anyone else. A lot of colleges out there know we need to change what is currently being done, because the current success rate in developmental mathematics is not very great for students. These schools know something needs to be done—these are the forward thinkers that are willing to try new things and take risks. There are others out there who want to continue to do the same old things, because that is what they are used to, and they are not as willing to take risks. My opinion is that you need to be willing to try something different. You need to keep in mind what is best for your school and students, not what is easiest for you. My college at Onondaga, which is part of the State University of New York system, was one of the first to take part in the Quantway pilot, and we are still quite active in doing that. We are hoping to convince more of our faculty to develop the strategies so that they will be able to teach these classes for us. I know that this is a priority for our provost. I had a conversation with her a couple of weeks ago, and she wanted to know how we could encourage more of our faculty—specifically adjunct faculty—to get turned on to teaching these courses. The answer to that, is that you need to have training available. When these teachers start to see results, they’ll want to teach these types of course.
Nolting: I know what you are saying. Some colleges believe that no change is progress. Other colleges believe progress can't happen without change.
Tanner: Yes. One thing that is in the Common Vision report, is that the status quo is unacceptable. I happen to agree with that. We have had a curriculum redesign group going on in my college for at least five years. Sometimes it feels like we are going around and around and around in circles. We are very fortunate that we are doing the Quantway pilot, but we are also still investigating other things (like the emporium model) for our students so that if they start a course, and they can get done faster in it than the traditional class, great. Then they can start the next class afterwards. Or, if they need more time, they can take it another semester and not have to start over again, so that they can just pick up where they left off the previous semester. So we are trying to do different things, always with the students in mind.
Nolting: You’re totally right. Research shows that you have to offer [redesigns] in several different ways. One way doesn’t really work, but a variety of ways does. I also want to ask you a quick follow up question. Some developmental students are now being placed directly in first credit courses. You see this across the country. How do you see the current state of these first credit courses?
Tanner: Well, the term “first credit course” is kind of hard to define. It may be one thing at my college, and a different thing at another college. What we are trying to do is make a student’s pathway from a developmental math class to a first credit math class as painless as possible. That is what some of these new strategies are doing. To get them through so that developmental math is not a stumbling block. There is a lot of data out there that talks about developmental math being “the killer of students’ dreams.” [They say this] because students can’t pass developmental math and therefore they can’t major in whatever they want to major in, and then they drop out of college, and they don’t achieve their dreams. That is not a good reputation to have. We want students to be successful, and that is why we have to consider a number of different ideas on different classes, both at the developmental level and at the first credit level. If a student is going into something like criminal justice, they probably don’t have to take a course where factoring polynomials is crucial. I would rather have them have a better understanding of the math in their everyday life or whatever they need to do to do well in their job performance. But I don’t think factoring polynomials or the quadratic formula helps them with that.
Nolting: One of the things we discussed with Tanya Paul last year involved how the redesign movement has shifted the paradigm for developmental mathematics by opening up formerly rigid pedagogical programs for adaptation, or by making room for entirely new plans and strategies. It seems one byproduct of this is that we now have countless intelligent and forward-thinking people offering solutions, which don’t always line up with one another. How do you think institutions should go about choosing a new design, or, for that matter, what should institutions do if they are torn between different designs? How do we avoid chaos as pride and conviction inevitably seep into this process?
Tanner: You have to buy in to any type of change. This has to be true both of the administration and the department members. I don’t think [a redesign] is going to be successful if it is coming from the top down—in other words that it is mandated from the administration. Sometimes administration does not know what they are talking about in terms of developing students who are successful in mathematics. It is not bad that there are different paths out there. You need to research what is out there. You can visit other schools that are using a certain method that might work for you, or attend the AMATYC and NADE conferences where there are other people going through things that you may be going through. There are a lot of different models out there, all in addition to the pathways focus. What needs to be done is that you spend enough time investigating so that you choose the best thing for your college—but you can’t necessarily take forever to do it, because then you aren’t accomplishing anything either.
Nolting: How is AMATYC helping with this process?
Tanner: As you know, we have our annual AMATYC conference. We have Webinars on pathways. We also provide access to information from other organizations out there like Carnegie and the Dana Center. The AMATYC board is kept up to date on these. As president, I make sure I include agenda items that talk about the different things that are out there. This is so that the board is knowledgeable and can pass this information along at regional meetings, or when any one of the schools in their area contact them. I think the best thing we can do is to stay current ourselves. We come up with position statements. A big one right now, for instance, is that intermediate algebra is not necessarily the prerequisite course for a student’s first credited math course. That took quite a while to get through. But that position statement allows an instructor to go to their administration and say, “Look a student does not need to take intermediate algebra, they should be allowed to take a pathways course of some sort, so that they can move on and be successful in whatever career path they pursue.”
Nolting: You have mentioned a Common Vision statement a few times. Do you mind going into more detail about what, exactly, that is?
Tanner: Yes. It was a report that involved representatives from five different organizations: AMATYC, AMS, ASA, MAA, and SIAM. I’d like to think that these are the key players in undergraduate mathematics education. Whereas AMATYC deals specifically with math in the first two years of college, there is actually math in the first two years in two year colleges, community colleges, junior colleges, universities, regular colleges, etc. We are sort of rebranding ourselves. Even though our name stands for American Mathematical Association for Two-Year Colleges, we like to think that we are actually representing math that is taught in the first two years of college, not just at community colleges. So we are trying to concentrate on getting other colleges involved with AMATYC that would not traditionally be considered community colleges.
Anyway, the five organizations [mentioned above] took part in creating this report. I believe it came out last year, 2015. It features an introduction, existing recommendations, common themes, curriculum, course structure, workforce preparation, and faculty development. It also talks about moving forward—how there should be short courses and workshops, curriculum development, policy initiatives, and public relations. It is a very interesting read. It quotes a lot from different famous documents from those five organizations. Again, I am happy that [AMATYC] is being seen as a player in how math is taught at the college level—even though we focus on the first two years of college. We are being recognized as knowing how math should be taught in the first two years of all [types of] colleges.
Nolting: Right. Because it is the first two years of college that get students into Calculus 1, 2, and 3.
Tanner: Right. You have to get there somehow. So [the Common Vision Statement] is kind of a neat partnership between these five organizations. In the introduction it presents a number of interesting statistics. Each year only 50% of students earn a grade of an A, B, or C in college algebra. That is kind of sad. Women are almost twice as likely as men not to choose to move beyond Calculus I, even when Calculus II is a requirement for their intended major. In 2012, 19.9% of all Bachelor’s Degrees were awarded to underrepresented minority students (9.5% to blacks, 9.8% Hispanic); however, only 11.6% of mathematics Bachelor’s Degrees were awarded to underrepresented minorities (4.9 to blacks, 6.4 to Hispanics). Failure rates under traditional lectures are 55% higher than the rates observed in more active modes of instruction. So all of that is right in the introduction. It is a hook that gets you more interested in how we can address these situations.
That just about wraps up Part One! Click here for Part Two!
Findings in Bellinger, Decaro, and Ralston's "Mindfulness, anxiety, and high-stakes mathematics performance in the laboratory and classroom."
Consciousness and Cognition recently released an interesting article on how "mindfulness" affects performance in the classroom. We were interested in enough in their results that we thought we would pass on their findings to our readers. Please seek out the original work for further detail in:
Bellinger, D. B., Decaro, M. S., Ralston, P., (2015). Mindfulness, anxiety, and high-stakes mathematics performance in the laboratory and classroom. Consciousness and Cognition 37, 123-132.
Authors Bellinger, Decaro, and Ralston designed two studies to determine whether mindfulness interventions will benefit math students taking high stakes math. Study one specifically tested the relationship between mindfulness and state anxiety, and subsequent math performance in a laboratory setting. Study two applied the same model to a cohort of first-time freshman who declared engineering as their major and enrolled in a calculus course. Study two also applied the original question to both low -stake math such as homework assignments and high-stake math such as tests and quizzes.
More specifically, Bellinger, Decaro, and Ralston examined the concept that mindfulness improves the emotional response to testing situations that provoke anxiety, which in turn frees up working memory and subsequent higher performance on math tests. They examined whether mindfulness increases performance on high-stake math by reducing anxiety.
The researchers were motivated to conduct these studies because too many students in the STEM (Science, Technology, Engineering, and Mathmatics) courses underperform due to anxiety. As a result, many of them drop out of the STEM programs.
Research Theoretical Basis
Bellinger, Dearo, and Ralston based their studies on the same research base as Brunye, T., Mahoney, C., Giles, G., Rapp, D., Taylor, H., & Kanarek, R. (2013). First, mindfulness is a state of mind that focuses on the present experience without bringing in thoughts and emotions from the past into the present experience, as well as not bringing emotions and thoughts about the future into the moment. Mindful people fully interact in the present moment. Since around 2000, research has established that mindfulness psychological well-being decreased anxiety and depression, reduced stress, increased emotion regulation. Mindfulness is associated with decreased negative cognition and rumination. Mindful individuals are able to let anxious thoughts pass through their minds without further rumination and negative thoughts. In addition, mindfulness increases cognition in that it increases self-regulation, attention, and working memory. Based on this research, educational researches began to apply mindfulness in the educational context. Soon, educational researchers found that mindfulness was correlated to the willingness to learn.
In the context of academic anxiety, mindfulness has shown to reduce state anxiety like test anxiety. Since anxiety and attention/focus use similar networks, minimizing anxiety frees up working memory, and subsequently can improve academic performance (Brunye, Mahoney, et.al. (2015).
This study tested the relationship between mindfulness and state anxiety, and subsequent math performance in high-pressure testing situations in a laboratory.
Participants were undergraduate students (N=112) in a psychology course who were unfamiliar with the modular arithmetic system and scored 50% or higher on a practice test which was administered after instruction about the rules to complete modular arithmetic.
Researchers created the high-stake environment. Participants were told that the computers recorded all their practice work up to this point. Participation payment would be based on whether they improve in speed and accuracy on the test by 20%. Secondly, the participants were told they had a partner in this test situation. Both of them had to perform at least 20% or better than their own individual practice performances in order for them to receive their participation payment. (At the end of the experiment, all received payment despite performance results.)
Researchers used the following self-report measures:
Mindful Attention Awareness Scale (MAAS; Brown and Ryan, 2003)
Toronto Mindfulness Scale –Trait (TMS-T; Davis, Lau, & Cairns, 2009)
Toronto Mindfulness Sale – State (TMS-S; Lau et al., 2006)
State-Trait Anxiety Inventory (STAI; Spielberger, Gorsuch, and Lushene, 1970) State portion.
Participants completed the mindfulness assessments (MAAS, TMS-T). They received instruction in how to do modular math with practice opportunities. Students who scored 50% or higher on the practice test continued on. They were told the high stake cover story, and took a modular arithmetic test. Afterwards, they participated in an unrelated task (post-test questionnaire, TMS-state and STAI). Finally, they were debriefed.
This test applied the same mediation model from study one to a calculus course with students who declared engineering as their major. This study also determined relationship of mindfulness to low-stake math such as homework and high-stake math such as tests and quizzes. This study also explored the general perception of anxiety toward test-taking.
Participants (N=248) were first-time, full-time freshman undergraduate engineering students enrolled in a calculus course who gave consent to the study.
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.