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
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.
American Mathematical Association of Two-Year Colleges presenter, Senior Lecturer-Modular