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
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.
Thought's on Brown and Ryan's "Mindfulness and its Role in Psychological Well-being.
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.
News Roundup from Around the Web
Hello readers! Today we thought we'd pass along a few links to various articles about math, its application in the classroom, and the students who have chosen to dedicate their lives to it. Enjoy!
Arizona State University
Arizona State University recently posted a fascinating interview with one of its award winning students about his decision to dual major in mathematics and physics. The student, Tin Phan, has a lot of interesting things to say about race and the general expectations he believes certain communities have in terms of potential career paths. "Aiming to be a mathematician is unthinkable for a vast majority of Vietnamese," he writes. "In my community, being either a doctor or lawyer is the only way for a person to be considered successful. So it is natural that although I have always been good at math, I never entertained the idea that I would spend my life learning it." Read more, here.
Throughout our conversations with numerous national math experts in recent months, we at the Academic Success Press Blog have noticed a common theme develop regarding whether or not instructors must find ways to spoon feed their students undesirable material. This article details the efforts of Dr. Eugenia Cheng to literally describe complicated mathematical concepts through the discussion of food! "While math is often seen as a dense, impenetrable, treacle-like subject," writes Elaine Burke, "Cheng’s energy and quick wit makes it as light and fluffy as a flaky pastry." Read more, here.
If food doesn't quite pique your interest, then here is another article that promotes a comparably artistic method! "Math education needs to show math as an art, with patterns that can be found, connections that can be made, relevant and irrelevant questions that can be answered, and logical thinking that can be used," writes Hilla Rogel. "No one really knows why math is so good at explaining the world, and that is why it is magical. When teachers transfer this passion to their students, during Mathematics Education Month and every day, it can be a beautiful equation." Read more, here.
Thoughts on Donovan and Whetland's "Placement Tools for Developmental Mathematics and Intermediate Algebra"
In 2008, the Journal of Developmental Education published an interesting article, written by Whetland and Donovan, which explored the placement process for the developmental mathematics department at an urban college in Ohio. The article particularly focuses on the use and efficacy of the ACT Mathematics and COMPASS Domain I (Algebra) placement scores for students entering college-level Intermediate Algebra courses.
The authors found that both of these tests are fairly accurate predictors of success in Intermediate Algebra; those students who perform well on the ACT and COMPASS tests are “more likely to succeed than fail.” This is important, they argue, for multiple reasons. First, they cite a study that shows that 22% of students in the 71% of colleges and universities that offer remedial math courses are either placed in or choose to enroll in one of these courses. From an institutional standpoint, this means that the efficacy of placement tests reverberate throughout a college’s entire mathematics platform. Second, for the students themselves, “the extent of a student’s need for remediation is inversely related to his or her eventual completion of a degree” (a 2005 quote they cite from Desimone, Smith, Baker, and Ueno). Those students who only need to take one remedial course are much more likely to persist through the process than those who are forced to take many remedial courses. Finally, the authors point out that remedial students acutely feel the effects of rising tuition costs, as they often need extra time to graduate. For students receiving financial aid, this puts an enormous amount of pressure on them to pass their first math course, as they risk losing aid upon failure.
With all of this in mind, the authors studied 1,694 students (49.1% female, 50.9% male), most of them first-generation college students, as they entered an Intermediate Algebra course. All of these students either scored highly enough on their ACT tests or passed a COMPASS placement test during orientation to earn entry into their respective courses. The authors then compared individual ACT and COMPASS scores to eventual success percentages. The authors found that those students who received grades of A or B in their Intermediate Algebra courses had significantly better scores on their placement exams. Students who received a C, however, did not perform markedly better on the placement exams than did those who received a D, though these same C students did drastically outperform those students who eventually failed their respective courses. These scores demonstrate, the authors contend, that effective placement exams directly correlate to a student’s ability to succeed in Intermediate Algebra.
Ultimately, the authors conclude that this information proves the overwhelming need for remedial math courses; however, placement exams must prove effective, as placing properly prepared students into remedial courses they don’t need wastes resources, while placing them in courses for which they are not prepared not only wastes resources but also largely jeopardizes a student’s chances to graduate. Universities must, then, set placement exam cutoff scores into extremely precise spheres, which do not allow borderline remedial students to slip through the cracks.
For more, see:
Donovan, W.J., Whetland, E.R. (2008) “Placement Tools for Developmental Mathematics and Intermediate Algebra.” Journal of Developmental Education Volume 32, Issue 2, Winter. Pages 2-11.
Hello Readers! To celebrate the success of the 2016 National Math Summit, Dr. Nolting wanted to briefly discuss the history of the conference and how this year's conference was possibly the best yet! Before we get to that, however, he wants to thank the following people:
Dr. Nolting would like to thank the co-chairs: Taunya Paul, Julie Phelps, and Rebecca Goosen; the committee: Nancy Sattler, Beverly Vance, Wanda Garner, Linda Zientek Barbara Illowsky, and Jane Tanner; the panelists: Hunter Boylan, Rebecca Goosen, Paula White, Jane Tanner, Cinnamon Hillyard, April Ström, Amy Getz, Julie Phelps & Barbara Illowsky; and the panel’s moderators Julie Phelps and Rebecca Goosen.
And now, without further ado, our chat!
ASP Blog: I’m curious as to how the National Math Summit originated. Can you talk a little bit about the event’s beginnings?
Nolting: The whole idea of developing a math summit came about probably in 2011. Many states were beginning to mandate different redesigns and instructors were coming to different professional organizations—mainly NADE, MAA, and AMATYC—and saying that they didn’t know how to do the redesigns that they’d been told to implement (accelerated, emporium model, modular, or contextualized courses). At some point, I talked to Hunter Boylan, who is head of the National Center of Developmental Education, and I said, “We really need a math summit to talk about ways to help students become more successful in math classes.”
The idea was that a lot of these organizations have what I call the “puzzle pieces of math success.” But we had never had a chance to put all of these pieces together. I talked to Hunter and we tried to get some support for a potential summit. It took us about a year, and eventually I talked to Jim Roznowski at a NADE conference. He was president of AMATYC at that time. He pretty much agreed in 2012, that we needed to get everyone together. At the same conference, I talked to Rebecca Goosen. At the time she was president of NADE. I asked her if NADE would be willing to join us, and she said yes. Then we asked Julie Phelps to help us because we needed extra help and she was a member of AMATYC, NADE and MAA and was considered a leader in these organizations.
As I started talking to different organizations such as the Carnegie Foundation and the Dana Center, the question became “How are we going to make this summit different from regular conferences?” Together we came up with the idea of not just doing the workshop itself, but also having time for faculty to meet with mentors and develop a math success plan. After getting help from an expert, faculty could go back to their college and use what they learned to help to develop curriculum. In November 2013, at the AMATYC conference, we had the first national math summit.
ASP Blog: Did it meet your initial expectations?
Nolting: At first we thought we’d only have 50 people. That’s what we agreed upon. Later on, we thought maybe 100 would show up. Then we had people calling us from all around the country trying to get in. We had the opportunity to bring attendance up to 150, but we still wound up turning away about 300 people who kept calling and wanting to get in. We couldn’t host any more than 150 because of the lack of space.
It wound up going very well. We field-tested the ideas of workshops and having mentors helping faculty develop their college Math Success Plan for College Innovation. The main comment after that summit was: “When can we have another one?”
After that we had a series of math summits at various conferences that were mainly panel discussions. The panel discussions went pretty well, but then people kept asking for another workshop format. This last March, NADE and AMATYC sponsored one as a NADE pre-conference. We had the panel, and this time we divided it up with different members from different organizations. We decided to have two strands. One strand was on redesign; the other was on assessment. Now we were able to address concerns from our colleagues who were saying, “We did what we were supposed to do, but we don’t know how to assess it”; or, “We did assess it, and it didn’t work too well. What now?” So this time we offered the redesign track and the assessment track, so people could have their specific needs met. Again, we thought we’d have about 200 people. We wound up with about 300.
ASP Blog: So the most recent summit went well?
Nolting: Yes. The workshops were really well attended. People had positive comments. Again we had time where mentors worked individually with instructors. In fact, the instructors actually signed up for different mentors based upon what they liked, based on their own issues and needs. It was very successful.
The reason I’m talking about this is that it has become clear through the math summits that working together is important. Between all of the organizations involved— NADE, AMATYC, the National Center for Developmental Education, the Dana Center, Carnegie Foundations, Mathematics Association of America, and myself— we have the answers to a lot of the questions faculty are dealing with. If we all get together and put the puzzle pieces together we can find a blueprint for math success.
When we start looking at what the Summit actually does, it develops a community of experts to help our math faculty and administrators find more success with their students. Our goal is to have students take math until they don’t need to take it. We want them to be successful in college, then in their careers. The whole point of the National Math Summit was to get instructors together with the best experts in the country to get trained on how to either assess or how to develop a redesign.
Once students are placed into accelerated courses, modular courses, emporium courses, where they get less instruction, we have to teach students to become better learners. The research now shows that affective characteristics of students’ learning is now responsible for 41% of the variance for their grades. We can’t ignore this anymore. We have to make students better learners. That transcends all curriculum. This makes it more important to add academic support through math labs and learning resource centers to compensate for the imbalance between math skills and the prerequisite requirements of math courses.
ASP Blog: What does the future hold for potential National Math Summits?
Nolting: What we want to do in the future is to use the National Math Summit to figure out the needs of instructors and administrators that we maybe haven’t thought of yet. We did ask participants this at the end of the discussion. Also, when we asked whether or not we should have another National Math Summit, over 100 people raised their hands. It looks like we might do it again at AMATYC in 2017. That is not for sure, but there is interest in doing it.
ASP Blog: Is there anything else you want to add?
Nolting: Another point I brought up is that we need to really focus on repeating students. We need to meet with students, and we need to use assessment to figure out what is blocking their ability to learn math. We need to determine their study skills, their motivation, their locus of control, their anxiety levels. Then we need to form specific math success plans. If we can have repeaters obtain the same or greater amount of success as their first time peers and then move on to their next courses, we will see a marked improvement in our overall success rates and graduation.
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