Academic Success Skills in Introductory College Mathematics
Explicit attention to academic success skills can effectively complement math pathways and corequisite reforms to support students’ development as successful and independent learners. The MIP leverages research about growth versus fixed mindsets, the nature of memory and expertise, the integration of academic and social communities, academic identity, stereotype threat, and study skills to equip instructors with the tools to help students become more effective learners.
Dweck and Legget (1988) conducted pioneering work on the interaction between individuals’ views of their intelligence and abilities with persistence and goal orientation. Individuals who viewed intelligence as innate and fixed typically adopted performance goals and tended to persist only in cases of perceived success, avoiding challenge when they perceived failure. In contrast, individuals who viewed intelligence as malleable and able to grow with use typically adopted learning goals, and tended to persist in seeking challenge regardless of success. Growing evidence supports this model generally, and specifically in the context of mathematics instruction (Blackwell, Trzesniewski, & Dweck, 2007). Aronson (2007) found the effects of these self-theories are magnified when gender or racial stereotypes of performance are activated in the learners, raising particular concerns for the performance and persistence of underrepresented populations in academic pursuits. Fortunately, these mindsets are not immutable psychological traits, and specific supports enable students to reconceptualize what it means to do mathematics and to be proficient at mathematics (Middleton, Tallman, Hatfield, & Davis, 2015). Other techniques, such as praising effort and process rather than success (Cimpian, Arce, Markman, & Dweck, 2007) and attributing mathematical talent to hard work and passion rather than innate ability (Good, Rattan, & Dweck, 2007) can also foster a growth mindset among students. In caution, directly focusing only on stereotypes can trigger rather than ameliorate stereotype threat, but it can enhance success when coordinated with the development of a growth mindset and when past underachievement is attributed to environmental, rather than genetic, factors (Aronson & Steele, 2005).
Students’ identities as learners and as legitimate members of the academic community in which they are being trained have significant impacts on their success. Students among underrepresented populations in academic fields often separate their academic and social lives to succeed in their K-12 studies, but this strategy results in high failure and dropout rates in college (Treisman, 1992). Women often leave gateway math courses with decreased confidence in their abilities and are more likely than similarly-performing men to be dissuaded from their career goals by early academic challenges (Ellis, Fosdick, & Rasmussen, 2016; Lubienski et al., 2013; Matthews & Pepper, 2007; Mujtaba, et al., 2014). Early college experiences developing support around students’ common academic interests and employing cooperative-learning and active learning techniques can reverse these patterns (Severiens & Schmidt, 2008; Treisman, 1992; Weiss et al., 2015). Such efforts should also cover study skills specifically relevant to learning math, persisting in solving difficult problems, self-assessing, checking for sensible results, practicing and checking work, and critical thinking. The MIP definition of academic success skills is that
Academic success skills foster students’ construction of their identity as learners in ways that enable productive engagement in their education and the associated academic community.
Academic Success Skills Initiation Workshop
MIP faculty collaborations on Academic Success Skills began with an Initiation Workshop in May, 2019. At this workshop, faculty identified the central academic success skills, such as problem-solving, persistence, collaboration, communication, work ethic, and a growth mindset, critical for success in entry-level college mathematics. Results of that workshop guide the direction of current MIP work, primarily that of the Collaborative Research and Development teams of faculty that will develop, test, and refine course materials to support the development of academic success skills as an integral component of learning by inquiry in entry-level math classes.
Mathematics anxiety initiates unproductive behavioral responses and makes mathematical reasoning, sense-making, and critical thinking more difficult, if not impossible. Because mathematics anxiety emerges from a variety of subjective appraisals and cognitive constructions, instructors can manage students’ anxiety by structuring various features of the learning environment—including the curricular resources they design for students—to reduce the likelihood that they will engage in the cognitive activity that results in their feeling anxious. A goal of entry-level mathematics instruction is to create the conditions for students to participate and engage in ways that are necessary for them to learn the mathematics meaningfully. A focus on reducing or even preventing students’ mathematics anxiety is essential to addressing this goal. Anxiety and its effects can be magnified when gender or racial stereotypes of performance are activated in the learners, and instructors need resources to help frame learning situations in ways that promote confident and productive participation by all students. [Explore the Details]
Problem-Solving and Critical Thinking
Developing productive problem-solving habits, and a disposition for critical thinking on which these habits rely, are essential components of mathematical proficiency. Additionally, problem solving and critical thinking provide a foundation for learning new mathematical concepts. A goal of entry-level mathematics instruction is to enhance students’ problem-solving ability while leveraging it as a foundation for their learning of central ideas. [Explore the Details]
Developing Classroom Communities
Feeling a sense of belonging to a community is essential to participating fully in that community’s activities. Engineering the social context of a classroom to foster the establishment of a community in collective pursuit of the joint enterprise of learning mathematics through inquiry is a complex and difficult process, and for this reason is often ignored or neglected. However, the potential affordances of developing such communities are significant. It is therefore a goal of entry-level mathematics to cultivate communities of mathematics learners that establish the social, cognitive, and affective conditions for students to engage in mathematical inquiry to develop productive conceptions of course content. [Explore the Details]
Students’ perspectives about the source of mathematical aptitude and the factors that contribute to its development either encourage them to engage productively in mathematics instruction, or not. A student who believes that enhancing her mathematical ability requires struggle, critical thinking, and sense-making will participate in and benefit from instructional experiences in ways that a student who considers mathematical ability an unalterable trait will not. A goal of entry-level mathematics courses is to foster the development of students’ growth mindsets with regard to mathematics learning so that they are prepared to engage in genuine mathematical inquiry. [Explore the Details]
Productive Struggle, Persistence, and Perseverance
Persistence and perseverance, and the productive struggle they enable, are often considered traits that some students possess, rather than behaviors that emerge from a variety of subjective appraisals students make in the context of particular situations. Productive struggle, perseverance, and perseverance involve a complex interplay between mathematical tasks, mathematics as an intellectual pursuit, and the goals, beliefs, interests, and resources students bring to the learning environment. It is a goal of entry level mathematics instruction to engage students in productive struggle and to foster the persistence and perseverance that engaging in genuine mathematical inquiry requires. [Explore the Details]
Motivation refers to the needs, desires, or purposes an individual seeks to satisfy through his or her engagement, and involves the individual’s situational and personal interests and goal orientations (Middleton et al., 2017). Because mathematical inquiry requires high levels of engagement, an instructor’s commitment to supporting students’ mathematical learning through inquiry requires fostering their development of needs, desires, and/or purposes that make such engagement possible. [Explore the Details]
Students often view mathematics as a disconnected set of procedures. It is common for them to believe that mathematical proficiency is most clearly evidenced by one’s ability to solve problems quickly. Students’ beliefs about mathematics influence the ways they engage with it and, consequently, their educational outcomes. For example, students who believe all problems can be solved in under five minutes or less (Schoenfeld, 1988) are unlikely to persevere to solve novel problems and thus fail to benefit from potentially valuable learning opportunities. [Explore the Details]
Academic Success Skills CoRDs and ARCs
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Productive Struggle, Persistence, and Perseverance (CoRD) Lucas Foster, Northeastern State University
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Learning mathematics can be a struggle. Sometimes, a student will experience multiple failures before enjoying a success. The idea of productive struggle is that the student persists throughout the process with creativity and determination until a solution presents itself. When students face problems that they don’t know how to solve right away, math educators do not want them to stop trying, but to continue with effort and think creatively to achieve a solution. If productive struggle is a central part of the learning environment, student success can be more evident and prevalent in math classrooms. In this study, investigators introduce the REACT framework, clarify how the framework reinforces the learning pillars of the Math Inquiry Project, and explore the effect that productive struggle has on student learning in an entry level college mathematics course.
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Dustin Gaskins, University of Oklahoma
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This activity is to help students monitor their time and how it is spent as well as evaluate tasks as being urgent or important. In this activity, the following mathematical content plays a role: pie charts, ratios, and unit conversions. The key underlying mathematical concept is the idea of a whole and a fraction of the whole and the task of identifying what the whole is.
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Jayne Ann Harder, Oral Roberts University
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Many students struggle with negative attitudes toward math, leading to disengagement and lower achievement. This paper explores how to transform this experience by examining the impact of emotions on problem-solving through affective pathways. It introduces the MIP Guiding Principles as a framework for cultivating a supportive classroom environment and provides actionable strategies that leverage these principles. By designing engaging activities, teachers challenge students to persevere and develop effective problem-solving skills. Furthermore, by establishing sociomathematical norms, teachers foster a collaborative mathematical culture. Through these approaches, students are likely to become more engaged, develop a positive math identity, and ultimately achieve greater success.
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This work is licensed under CC BY-NC-SA 4.0
