David Clausen, Department of Mathematics

When teaching introductory college math courses, one finds a wide variety of students. In a calculus class, you might have people majoring in mathematics who need a conceptual understanding of “why” as well as facility with computations. They might be sitting next to students in STEM fields for which it is a prerequisite who will be more focused on using the material solve problems from their major. Also, there may be students taking it as a general education requirement for graduation, with little interest in math beyond calculus.

Another division might be between students for whom math has been an area of shame, who might lack or have incorrect basic algebra skills needed for the course. These students might be taking the class along with students who took calculus in high school for whom half the course is review. How are you supposed to engage all the students so that they learn the material from the course, providing challenges to students who might have a strong head start while encouraging students who struggled in math that if they put in the effort they can eventually succeed?

Growth Mindset Versus Fixed Mindset and the Neuroscience of Learning

One of the first ways to help both students who are struggling and succeeding is to encourage a growth mindset [1]. Rather than a fixed mindset of “I am bad at math”, a growth mindset says “I need to work harder to be better at math” and holds that a student can improve and when they succeed, it is because of their effort [1]. Often students who struggle believe they are simply “bad at math” –  this is a fixed trait [1]. Also, students think “I am good at math” tend to shy away from taking risks, as any failure would impact their identity of being strong at math [1].

Not only does this discourage them from putting in the full effort, but it is opposite to our current understanding of the brain. Our learning occurs when neurons in our brain form connections with each other [1]. These connections become stronger the more we use them, so the more we work at a subject like mathematics, the better we will learn. Having a fixed mindset leads to “panic, anxiety, stress, trauma, fear, … “ (Anastasia, 1) about math and these emotions release cortisol that inhibits the forming of connections. Changing this mindset is a way to help both struggling and succeeding students by focusing on their success based on their effort rather than any innate trait [1].

How Instructors Can Use Active Learning in Math to Teach to Students at Different Levels

Another way to use effective teaching strategies for both confident and uncertain students is through active learning. By encouraging students to use active learning, students at all levels are engaged with the material, and the students who struggle actually show greater gains in learning than traditional lecture alone [2]. Examples of active learning, such as a jigsaw activity where students work on problem in a group, then form different groups and each student presents the solution, work well to engage all students with the material and improve their skills at explaining the material to others. Andrew Cavanagh did a research study and showed that “Results revealed a consistent and strong relationship among trust, commitment to active learning, engagement, and final grade. These findings highlight the importance of student–instructor interactions in contributing to student commitment to and engagement in active-learning classroom contexts.” (Cavanagh, 3)


  1. Sofroniou, Anastasia, and Konstantinos Poutos. “Investigating the Effectiveness of Group Work in Mathematics.” Education Sciences, vol. 6, no. 4, 2016, p. 30.
  2. Ahmad, Sabri, et al. “Learning Styles towards Mathematics Achievements among Higher Education Students.” Global Journal of Mathematical Analysis, vol. 2, no. 2, 2014.
  3. Cavanagh, Andrew J., et al. “Trust, Growth Mindset, and Student Commitment to Active Learning in a College Science Course.” CBE—Life Sciences Education, vol. 17, no. 1, 2018.

Matthew Mahavongtrakul edited this post on December 2nd, 2019.