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IMPACT Plus - Strategies for Student Engagement

By Paul Nolting posted 01-11-2021 08:38:30


A new year and semester. Many of us hope that instruction may return to some type of  “normal” circumstances; however, challenges still remain in virtual classrooms and labs. Along with students taking next sequence math courses for the first time, many repeating students will need additional motivation, active learning, and academic support. Students repeating math classes have a less chance to pass it the second time and even smaller chance the third time.  Promoting motivation and active learning to improve student engagement can improve success. It requires a combined set of strategies from instructors, students, and academic support labs. This blog will explore strategies to enhance student engagement based on IMPACT Chapter 5, research articles and individual faculty suggestions. The blog  also discusses different variables that negatively impact motivation, active learning, and engagement such as poor math self-efficacy, math anxiety and test anxiety. 

Classroom Instructional Motivation Strategies

Improving student motivation, the first variable of the engagement equation, is influenced by classroom instruction, faculty assignments and student practice. In Chapter Five of the IMPACT document the focus is on student engagement through developing curiosity and motivation. The chapter discusses how to engage students inside and outside the classroom. Students are more motivated in an environment where they can talk to faculty and peers about matters, receive frequent feedback, all of  which can lead to better grades, more satisfaction with the college and persistence. Also, an environment that fosters active student engagement, encourages creativity and risk taking promotes shared student and faculty responsibility for successful learning. Additional sited research indicates that when students feel like they have a voice in classes, they are 7 times more academically motivated.  So, instructors need to ask students for suggestions to develop different types of learning environments. Instructors can guide the students by discussing and giving examples of the three components of the learning environment: learner-center, knowledge-centered and reflective learning. These components can lead to an improved environment, peer interactive learning.  The result?  Motivation.

Another way to improve classroom student motivation is developing teaching strategies to improve math self-efficacy. The four areas of math self-efficacy are: enactive mastery experience, vicarious experiences, verbal persuasion, and physiological and affective states which explain up to 35.8% of math learning variance (Zientek, Fong and Phelps, 2017). This article lays out a blueprint to improve math self-efficacy and student motivation. The authors expand on Bandura’s (1997) [Google Scholar] self-efficacy research and apply the strategies to mathematical learning. Instructors must discuss the four areas of math self- efficacy. 

Mastery experience is the first component and the most powerful. Early in the semester, instructors  need to develop mastery experiences beyond online homework that students can successfully complete. Successful experiences remain in students’ minds, motivating them to solve more difficult problems. Instructors can scaffold the mastery experiences to raise a student's level of math self-efficacy. Remember: Success breeds more success.

The second component is vicarious experiences which can improve motivation. Students want to know that people like themselves have become successful math learners. As learners they vicariously judge their own competencies for success through the success of others. That way these students will think positively about their own capacity to pass math. Instructors need to become good real life story tellers. Instructors have stories about students who struggled with math and became successful.  These stories should include students like the ones in the class. For example: first generation, women/men returning to school, single parents, did poorly in high school, hate math, students with disabilities, veterans, low income, and working several jobs. However, it is not good enough just talking about their background without discussing how they accomplished becoming successful.

The third component is social persuasion which is also called verbal persuasion. This persuasion is through timely, constructive, and specific feedback that will encourage students to improve their work and effort. For example, during mastery learning it is encouraged to provide early chances (besides online homework) to demonstrate math knowledge. When using an in class assessment, feedback needs to be as soon as possible. A good rule of thumb is to walk around the room or visit a virtual setting and “catch” them doing something right and praise them. This is an immensely powerful positive message. Students need to be thanked for completing that assignment and praised for effort. When returning assignments, include specific notes on correcting the missed problems. Also, more difficult completed problems should receive a note praising such as, “Good job.”  Students not successfully completing difficult problems should be praised for their effort. For example, “Good try on this problem. You may want to review your notes or textbook to solve this problem or come by my office.” For test feedback use the Six Types of Test Taking Errors that specify different types of student errors. When grading tests use a green or blue pen. When some students see red ink, it reminds them of previous failed math tests, and do not review the test. Also, again let the students know that they did a good job and praise them for effort. Use the scaffold technique to give more feedback at the beginning of the semester and taper off.

The fourth component is the psychological and affective states. The physiological states pertain to math and math test anxiety. These states need to be addressed as real conditions affecting math learning and demonstrating math knowledge. Instructors should limit time pressures in problem solving situations and competition due to potentially causing anxiety and classroom avoidance.  Also, read and discuss  Maloney and Beilock (2012) article on how math anxiety affects affective factors and that just doing more math problems is not the solution. Instructors need to explain the effects of anxiety on working memory which is essential in completing homework and taking tests. Anxiety limits the amount of working memory in the brain (O’Donnell 2016).  It is like removing RAM from a computer. Instructors need to teach students anxiety reduction techniques to improve learning and demonstration true knowledge.  Nolting ( 2020) explains several effective student test anxiety reduction techniques such as “Tensing and Relaxing”, “Visualization” “Deep Breathing” and “Positive Self-statements”. Then discusses how  mindfulness techniques support anxiety reduction by having students focus on what they can do in the present instead of the past (causes depression) and the future (causes anxiety). Instructors must teach students how to reduce math and test anxiety.

 External Motivation and Giving Hope

The focus now changes to how instructors can help students motivate themselves. Some students need outside forces of reinforcement to improve math success. The most powerful external motivation is money. Students need to see the correlation between math courses and money. Nolting (2020) developed two charts, one for A.S. degreed and the other for B.S. degrees, that graph income vs. range of math courses. Students reviewing the graphs conclude that more math courses means more money.  Show this graph and have a discussion. Indicate even students who dislike math become more motivated.

The next step is motivating unsuccessful math students. This discussion focuses on Attribution Theory (Hooper, 2020) which looks at a students’ beliefs that they can enact a certain behavior (passing math) or not based on their current circumstances. If they can not enact that behavior (passing math) the question is what do they contribute to that failure and can they change that attribute. If students contribute not being successful at math to something they can control and change, then they will put forth the effort. Students who contribute math failure to something they cannot control (lack of  brains) will not put forth the effort which may lead to learned helplessness.  Other words the students need hope to be motivated and change their behaviors. Using the free Math Study Skills Evaluation (username “msse” and password “seventh”) can indicate there is hope.  It measures part of the affective domain not cognitive math skills. Since almost all the Math Study Skills Evaluation (MSSE) scores are low this is great motivational news because that implies poor math study skills are a major part of their learning problem, not their math intellectual abilities.  Also, it is not their fault they have poor math study skills. Students can be taught math study skills as strategies to improve learning and grades. Instructors can have students take the MSSE to give them hope.

Active Learning Strategies

 Active learning is the second variable in the equation that leads to engagement. Active learning can improve learning through student-to-faculty and student-to-student interactions. Active learning has been used for many years and can be applied to any level or type of math course. For example, think-pair-share is a popular active learning activity. Just Google “active learning activities college” for       additional examples. However, in this blog we want to discuss the constructs of good active learning activities. Nabb (2020) in his MathAMATYC Educator article recommends using the Five Practices for Orchestrating Productive Mathematical Discussions (Smith & Stein, 2011, 2018) for providing  structure to develop active learning activities. The Five Practices are anticipating, monitoring, selecting, sequencing, and connecting. The first practice of anticipating is when the instructor identifies the goal of the lesson and develops tasks to accomplish that goal. The second practice is monitoring the given activity to identify group strategies being used and to  keep the students on task. Practices 3 and 4 can go together. As groups finish the activity, they decide  which groups should contribute to whole-class discussion and the order of the presentations that makes pedagogical sense. Now the instructor can connect the approaches so the students can see similarities and differences across the strategies. These connections should meet the intended lesson goal or learning concept. Kabb (2020) continues to give examples for different types of math classes. His conclusions which are supported by additional research are: (1) Students persist longer and perform at higher levels, (2)  Students feel a sense of belonging and mathematics learning is a more balanced and equitable experience,  (3) Students become more risk takers in their mathematics learning, and (4) Instructors know their students on a much deeper level compared to just lecturing. His final suggestion is to start small with a few lessons, obtain student feedback, reflect, and continue.  Active learning strategies can be conducted in virtual classrooms through different virtual rooms.


Instructors have a great opportunity of improving student engagement with motivation and active learning. Instructors can use a variety of the discussed strategies to help students become more engaged. Without motivation students will be less likely to participate in active learning. Active learning research is voluminous and has been the subject of many workshops. However, what is needed is a design to implement and evaluate active learning practices. To obtain the best engagement, instructors need to train and empower students and other departments. To increase student success and become “math heroes”, implement the best instructional and student motivation strategies along with including supportive departments.  Instructor engagement training can continue at the 4th National Mathematics Summit sponsored by AMATYC and NOSS at the June 14 and 15 NOSS pre-conference in Las Vegas, NV.


Hopper, Elizabeth. "Attribution Theory: The Psychology of Interpreting Behavior." ThoughtCo, Aug. 25, 2020,

Nabb (2020). Active Learning in Undergraduate Mathematics: The Five Practices and the Five Dimensions of TRU Math. MathAMATYC Educator, 12, 1,  30-35.

Nolting, P.D. (2020). Winning at Math: Your Guide to Learning Mathematics Through Successful Study Skills (7th ed.). Bradenton, FL: Academic Success Press, Inc

Smith, M. S., & Stein, M. K. (2011). Five practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics (NCTM).

 Smith, M. S., & Stein, M. K. (2018). Five practices for orchestrating productive mathematics discussions (2nd ed.). Reston, VA: National Council of Teachers of Mathematics (NCTM).