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IMPACTful Thoughts - Three Components of Student Engagement

By Scot Pruyn posted 12-31-2021 17:35:53


What are some of your common frustrations about student performance in your classes? Maybe students aren’t putting in the time necessary to struggle with problems and understand concepts. Or they provide surface-level responses to your questions that were designed to make them think more deeply and make connections. Perhaps you just want students to be more precise with their notation or vocabulary when writing or speaking about mathematics.

The root of many of these issues is a lack of engagement. If students are going through the motions that they’ve learned through years of school will get them a passing grade, they are not engaged and we will see that in their work.

But what does it mean for a student to be engaged, and how do faculty contribute to student engagement? This month, IMPACT Live! will focus on these questions as we explore how a combination of motivating teaching practices and active learning can make a big impact on student engagement.

Engagement is a very broad term, and there is no “silver bullet” that will get students engaged in our classes. However, it can be broken down into three main components, and each of these are totally attainable for any instructor.

Student - Content Engagement

"There is no other decision that teachers make that has a greater impact on students' opportunity to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics" (Lappan and Briars, 1995).

Students’ engagement with mathematics is inextricably tied to their engagement with the content we provide. It is crucial that this content is designed for students to make connections to their prior knowledge, gives them opportunities to be creative, and fosters an intellectual need to study, practice, and learn new things.

A couple of easy things you can try:

  • Assign students to do some research into their major or future career, and why they are being asked to take this math class as part of that training.
  • Incorporate a 3-Act Task at the start of one of your lessons.
  • Assign writing prompts in addition to traditional homework, asking students to reflect on their learning and make connections with prior knowledge.

Student - Content engagement is important, and is often the first thing we think of when we hear “engagement”. However, without additional engagement with their peers and instructor, students may not develop their mathematical communication skills. Engagement with other learners is crucial for this.

Student - Student Engagement

We all want to help students develop problem solving skills. However, so often in a math class, students aren’t given the opportunity to truly problem solve because they can use context clues to determine exactly what they are supposed to do on a given problem. Problem solving is what we do when we don’t know what to do. The reasons for eliminating problem solving in the classroom are varied, but mostly instructors are wary of overwhelming or frustrating their students with problems for which they have not been shown an example. Having students solve problems collaboratively, with the right facilitation and group size, can remedy this. In addition, group problem solving requires students to consider multiple approaches and improve communication skills by explaining their own reasoning.

A couple of easy things you can try:

  • Rather than handing out a worksheet for students to work on in groups, assign one problem at a time. Have students work on a single white board or other non-permanent surface, and set a goal of every student being able to explain the work of the group.
  • Give students an opportunity for discovery by giving tasks that students have not seen an example of before. Give hints, encourage the use of technology, illuminate student voices who share ideas, but resist the urge to just walk through your own solution.

Group work is abundant in the modern math classroom, but putting students in groups to work on a task is just the first step. Without content engagement, students might just be focused on procedures and the “what to do” rather than the “why.” Without instructor engagement, students often have a bad experience with group work when they feel their grade will be affected or that they are being asked to “teach themselves.”

Student - Instructor Engagement

Students need to know that they matter to their instructors. A sense of belonging can come from something as simple as learning and using students’ names. In addition, it’s important to show students that we care about their learning, and our relationship is not just transactional (assignments for grades). This can take a couple of forms. First, give meaningful feedback - both positive and negative - that focuses on the learning outcomes of the class. Allow students to make mistakes and learn from them. Prepare supports and extensions so that everyone can engage with problem solving during class. Consider whether the class is equitable - is everyone participating? What other types of experiences might benefit those in the class not currently engaging? Rather than all group work every day, some students might benefit from quiet reflection time, or one-on-one discussions with the instructor.

A couple of easy things you can try:

  • Ensure students are utilizing feedback by allowing revisions of some assignments, where students must incorporate instructor feedback in their revision. Of course the prerequisite to this is giving meaningful feedback shortly after the assignment is first turned in!
  • Check in with each student at least once in the first two weeks of the term. This might be a 2-minute conversation in the classroom, an email with some encouragement or suggestions, or a phone call if a student has not been attending or responsive to email.

Finally, it’s worth mentioning one other type of engagement:

Instructor - Instructor Engagement

To improve in any of these areas, it’s crucial to work together with others in our departments. It can take several weeks to set up the class expectations and culture so that students are fully engaged. However, if students were previously in a math class with similar expectations and requirements, they will acclimate much quicker and be ready to focus on the math. Engage with your colleagues and find out what practices they are using to promote student engagement, and share your own practices. The benefits to students from having a consistent experience will be well worth it.

This month the members of the Teaching for PROWESS (a joint NSF and AMATYC project) will be doing a deep-dive into student engagement in the mathematics classroom. Join in the discussions this month and also consider applying for funding to become a Teaching for PROWESS IMPACT College during Phase 2! Details on applying can be found at

1 comment


01-04-2022 22:58:22

Thanks, Scot! This is a great post showing helpful and practical ways to engage our students in actively making sense of mathematical ideas and developing problem solving skills! Thanks!