Sparking Student Engagement in Math: Moving from Passive to Collaborative Learning

When we talk about engagement in the math classroom, we usually picture students leaning forward, hands raised, and enthusiasm on their faces. But what exactly does engagement mean? 

Understanding Engagement and Why It Matters

If you’ve ever had one of those remarkable teaching days where students are energetic, sharing ideas, and focused on the learning, then you know the power of engagement. The challenge is, how do we get there? How do we create those moments when students are invested and learning deeply? 

It starts with understanding that not all engagement is the same. Cognitive engagement measures the extent to which students are engaged—actively invested—in their learning. Experts in cognitive engagement have found that it’s not the presence of engagement but the extent of that engagement that makes a big difference for learning outcomes.

Highly engaged students are those who:

• Learn deeply by connecting with others on a social, emotional, and cognitive level.
• Retain and construct knowledge because the learning experience is meaningful and memorable.
• Build confidence in concepts they may have previously found intimidating.
• Develop language and math discourse through exploration and collaboration.
• Begin to see themselves as problem-solvers and capable mathematicians.

The ICAP Framework for Engagement

As we’ve seen, some forms of engagement lead to better learning outcomes than others do. One great way to measure engagement is with the ICAP Framework, which was developed by Dr. Michelene Chi and her team. 

Each letter in ICAP represents a different mode of engagement:

Interactive > Constructive > Active > Passive 

Picture a ladder with four rungs. At the bottom of the ladder is passive engagement, and at the very top of the ladder is interactive engagement. 

ICAP Framework: Levels of Engagement

The evidence-based ICAP research indicates that learning outcomes improve as students engage at higher levels of the framework.

How to Move Up the Engagement Ladder

You don’t need to overhaul your teaching routines to move up the engagement ladder. Instead, start small. Moving up the ladder doesn’t abandon lower-level engagement—it expands and builds on it! Aim to move up one rung of the ladder at a time.

To move from passive engagement to active engagement, you can have students simply point to something or click an answer choice to increase engagement. 

To move from active engagement to constructive engagement, ask open-ended or content focused questions. This gets students responding and talking productively about the learning.

The real power in constructive engagement is productive struggle. Productive struggle isn’t about overwhelming students with overly challenging work; it’s about purposeful tasks that have a higher cognitive demand. Students make stronger connections and deepen their learning when they persevere in what education scientists call effortful thinking.

To move from constructive engagement to interactive engagement, use dialogue-promoting questions or routines to get students talking equally as a group. Step back a bit so you’re no longer leading the discussion, but you’re available to support and help keep them on topic. This allows students to collaborate meaningfully through shared discourse.

Watch the Webinar: Climbing the Engagement Ladder in Math

Watch our on-demand webinar where we break down the research, share real examples for your math classroom, and give you practical tools to move your students up the engagement ladder.

Works Cited

Chi, Michelene T. H., and Ruth Wylie. “The ICAP Framework: Linking Cognitive Engagement to Active Learning Outcomes.” Educational Psychologist 49, no. 4 (Oct. 2014): 219–243. https://doi.org/10.1080/00461520.2014.965823.

Deans for Impact. Prompting for Effortful Thinking. Austin, TX: Deans for Impact, 2025. https://www.deansforimpact.org/files/assets/lbsdanchorcharteft.pdf. 

Fredricks, Jennifer A., Phyllis C. Blumenfeld, and Alison H. Paris. “School Engagement: Potential of the Concept, State of the Evidence.” Review of Educational Research 74, no. 1 (Spring 2004), 59–109. https://doi.org/10.3102/00346543074001059.