“Mrs. Mastel, we were so busy thinking about math we didn’t even realize we worked right through recess again!” Powerful words in a 4th grade classroom. Even more powerful when they are said with a smile and a shoulder shrug.
How is an engaging mathematical classroom defined? To answer this question, we need to ask ourselves three more - How does it sound? How does it look? How does it feel?
In my classroom, it was what I heard students say about the mathematical ideas we were studying, the way they interacted with each other and the math tasks at hand, and the energy generated during the lessons that defined engagement. My goal was the same every year - to create an environment that allowed my students to become a community of mathematical thinkers and collaborative learners.
To help meet this goal, I kept these synonyms for engagement in mind – involve, engross, enthrall, fascinate, immerse, interest, intrigue. It was seldom enough for students to look engaged, as in “just being busy with completing a task.” I wanted to know what they were thinking about the math, what questions they had, and how they approached problem solving.
In order to build a mathematical community, my students needed time – time to investigate mathematical concepts and ideas; time to organize their thoughts about math; time to think through their strategies; time to share their thoughts in a safe environment; time to listen and consider the thinking of others; time to reflect on mistakes and adjust their thinking; time to agree, disagree, and justify conclusions; time to feel safe to share and that their ideas would be encouraged and respected. Any teacher knows, time is a commodity within a classroom. Taking the time to provide my students these opportunities proved to be priceless as we became a learning community connected by our understandings and intrigued by the ideas of others.
Math discussions (math talk) became an integral part of helping my students grow into a community of engaged learners. Using communication in the classroom to represent, explain, justify, agree, and disagree shaped the way we learned mathematics. Providing frequent opportunities for classroom dialogue engaged my students in critical thinking and collaboration, encouraged them to learn more, and allowed for deeper exploration of the mathematical ideas, strategies, and generalizations I needed them to understand.
As a result of the collaborative explorations, I witnessed my students become confident and competent in their understandings about math. So much so that during a demonstration of a math talk about multiplication strategies during a Grandparents’ Day celebration, one of my students boldly acknowledged he knew his solution was incorrect but wanted the opportunity to explain where his mistake in thinking was. The fact that this student had not been willing to share his thinking the previous year added to the significance of this moment. His grandparents were not in the classroom that day, but his actions certainly impressed another grandfather. I still remember his strong stature and pristine cowboy hat as he began to speak when we had concluded our math talk. (It’s amazing how being a little nervous can burn images into your mind. After all, this definitely was not what these grandparents experienced in grade school). I still hear his words as if it was yesterday.
“When I was a student, I did not let my teacher know what I was thinking. I certainly would never admit my answer was wrong and then have the confidence to correct my mistake in front of everyone. Whatever you are doing, it is definitely working.”
This, along with a few other key moments I experienced as both a learner of math and a teacher, cemented my convictions about the definition of engagement in a math classroom. Learning mathematics cannot be a passive activity for students. Learning mathematics is a process of making sense and establishing meaning, both individually and collectively. Collaboration and communication are critical elements in establishing an environment that engages students in mathematical thinking - engagement that leads to deeper understanding, productive discourse, and creative problem solving within our classrooms.