"Eyes on Progressive Education" Blog
A Green Acres School journal that chronicles progressive education in action, the research that supports and informs our practice, and ways in which we live out our mission each and every day.
Math and the Engaged Mind
Tracey Marks, Ed.D., Lower School Head
When I was in elementary school, math involved memorizing formulas and calculating correct answers to fact-driven questions. My teachers would present one way of solving problems, and my job was to mimic their use of that strategy to arrive at the right answer. It was never clear to me why what I was learning was important, or how I might use what I had learned in my life outside of school. I recall that we knew which students were “good at math” and which students were not members of that group.
Fast forwarding many years, I enter our Green Acres classrooms and observe math instruction, feeling transported into a mathematical world quite different from what I experienced as a child. A focus on conceptual understanding has replaced the memorization that I remember. Green Acres teachers emphasize that arriving at a correct answer is a worthy goal, but that understanding the concept of what is being taught is the primary aim.
The math instruction that I recollect was first a whole-class experience, with the teacher explaining how to do something and the students listening and, when older, taking notes. Then, the experience became a solitary one, in which each of us worked on problem sets. If we required help, we needed to ask our teacher, since getting classmates to assist us was considered “copying.”
This contrasts sharply with the collaborative math work that I observe every day at Green Acres. Our students are in partners, in small groups, and on teams working together toward a common instructional goal, playing math games, and helping one another generate solutions to problems. There is give-and-take in this process, and each group member is perceived as someone who has something important to contribute. Everyone is “good at math,” not just a few. The approach is collaborative, rather than competitive in nature, a hallmark of progressive education.
When teaching math, our teachers recognize that there are numerous approaches and strategies that children can use to solve a problem. Students may arrive at the same solution, but they discover that there are multiple ways of getting there. Our teachers encourage children to explain their strategies and describe the paths that they followed to calculate an answer. Moreover, we recognize that integrating topics and skills across subject areas deepens learning and enables children to actively construct meaning from their experiences. This is why our students often engage in “writing to explain” during math time, describing their approaches to problem solving in writing, thereby weaving together the disciplines of math and writing.
Our hands-on approach is emblematic of Green Acres’ progressive philosophy. In math, this often involves students manipulating materials in order to understand the concepts behind operations. For example, using base ten blocks and ordering them on a place value mat allows children to see why they need to “borrow” when subtracting some large numbers. Green Acres teachers help students who need support and extend and enrich activities for children who are ready for more challenging work.
At Green Acres, teachers emphasize that math is relevant to children’s lives, both inside and outside of school. They explain to their students why they are learning particular skills and strategies, and, when planning math lessons, teachers often focus on real-life situations and applications. A good example of this is when students opened a pretend restaurant, calculating the change owed to their customers.
Our teachers make learning math both rigorous and fun. Students often play math games, reinforcing skills and encouraging collaboration. For example, last week, I observed students playing a game that involved them working in small groups to create equations based on playing cards. If children enjoy math and consider themselves to be mathematicians, their motivation and confidence increase, and they develop the habit of persisting when problems become difficult. Green Acres teachers create math opportunities for children that enable them to be skillful problem solvers in their grades and prepare them to excel in math in Middle School and beyond.
Hearkening back to my own experiences as a math student, I realize that as a child, I might have felt quite differently about math and about myself as a mathematician had I experienced what our Green Acres students do in math every day. I might have been a more motivated and interested math student, perhaps even viewing myself as one of those people who is particularly “good at math.”
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