Student achievement in mathematics continues to be a critical equity issue in the United States (Bohrnstedt, et al., 2015; Lee, 2002). What math courses a student takes in high school strongly correlate with economic success a decade later, and account for up to one quarter of the future income gap between students from low socioeconomic backgrounds and their more affluent counterparts (Rose, 2004). The starting point for achieving mathematical equity is to understand that conventional approaches to math education in the USA are structured for inequitable access and promote a lack of engagement. As early as elementary school, many students see math as something they cannot do (Boaler, 2014). Due to this lack of mathematical agency (i.e. the belief that I can do math), many students interpret struggle in math as a lack of ability, and consequently fail to persist. Unfortunately, math classrooms often reinforce this lack of agency by rewarding speed and procedural fluency over deep understanding of mathematical concepts and problem solving ability.
Evidence from brain research suggests that while concepts can be compressed in the brain, procedures cannot (Gray & Tall, 2007). This has significant learning implications for students in procedurally oriented math classes or who experience similarly narrow math remediation. By focusing on procedural fluency – often by memorizing strategies or ‘tricks’ to solve problems – educators prioritize answer-getting and computational speed, ultimately limiting their students’ ability to develop a deep conceptual understanding of the underlying mathematics.
When math is taught in this way many students feel that math is not relevant to their lives and holds little value.
In addition, a focus on ‘getting the right answer’ to narrowly defined problems promotes fixed mindsets in students and creates an atmosphere where many students, including both lower and higher achieving students, feel like they do not belong (Boaler, 1997; Boaler, William, & Brown, 2000; Solomon, 2007, Moser et al., 2011). Unfortunately, this narrow focus on procedural speed and fluency does not translate into deeper understandings of mathematical concepts, or even higher test scores. Of the thirteen million students worldwide that participated in PISA tests, students who relied upon memorization strategies scored the lowest (Boaler, 2015; OECD, 2014).
Neuroscience research suggests that everyone has the capacity to engage in mathematical reasoning, and researchers of mathematics education point out that mathematics – the exploration of patterns and a way of making sense of the world around us – is a deeply human activity (Gutiérrez, 2012; Boaler, 2015; Carpenter, Fennema, & Franke, 1996). In light of this understanding, how might we re-humanize mathematics for our students and disrupt the harmful narratives that feed into our societal biases? How can we honor and further develop the sense-making and innate problem-solving skills within our students? A first step is to understand the roots of our biases and the classroom structures that have shaped our understanding of math.
The student-centered practices outlined in this study maximize the unique strengths each child brings to the math classroom and use them as the foundation for instruction. By focusing classroom discussion on student sense-making of each other’s mathematical ideas and exploring multiple problem solving strategies, students begin to recognize that there is no ‘one right way’ to be mathematical, and that everyone has something of value to contribute (Boaler, 1997, 2006; Gutiérrez, 2000). When teachers create a learning environment based on deeply understanding their students thinking, every student is able to bring their full self into the math classroom.