By Sam Rhodes & Christopher R. Gareis
All students can learn. It’s a clear enough statement, and one that few would debate. Yet we abandon the sentiment when it comes to mathematics. Adults and children alike are quick to identify as “non-math people,” when the root cause may in fact be chronic frustration resulting from deadening, discouraging, ineffectual experiences with mathematics. The unwelcomed effect is that countless students develop math-phobia and are pushed away from mathematics. Here are some suggestions to reverse the math–phobia tide.
The Perils of Traditional Mathematics Instruction
In a traditional math classroom, the teacher starts with an instructional objective and then designs a lesson with the goal of students demonstrating proficiency. These lessons involve guided notes, teacher-generated examples, and questions posed to students, with correct responses affirmed and incorrect responses corrected. Although focused and efficient, this model of instruction (Figure 1) relegates equity to an afterthought, inadvertently positioning many students as passive observers of mathematics. This position, over time and experiences, begins to imbue a student’s sense of self relative to the subject, which is often a sense of disinterest, inadequacy, and disenfranchisement.
The structure of this instructional progression positions the teacher as the expert and the student as the receiver. Consequently, students who can quickly provide correct answers are perceived to be smart or capable, leaving other students with a negative perception of their mathematic ability. Critically, these negative outcomes are often compounded for students from diverse backgrounds who are being asked to think and reason like their teachers rather than relating their learning to their own lives.
What should be done?
If we want to change these outcomes and work toward more equitable and humanizing mathematics instruction, we cannot leave considerations of student identities to the end. Rather, we need to consider what dispositional outcomes we intend for students and their position relative to the academic and dispositional objectives. As depicted in Figure 2, this kind of backwards design begins with the aims of equity and sense of self in mind.
A Vision of Mathematics with Equity in Mind
Start by formalizing a mission statement for the school’s mathematics program that clearly articulates the purpose of mathematics and conveys what teaching mathematics should look and feel like in the school. We share an example in Figure 3:
Establishing a curricular mission statement allows teachers to codify the beliefs and identities that they aim to foster in students. Conversations about students’ mathematical identities and sense of relationship to the subject then become the norm rather than the exception. Vibrant mathematics classrooms full of critical thinking and discussion are more apt to flourish, and instructional decisions can be made as a result of intentionally considering student positioning rather than as a result of teacher preferences or habits.
As a result, instruction is designed with this question in mind: “How can I design instruction to position all students as doers of mathematics whose thoughts, experiences, and ponderings are valued within our learning community?”
Positioning Students as Doers of Mathematics through Discourse
As conversations about student positioning become operationalized in classrooms, student-centered discourse becomes a catalyst for ensuring that all ideas are equally celebrated and that all students have an active role in the creation of mathematical knowledge. Let’s look at how this happens.
- Language and thought: As students share their thinking about mathematics, teachers have opportunities to build from students’ conceptions of mathematics rather than their misconceptions. Whereas a focus on answers results in judgements of correctness, a focus on thinking builds and refines understandings from what students know and understand. Students are no longer positioned as correct or incorrect, but are perceived as mathematicians, asking questions and positing strategies and ideas. Mistakes are not something to be avoided but are essential to the learning process and are to be wrestled with as a community of learners.
- Funds of knowledge: Children innately explore the mathematics inherent in the world around them. From young ages, we quantify, recognize patterns, and question the equivalence of things, even before we have those words for it. As we grow, these informal learning opportunities are intrinsically tied to home and cultural experiences and identities. It is crucial, therefore, that teachers use mathematical discourse to draw on these experiences to create mathematical understandings that are inherently connected to the lives of their students.
- Enhanced learning for all: As students share their thoughts and experiences, diversity of thought enhances learning opportunities for all students. Consider the problem 13 x 24. In teaching the algorithm shown in Figure 4, repetition is often used until procedural fluency is attainted through hours of practice. Despite hard work and practice, students often still struggle to understand how place value is being attended to. For example, why do you add the zero in red?
However, rather than analyzing students through a deficit-based lens, such as focusing on the struggle of students who don’t get a sense of place value when the algorithm shown in Figure 4 is used, leveraging diverse perspectives can enhance the learning for all students. There are myriad methods for multiplying numbers, and discourse allows students to share their own strategies. Figure 5 shows the same problem being solved using line multiplication. Place value is readily apparent in the method as the numbers are decomposed by place value. Thus, when looking at the factors individually, the lines shown in red represent the tens place while the lines in blue show the ones place. After performing the multiplication, the result of multiplying the two factors can be seen as the intersections of lines. In this example, the two sets of blue lines form the ones place, the intersection between red and blue lines is the tens place, and the intersection of two sets of red lines creates the hundreds place. The point is that by allowing for multiple methods, students can explore pathways to their own thinking developing understandings of multiplication and also a sense of relation to it.
- Problem-solving: Problem-solving is part-and-parcel of mathematics. Allowing students to struggle productively as they solve rigorous problems sends the message that the teacher believes students are capable of doing and creating mathematics and positions students as inquisitive mathematical thinkers. Student discourse flourishes as diverse solutions and strategies are shared and exchanged, thereby creating an atmosphere where every student has an opportunity to learn mathematics at the highest level.
Towards Equitable Mathematics
Math trauma and math-phobia in our society are but the tip of the iceberg when considering the ways that inequitable mathematics instruction impacts our students. Working towards a solution to this problem requires starting with a critical analysis of what identities we want students to develop. We believe that all students are capable of doing mathematics…and capable of embracing mathematics as a joyful discipline. We believe that diversity of thought enhances understandings of mathematics for all students, and we believe that allowing student voices and experiences to shine in mathematics classrooms is a crucial step towards rehumanizing students.
Realizing this vision requires that students be given opportunities to think critically about mathematics, discuss and share their thinking with others, and build new understandings. We believe that these experiences must come from putting equity first and allowing that goal to undergird the development of a clear vision of excellence and equity in mathematics education that produces the learning experiences, sense of self, and sense of subject that ultimately create a more mathematically literate world.
Sam Rhodes is an Assistant Professor of Elementary Mathematics Education in the College of Education at Georgia Southern University. Christopher R. Gareis is a Professor of Educational Leadership in the School of Education at William & Mary. Connect with them on Twitter @srrhod.