Positioning and Pathways
August 2022
How we position others and ourselves in the teaching and learning of mathematics has a major impact on the future of our society. This positioning has many implications, but I want us to particularly attend to the implications of positioning on pathways for students to engage in meaningful mathematics. The question is, How do we position students, teachers, and mathematics in classrooms, policies, instructional practices, course structures, and pathways of opportunities to continue to engage in PK–12 mathematics and beyond?
NCTM—along with many in the mathematics community—has called for rethinking the varied pathways available to students in high school and postsecondary school. One of the key recommendations in NCTM’s Catalyzing Change in High School Mathematics: Initiating Critical Conversations (2018, p. 7) states,
High schools should offer continuous four-year mathematics pathways with all students studying mathematics each year, including two to three years of mathematics in a common shared pathway focusing on the Essential Concepts, to ensure the highest-quality mathematics education for all students.
These pathways should be mathematically meaningful, rigorous, and include statistical and data literacy.
Currently, pathways are qualitatively different with low expectations for many in ways that lessen deep understanding of mathematics and do not provide a foundation for students to build on to continue a rich study of mathematics. What results is an opportunity gap with marginalized students left without mathematics that will position them to advance, both professionally and personally, limiting future opportunities.
Re-Envisioning Mathematics Pathways to Expand Opportunities (2022), a recent report co-developed by the University of Texas at Austin Charles A. Dana Center, Student Achievement Partners, and the Education Strategy Group, highlights findings from a study of several states regarding middle and high school student course-taking to investigate how high school pathway reforms are influencing choices that students are making in what mathematics courses they take or have opportunity to take. Many states are already engaged in this work. Although the publication reports multiple findings, the one I highlight here relates to potential barriers encountered when planning and implementing varied mathematics pathways. This finding relates directly to how we position students, teachers, and mathematics in this work.
Some internal systemic barriers that state leaders identified were related to existing ideologies, structures, and capacity. Some external barriers were related to social contexts, equitable access, and building postsecondary connections. (p. 2)
From the data and various responses collected on this work, three actionable steps were identified to move pathways work forward, address challenges, and build on success:
- Build collaborative bridges with higher education and mathematics networks
- Center equity and leverage data
- Highlight progress (pp. 42–46)
Many stakeholders should be involved in addressing these internal and external systemic barriers through intentionally and strategically engaging in the three steps identified (building collaborations, centering equity, and acknowledging progress). Let’s consider ways that we as teachers, our students, and the mathematics itself are positioned or could be positioned to address these barriers and take actionable steps related to classrooms, policies, instructional practices, course structures, and pathways of opportunities to engage in PK–12 mathematics and beyond.
Positioning
Wagner and Herbel-Eisenmann (2009) described positioning as “the ways in which people use action and speech to arrange social structures” (p. 2). Although their work is directed at the classroom, it has broader implications across other areas affecting student opportunity to learn mathematics. Discourse research often identifies three types of positioning interactions—student-student, teacher-student, and mathematics—that send messages about who is part of the interaction and its impact (Busby et al. 2017). Let’s consider these three positionings in relation to how they connect to pathways of opportunities for all students to learn mathematics and to our broader question.
Student-Student Interactions: These interactions, spoken and unspoken, raise questions of whose voice is recognized and valued; who is capable and can manifest themselves in structural ways, such as tracking or ability grouping where students are positioned in certain ways, in particular in ways that marginalize many students and influencing their confidence, identity, and access? When we think about considering pathways across PK–12 and beyond, are students thinking about this? They should be positioned to engage in conversations and actions to address pathways. They are mathematicians as both present and future leaders in mathematical learning.
Students need to be positioned to be in conversation with one another in not only mathematics learning within the classroom but also in considering pathways of learning across PK–12 and beyond.
Teacher-Student Interactions: Often as teachers we decide what mathematics is talked about in the classroom, who is to talk and to whom, how the talk should go, who gets more opportunity to engage, and who gets less. Many times these actions highlight or send a message about who is perceived as competent in mathematics and who is not. This connects to agency and authority in the mathematics classroom. But in thinking about our broader question, who is given agency and authority in considering pathways of learning mathematics? Teachers and students must engage in these conversations and must position themselves and be positioned to engage in discussions of structures, policies, and practices to re-envision pathways in mathematics.
Positioning Mathematics: Selecting particular aspects of mathematics to engage students positions mathematics in certain ways. The choice of task or problem affects how mathematics itself is positioned. A classroom culture that encourages students to discuss and communicate mathematically, provide justifications, and ask questions as well as one that supports choosing to deeply engage with mathematics and know what mathematics is to them is critical to positioning mathematics as essential and inclusive for all. We must position mathematics in a way that positions students as mathematical thinkers and doers and that supports rich pathways for each and every student rather than inhibits access.
As Catalyzing Change in High School Mathematics (NCTM 2018) describes reasons for broadening the purposes of mathematics, it reminds us that if we limit the position of mathematics, we limit the position and future of our students. We often describe mathematics as furthering education, supporting employment, and preparing for college and career readiness. These are important, but they limit the position of mathematics as potentially only utilitarian and possibly restrictive, that it is for some in certain ways and not for others. Do not misunderstand; mathematics is critical for the future, especially with the needs in both STEM (science, technology, engineering, and mathematics) and non-STEM fields, given the role of quantitative literacy, to expand professional opportunities for all.
The purpose of mathematics is more. It is not only to expand professional opportunities, but also for us to understand and critique our world and engage in mathematics to experience its wonder, joy, and beauty. Therein, “mathematics can be rightfully repositioned to its place as a natural and enjoyable human endeavor.” (NCTM 2020, p. 15) Thus, students are positioned to more likely successfully continue in the study of mathematics, across PK–12 and beyond. It is essential to expand the purposes of mathematics to ensure that each and every student is positioned to contribute and lead as a citizen in a democratic society.
The work of equitable pathways for each and every student to engage deeply in mathematics throughout PK–12 and beyond is nonnegotiable. We must position students, teachers, and mathematics in ways that are empowering in this work or we risk dead-end pathways that inhibit learners’ future and devalue their mathematical brilliance.
Trena Wilkerson
NCTM President
@TrenaWilkerson
REFERENCES
Busby, Laurie, Cynthia Goff, Dean Hanton, Beth Herbel-Eisenmann, Leah Jones, Cindy Loeffert, Evelynne Pyne, and Jodi Wheeler. 2017. “Supporting Powerful Discourse through Collaboration and Action Research.” In Access and Equity: Promoting High-Quality Mathematics in Grades 6–8, edited by Anthony Fernandes, Sandra Crespo, and Marta Civil, pp. 59–76. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics (NCTM). 2018. Catalyzing Change in High School Mathematics: Initiating Critical Conversations. Reston, VA: NCTM.
National Council of Teachers of Mathematics (NCTM). 2020. Catalyzing Change in Middle School Mathematics: Initiating Critical Conversations. Reston, VA: NCTM.
The University of Texas at Austin Charles A. Dana Center, Student Achievement Partners, and Education Strategy Group. 2022. Re-Envisioning Mathematics Pathways to Expand Opportunities: The Landscape of High to Postsecondary Course Sequences.
Wagner, David, and Beth Herbel-Eisenmann. 2009. “Re-Mythologizing Mathematics through Attention to Classroom Positioning.” Educational Studies in Mathematics 72, no. 1 (September): 1–15.