Mathematics with Rigor, Relevance, and Responsiveness
Consider these three “Rs” of mathematics: Students should engage in rigorous and challenging mathematics that is relevant to their lives and is responsive to their background experiences, cultures, interests, and knowledge. But what do rigor, relevance, and responsiveness mean in teaching and learning mathematics?
I was recently on a panel for a
Data Literacy STEM webinar, and we were asked what rigor was. We shared that sometimes people think rigor is something difficult or unattainable and may be associated with the mathematics of only calculus and beyond. We countered that rigor in mathematics is about challenging students to think deeply about and with mathematics. Rigor is not memorizing a myriad of procedures but being able to flexibly analyze and apply mathematics to different situations with a focus on concepts and relationships. A rigorous approach develops students’ understanding through making connections both within and across mathematics and to other areas of their lives. Rigor works to increase a positive mathematical identity and agency and includes the development of problem-solving skills, conceptual understanding, procedural fluency, and essential mathematical processes and practices.
Catalyzing Change series calls us to engage students in rigorous and intellectually challenging mathematics through meaningful, high-quality mathematical experiences. This can be challenging with a vast amount of content, a broad range of standards, varied prior knowledge and experiences of students, and limited instructional time. Teachers are rising to this challenge daily by organizing a coherent, cohesive curriculum; implementing effective, equitable teaching practices; providing
scaffolding and support to students; and maintaining high expectations for all students to engage in rigorous mathematical learning. NCTM past president Linda Gojak reminded us that “students who are successful in a rigorous learning environment take responsibility for their learning. They learn to reflect on their thinking” (
February 2013 President’s Message).
All students deserve the opportunity to learn mathematics with rigor, but another essential aspect is relevancy.
Engaging in mathematics through relevant contexts helps students build meaning for mathematical concepts or processes, see how it relates to their own lives, and learn to mathematize their world. Relevancy supports students in broadening their understanding of mathematics; critiquing their world; developing reason and sense making; and as many of you know, my favorite, bringing in the wonder, joy, and beauty of mathematics. This provides a trajectory for students to learn mathematics, strengthens their positive mathematical identify, and gives them opportunities to see themselves as thinkers and doers of mathematics. Many curriculum frameworks and standards across states and provinces include problem solving and relevancy to real life in learning and applying mathematics. Engaging students in real-world problems in contexts that are interesting and important to them gives meaning and relevancy to the mathematics. Students need to engage in mathematical experiences that support their understanding of mathematics in their lives and position them for increased opportunities.
Gloria Ladson-Billings (2014) shared that culturally relevant pedagogy requires attention to three components at the same time: (1) academic success, (2) cultural competences, and (3) sociopolitical consciousness. Attending to these three supports students’ learning and appreciation of their own and others’ cultures and takes learning beyond regular classroom structures to applying their knowledge to engage in real-world problems. Ladson-Billings encouraged us to continue to grow in our understanding and implementation by considering a move toward culturally sustaining pedagogy. She stated that “teachers undertaking culturally informed pedagogies take on the dual responsibility of external performance assessments as well as community- and student-driven learning. The real beauty of a culturally sustaining pedagogy is its ability to meet both demands without diminishing either” (pp. 83–84).
Let’s now consider our third “R,” responsiveness, because “curriculum implementation that is not flexible and responsive to local contexts denies children access to rigorous and relevant mathematics learning opportunities” (NCTM 2020a, p. 26).
Learning environments should be responsive to students’ curiosity, to their questions and their lives, to their mathematical wonderings and noticings, to their strengths and backgrounds, and to their social and emotional needs. In particular, culturally responsive teaching reflects students’ interests, needs, lives, culture, gender and sexual identities, and experiences, and it fosters positive mathematical identities. When teaching is culturally responsive, it reflects a learning environment that is meaningful and is situated in the experiences of the students, and it recognizes its importance (Gay 2018; NCTM 2020b).
NCTM has begun curating instructional resources to support teachers in
culturally responsive pedagogy. Student engagement and learning increase with relevant and personally meaningful content. We come to know our students by understanding their cultures, languages, traditions, and interests. In this way, we can create meaningful learning experiences so that students develop a deep understanding of mathematics; make meaningful connections both in their lives and in mathematics; and develop a strong sense of identity, agency, and authority in mathematics. See the latest set of resources focused on
supporting and celebrating LGBTQ+ students and teachers in learning and teaching mathematics.
Rigor, relevance, and responsiveness are not new. In 1933 Breslich shared that the purposes of mathematics include the power of understanding, analysis, being able to use it in real life and in other disciplines, appreciating mathematics, and understanding the needs of students. “The continued study of mathematics should bring power to the individual. The ultimate objective is power to think, to appreciate, and to do” (p. 154).
Rigor, relevance, and responsiveness are as important now as ever before!
Breslich, Ernst R. 1933. The Administration of Mathematics in Secondary Schools. Chicago: The University of Chicago Press.
Gay, Geneva. 2018. Culturally Responsive Teaching: Theory, Research, and Practice. New York: Teachers College Press.
Ladson-Billings, Gloria. 2014. “Culturally Relevant Pedagogy 2.0: a.k.a. the Remix.” Harvard Educational Review 84, no. 1 (Spring): 74–84.
National Council of Teachers of Mathematics (NCTM). 2020a.
Catalyzing Change in Early Childhood and Elementary Mathematics: Initiating Critical Conversations. Reston, VA: NCTM.
National Council of Teachers of Mathematics (NCTM). 2020b.
Catalyzing Change in Middle School Mathematics: Initiating Critical Conversations. Reston, VA: NCTM.