The Wonder of Questions
By Nathan Dilworth
ISA's Director of Teaching and Learning
Questions, to me, are wonder-filled. An invitation to explore. They are both the beginning of a quest to understand and the fuel for the quest’s continuation. This is, in part, why questions are an essential part of our work with teachers, school, and district leaders as we collaborate to cultivate inquiry-focused instruction in classrooms and support school communities in their continuous improvement efforts. As we close out an unprecedented school year, many questions are being asked about the instructional ramifications of this year for the start of next school year, when many more schools expect live in-person instruction to be more prevalent. Conversations are happening across the spectrum, from discipline-focused professional organizations to grade-level teams in schools.
As a former mathematics teacher, I’m particularly attuned to the conversation as it relates to mathematics.
Recently, the National Council of Teachers of Mathematics (NCTM) held a webinar to focus was on how to support students next year. Webinar panelists made a number of wonderful points about meeting the whole student where they are next year. Among the exhortations from the panelists was a call to maintain focus on grade-level standards and to hone in on the big ideas, those that span grade levels and standard bands. In other words, what are the big questions that help us get deeper as the content evolves? I love these kinds of questions because they can accentuate the coherence inherent in mathematics. So I wanted to offer one question I’ve used with students and teachers that has helped deepen connections and focus on one of the big ideas within mathematics: What is the power of equality?
This question asks that we understand (a) the relational essence of equality, (b) the way equality manifests in different mathematical representations, and (c) the way in which maintaining the relationship allows us to manipulate expressions and solve problems. As a question that can span grade levels and standard bands, “What is the power of equality?” works for elementary students beginning to understand the relational essence when using operations (1 + 2 = 3) or placing equivalent numbers or expressions at the same place on a number line, so that we see that equality doesn’t require that equivalent numbers or expressions look the same (3/4 = 6/8 = 0.75 = 1 – 1/4 = 1/2 + 1/4). This question also works for middle school students, as they begin to solve equations by keeping the expressions on each side equivalent or comparing the rates of change of linear relationships. The algebra student solves systems of equations and substitutes an expression for a variable because they are equivalent. The examples could continue into other parts of mathematics. Thus, “What is the power of equality?” is a question that can travel with students.
Often, we wonder how to connect mathematical content to historical, political, and social moments. Considering this with equality in mind, there’s an opportunity to engage our students in dialogue about,
- “…all men are created equal…,” the United States Declaration of Independence
- “…equal protection of the laws,” 14th Amendment to the Constitution of the United States
- Equal Pay Act of 1963
- Equal Pay Day, March 24
- “…separate but equal…,” Plessy v. Ferguson
Furthering the inquiry to understand what equality is intended to accomplish in these and other instances raises more questions: What’s being set as equal? What’s the basis of the equivalence? In what terms was equality upheld or not? How does or doesn’t the use of equality align with our mathematical notion of equality? The relational ideas in mathematics are entry points for deepening our understanding of mathematics and a tool for understanding events past and present.
As this year comes to a close and planning for next year continues, it’s both the community and the questions that drive inquiry and improvement. It matters who’s part of the question-asking and what questions are made central in shaping supports, curricular or otherwise, for students, teachers, and administrators in the coming school year.
So now my questions to you are:
- What’s a question you and your community are exploring?
- What’s a question you embed in your curriculum that takes you and your students deeper?
- What other mathematical concepts can we connect to the world around us?
Share them with us (@ISAachieves) using #coachingISA.
National Council of Teachers of Mathematics. (2021). Understanding and reframing “learning loss” in mathematics: Goals, policies, and practices for strengths-oriented and equitable solutions. https://www.nctm.org/online-learning/Webinars/Details/551
(Photo courtesy of Allison Shelley and the Alliance for Excellent Education. More info here.)
Want to learn more about our work at ISA in the area of mathematics, coaching, and social, emotional, and academic development (SEAD)? See this webinar focused on a SEAD strategy called Maze Moment.
See also this mathematics class at ISA partner school Innovation High School in Newark, NJ, where students engage in self-assessment practices across the curriculum every day.