Learning More About Effective Teaching Practices

  • Learning More About Effective Teaching Practices
    January 2022

    What will 2022 bring us with regard to teaching and learning mathematics, and what will we bring to 2022? Although I usually do not make New Year’s resolutions, I do think this is a great time for us to reflect on the eight Effective Teaching Practices identified in NCTM’s Principles to Actions: Ensuring Mathematical Success for All (2014, p. 10) as we move into the new year. Perhaps we can commit to selecting one, or more, to dig into, to learn more about, and to more effectively implement in our teaching of mathematics.

    1. Establish mathematics goals to focus on learning.
    2. Implement tasks that promote reasoning and problem-solving.
    3. Use and connect mathematical representations.
    4. Facilitate meaningful mathematical discourse.
    5. Pose purposeful questions.
    6. Build procedural fluency from conceptual understanding.
    7. Support productive struggle in learning mathematics.
    8. Elicit and use evidence of student thinking.

    These practices provide a research-based framework for guiding and strengthening the teaching and learning of mathematics. When implemented effectively, they are high-leverage, essential, equitable practices; and taken together, they support and promote a deep learning of mathematics. All are essential, but in my work with teachers, I have found that we often discover that some practices are our strengths, others we want to improve, and still others stand out as a priority depending on our students or the content being addressed. Teachers share that any one of them always leaves room to grow and some lessons reflect the practices effectively whereas others fall short of what we want. Yet we keep striving to grow and improve to meet the needs of our students.

    During the past few years, I have used the practices to frame my secondary mathematics methods course so that my preservice teachers learn more about each practice and have opportunities to work on them in their field placements. For the past five years, a colleague and I have used them as a focus for professional development with grades 5–12 mathematics teachers. Initially we did an overview of all eight, and then in subsequent years, we focused primarily on one. In each of those focused years, we engaged in studying the research behind the practice, examined videos of teachers using these practices with both productive and unproductive actions, worked through tasks to strengthen our understanding, and then set goals in planning for the school year regarding the practice. 

    For me, I have decided to intentionally work on the mathematics teaching practice to implement tasks that promote reasoning and problem solving, and most specifically on the problem-solving aspect. Problem solving has been a mathematical process of focus for me for many years. I have worked on promoting problem solving through the use of literature, representations, and the role of communication. But I want to examine some other aspects, such as under what conditions does a problem or task really support problem solving for an individual student? Is it different from one student to another, and in what ways? How is implementing a task that promotes problem solving connected to other practices? I know that it is related to the cognitive demand of the task or problem; that it connects to whether the problem has multiple solutions, multiple entry points, or varied useful strategies for solving; and that sequencing tasks are considerations. But I want to learn more about how these can vary from student to student and across mathematical concepts. So, I will read more of the research, study student work on particular problems, and examine the connection to access and equity. In what ways do problem-solving tasks provide access to all students, and when do they not?

    Problem solving is a key process standard that supports students in thinking critically, an essential 21st-century skill. I am reminded of the statement by Martin Luther King Jr. that “the function of education is to teach one to think intensively and to think critically” (King 2005). Engaging students in ways that develop their problem-solving skills is nonnegotiable in teaching them to understand and critique their world. Here are ways that we can continue our learning on these practices:

    • Read related research and practitioner articles.
    • Explore tasks and problems examining their cognitive demand and accessibility.
    • Examine and analyze student work on a particular problem.
    • Engage in approaches such as action research or lesson study to study our practice.
    • Work with colleagues, holding one another accountable and exchanging constructive feedback on our practice.
    • Organize a book study.
    • Join a discussion group on social media.
    • Engage in professional development workshops.
    • Attend a mathematics education conference and focus on sessions about the selected practice.
    • Participate in webinars.

    As addressed in the NCTM Taking Action series (2017), which unpacks each practice by grade band, we need time to reflect on our current teaching practices and make changes as needed so that we can support students’ learning of mathematics. It is a process and a journey, not something that we master overnight. “Persistence and commitment will help  [us] continue the journey to instructional improvement” (NCTM 2017, p. 228).

    I commit to spending more time on deepening my own understanding of the practice to implement tasks that promote reasoning and problem solving. Perhaps that is a New Year’s resolution! Will you join me and select a practice to be a focus for you this year? Let’s hold one another accountable for growing in our understanding of teaching mathematics. We can continue to learn. We must—to ensure that each and every student is supported in developing a deep understanding of mathematics and developing as a thinker and doer of mathematics. 

    Trena Wilkerson
    NCTM President


    Boston, Melissa, and Frederick Dillon. 2017. Taking Action: Implementing Effective Mathematics Teaching Practices, Grades 9–12. Reston, VA: National Council of Teachers of Mathematics.

    King, Martin Luther, Jr. 2005. The Papers of Martin Luther King, Jr., Volume V: Threshold of a New Decade, January 1959–December 1960. Edited by Clayborne Carson, Tenisha Hart Armstrong, and Adrienne Clay. Berkeley: University of California Press.

    National Council of Teachers of Mathematics (NCTM). 2014. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM.