Effective teaching and learning in mathematics

An effective teacher of mathematics supports student learning by integrating teaching practices into their daily lessons. The National Council of Teachers of Mathematics (NCTM) recently released current research supporting effective teaching practices in Principles to Actions: Ensuring Mathematical Success for All. This book is broken into 3 sections: Effective Teaching and Learning, Essential Elements, and Taking Action. The primary focus of this series of articles will be on supporting teachers in implementing the 8 Effective Teaching Practices outlined in the book.

These are:

  1. Establish Mathematics Goals to Focus 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

Other resources that are available to support understanding of the 8 Teaching Practices can be found on the NCTM Principles to Actions Toolkit webpage.

In this series of instructional articles we will discuss several of these Effective Teaching Practices. The first of these is practice 4, Facilitate Meaningful Mathematical Discourse. This teaching practice supports the engagement of students in advancing the mathematical learning of the class as a whole. Providing opportunities for students to share their thinking, clarify their understanding, and learn from other perspectives supports the development of conceptual understanding and adds meaning to the mathematical learning.

An effective teacher supports opportunities for mathematical discourse as they facilitate the discussion with guiding and/or probing questions. An emphasis on the appropriate use of academic vocabulary during discourse provides opportunity for students to grapple with the language of mathematics, providing support in becoming a clear and effective communicator within the content area. Ensuring students have opportunity to talk about the mathematics in which they are engaged in supports building a deeper understanding of how and why it works. They need this to construct viable arguments and critique the reasoning of others, which is mathematical practice 3 in our College and Career Readiness Standards. The website Illustrative Mathematics provides classroom resources, such as tasks, teachers can use to support students in constructing viable arguments and critiquing the reasoning of others.

Recent research around mathematical discourse has led to the publication of 5 Practices for Orchestrating Productive Mathematics Discussions. In this text 5 practices are identified, discussed, and illustrated. These practices are:

  • Anticipating what students will do–what strategies they will use–in solving a problem
  • Monitoring their work as they approach the problem in class
  • Selecting students whose strategies are worth discussing in class
  • Sequencing those students’ presentations to maximize their potential to increase students’ learning
  • Connecting the strategies and ideas in a way that helps students understand the mathematics learned

Another recent publication, Making Number Talks Matter, provides a focus on mathematical discourse based on the four operations (addition, subtraction, multiplication, and division). In the text there are 10 guiding principles identified in support of number talks. These are:

  1. All students have mathematical ideas worth listening to, and our job as teachers is to help students learn to develop and express these ideas clearly.
  2. Through our questions, we seek to understand students’ thinking.
  3. We encourage students to explain their thinking conceptually rather than procedurally.
  4. Mistakes provide opportunities to look at idea that might not otherwise be considered.
  5. While efficiency is a goal, we recognize that whether or not a strategy is efficient lies in the thinking and understanding of each individual learner.
  6. We seek to create a learning environment where all students feel safe sharing their mathematical ideas.
  7. One of our most important goals is to help students develop social and mathematical agency.
  8. Mathematical understandings develop over time.
  9. Confusion and struggle are natural, necessary, and even desirable parts of learning mathematics.
  10. We value and encourage a diversity of ideas.

In addition to these principles, the text also provides examples and illustrations of number talks in the four operations across grades 4-10.

Explore the resources provided in this article and consider how you will apply them in your classroom to support opportunities for your students to participate in mathematics discourse!

For further information, contact Maine DOE Mathematics Specialist Michele Mailhot at michele.mailhot@maine.gov.