Overview
This lecture provides an overview of the eight effective mathematics teaching practices outlined by the National Council of Teachers of Mathematics to enhance learning and teaching in mathematics classrooms.
Establish Mathematics Goals to Focus Learning
- Teachers set clear goals to guide student learning and instructional decisions.
- Students use these goals to monitor their understanding and progress.
Implement Tasks that Promote Reasoning and Problem Solving
- Teachers select tasks that engage all students in challenging, meaningful math problems.
- Tasks are designed with “low floor, high ceiling” to ensure accessibility and challenge.
Use and Connect Mathematical Representations
- Teachers encourage students to use multiple representations (diagrams, drawings, manipulatives) to deepen understanding.
- Students explain and link different mathematical representations.
Facilitate Meaningful Mathematical Discourse
- Teachers support student-centered discussions to share mathematical thinking.
- The “five practices” (anticipate, monitor, select, sequence, connect) guide discourse.
Pose Purposeful Questions
- Teachers use intentional questions to promote explanation, reasoning, and justification.
- Questions are designed to focus student thinking (“focusing” and “funneling” types).
Build Procedural Fluency from Conceptual Understanding
- Teachers provide opportunities to develop conceptual understanding before building procedural skills.
- Connections between student strategies and efficient procedures are emphasized.
Support Productive Struggle in Learning Mathematics
- Teachers allow students to grapple with challenging tasks and support them appropriately.
- Students persist and support each other through difficult problems without giving up.
Elicit and Use Evidence of Student Thinking
- Teachers gather and use evidence of student understanding to inform instruction.
- Students reflect on and assess their learning using feedback and discourse.
Key Terms & Definitions
- Low Floor, High Ceiling — tasks accessible to all students but still provide challenge.
- Representations — various ways (diagrams, manipulatives, drawings) to express mathematical ideas.
- Productive Struggle — student effort on challenging tasks leading to deeper understanding.
- Procedural Fluency — efficient and accurate execution of mathematical procedures.
Action Items / Next Steps
- Visit the NCTM Principles to Actions Professional Learning Toolkit for more information on the eight effective teaching practices.