Math Teaching Practices

Teaching is a complex endeavor and it is unrealistic for teachers to focus on improving everything they do at once. In practice-based teacher education (Ball & Cohen, 1999; Ball & Forzani, 2009; Forzani, 2014), teachers identify key aspects of their teaching practice and focus on systematically improving them through cycles of planning, enactment, and feedback. Teaching is treated as a skill to be practiced and refined, and not something that "comes naturally" or is improvisational in nature. Below are two good sources for a list of teaching practices and resources to help teachers improve on each of them.

These and other tools are part of the District Sample Curriculum Project's (DSCP) Phase IV focus on instructional strategies.

Mathematics Teaching Practices

Source: National Council of Teachers of Mathematics (NCTM)

In the book Principles to Actions: Ensuring Mathematical Success for All (2014), NCTM identifies eight research-based essential Mathematics Teaching Practices:

• Establish mathematics goals to focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.
• Implement tasks that promote reasoning and problem solving. Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.
• Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.
• Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.
• Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.
• Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.
• Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.
• Elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

Principals to Actions details each of these practices in 5-6 pages, including examples and clear descriptions of what both teachers and students should expect to be doing when the practice is being used.

High-Leverage Practices

Source: TeachingWorks, University of Michigan

The nineteen "high-leverage practices" from the TeachingWorks project at the University of Michigan describe fundamental capabilities teachers must have. These are not specific to mathematics and are finer-grained than those in Principles to Actions.

1. Leading a group discussion
2. Explaining and modeling content, practices, and strategies
3. Eliciting and interpreting individual students' thinking
4. Diagnosing particular common patterns of student thinking and development in a subject-matter domain
5. Implementing norms and routines for classroom discourse and work
6. Coordinating and adjusting instruction during a lesson
7. Specifying and reinforcing productive student behavior
8. Implementing organizational routines
9. Setting up and managing small group work
10. Building respectful relationships with students
11. Talking about a student with parents or other caregivers
12. Learning about students' cultural, religious, family, intellectual, and personal experiences and resources for use in instruction
13. Setting long- and short-term learning goals for students
14. Designing single lessons and sequences of lessons
15. Checking student understanding during and at the conclusion of lessons
16. Selecting and designing formal assessments of student learning
17. Interpreting the results of student work, including routine assignments, quizzes, tests, projects, and standardized assessments
18. Providing oral and written feedback to students
19. Analyzing instruction for the purpose of improving it

The TeachingWorks website has short descriptions of each of the above practices along with other resources and professional opportunities.

References

Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–32). San Francisco, CA: Jossey-Bass.

Ball, D. L., & Forzani, F. M. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5), 497–511. http://doi.org/10.1177/0022487109348479

Forzani, F. M. (2014). Understanding “core practices” and “practice-based” teacher education: Learning from the past. Journal of Teacher Education, 65(4), 357–368. http://doi.org/10.1177/0022487114533800