Mark Roddy, Ph.D. Seattle University Effective Teaching Practices in Mathematics from the Marzano 9, to the NCTM 8, to your classroom

Marzano’s High-Yield Strategies: 2 Identifying Similarities and Differences Summarizing and Note Taking Reinforcing Effort and Providing Recognition Homework and Practice Linguistic and Nonlinguistic Representations Cooperative Learning Setting Objectives and Providing Feedback Generating and Testing Hypotheses Questions, Cues, and Advance Organizers High Yield Instructional Strategies 45% 34% 29% 28% 27% 23% 22% Source: “Original CT4GC Day 3 afternoon Math Strategies--Ashland--PM For Presenting.pptx” Percentile gains

High Yield Instructional Strategies 3 Yields 45% Increase! #1 Marzano, R. J., Pickering, D., & Pollock, J. E. (2001). Classroom instruction that works: Research-based strategies for increasing student achievement. Alexandria, Va: Association for Supervision and Curriculum Development.

High Yield Instructional Strategies 4 Yields 34% Increase! #2

High Yield Instructional Strategies 5 Yields 29% Increase! #3

High Yield Instructional Strategies 6 Yields 28% Increase! #4

High Yield Instructional Strategies 7 Yields 27% Increase! #5

High Yield Instructional Strategies 8 Yields 23% Increase! #6

High Yield Instructional Strategies 9 Yields 23% Increase! #7

High Yield Instructional Strategies 10 Yields 23% Increase! #8

High Yield Instructional Strategies 11 Yields 22% Increase! #9

High Yield Instructional Strategies 12

Effective Mathematics Teaching Practices 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. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.

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. #1 What will we learn? Why is it important? How does it relate to what we already learned? Where are we going with this?

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. #2

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. #3

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. #4

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. #5 IRE Questions Funneling Questions Focusing Questions

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. #6

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. #7 “I don’t know how to do that. I give up  ” (fixed mindset) “I don’t know how to do that. I give up  ” (fixed mindset) “I don’t know how to do that but I think I might be able to try …” (growth mindset) “I don’t know how to do that but I think I might be able to try …” (growth mindset)

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. #8 Formative Assessment!

Effective Mathematics Teaching Practices 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. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author. Your Favorite?

Where are the strongest matches?

This module was developed by Amy Hillen, et. al., University of Pittsburgh Institute for Learning. Video courtesy Patterson Public Schools and the University of Pittsburgh Institute for Learning. These materials are part of the Principles to Actions Professional Learning Toolkit: Teaching and Learning created by the project team that includes: Margaret Smith (chair), Victoria Bill (co-chair), Melissa Boston, Fredrick Dillon, Amy Hillen, DeAnn Huinker, Stephen Miller, Lynn Raith, and Michael Steele. Principles to Actions Effective Mathematics Teaching Practices The Case of Millie Brooks and the Half of a Whole Task Grade 3 Principles to Actions Effective Mathematics Teaching Practices The Case of Millie Brooks and the Half of a Whole Task Grade 3 Note: You may need to be a member of NCTM …

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. 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. Teaching strengths? Weaknesses? Effective Mathematics Teaching Practices

This module was developed by Victoria Bill, et. al. Video courtesy of Paterson Public Schools, New Jersey, and the University of Pittsburgh Institute for Learning. These materials are part of the Principles to Actions Professional Learning Toolkit: Teaching and Learning created by the project team that includes: Margaret Smith (chair), Victoria Bill (co-chair), Melissa Boston, Fredrick Dillon, Amy Hillen, DeAnn Huinker, Stephen Miller, Lynn Raith, and Michael Steele. This module was developed by Victoria Bill, et. al. Video courtesy of Paterson Public Schools, New Jersey, and the University of Pittsburgh Institute for Learning. These materials are part of the Principles to Actions Professional Learning Toolkit: Teaching and Learning created by the project team that includes: Margaret Smith (chair), Victoria Bill (co-chair), Melissa Boston, Fredrick Dillon, Amy Hillen, DeAnn Huinker, Stephen Miller, Lynn Raith, and Michael Steele. Principles to Actions Effective Mathematics Teaching Practices The Case of Victoria Bill and the Bubble Gum Task Grade 3 Principles to Actions Effective Mathematics Teaching Practices The Case of Victoria Bill and the Bubble Gum Task Grade 3 Principles-to-Actions-Toolkit/The-Case-of-Victoria-Bill-and-the- Bubble-Gum-Task/

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. 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. Teaching strengths? Weaknesses? Effective Mathematics Teaching Practices

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. 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. T/P/SUsing what you know about the CCSSm, the SBAC, your school and your students, consider the teaching practices, and pick one or two that seem most important. Explain your selection.

For the second hour of this module: Step 0 10 min. Identify a partner for the next steps. Take a break, then reconnect. Step 1 5 min. On your own, consider the 8 NCTM Mathematics Teaching Practices and order them from the one that is easiest for you to the one that is hardest. Step 2 5 min. Briefly discuss your order and your rationale for this order with your partner. Make sure both partners have time to talk. Step 3 10 min. On your own, consider a topic you teach often and the specifics of how you teach it. Now think of ways in which you could more effectively address at least one and at most three of the 8 NCTM Mathematics Teaching Practices. Take your time with this. Write some notes. Arrange to reconnect with your partner at a specific time (e.g., 5:00). Step 4 10 min. Share your thoughts with your partner. Why did you choose the specific Teaching Practice(s) that you did? What will be difficult/easy about this? Make sure both partners have time to talk.

Module 21 Assignment to be Uploaded STEP min. Using the work you did in Steps 3 and 4, respond to the following prompts and submit the completed document for Module 21. What mathematics topic and what grade level have you selected? Identify at least one and no more than three specific changes you will make in the way you teach this topic. Use this format for each response: “In order to address NCTM Mathematics Teaching Practice x, I will … “ “This will be effective because, … “ Please upload your work to Drop Box in two locations. 1. Upload it to your own SBAC folder for your record. 2. Upload it to X-Module > Module 21 folder. Trainers have access to this folder. If you don't have the access, please your work to the trainer in your school and have her/him upload it. To upload, find folder "X-Module,” then find folder “Module 21.” Upload the file in this folder (X-module > Module 21).