1. Fostering Exemplary Mathematics Teaching and Learning in Your School
Sheryl Stump, Ball State University
Angela Snyder, Carmel Clay Schools

2. Goals
At the end of the session, participants will be able to identify and describe:
What to look for in the K-12 mathematics classroom.
How to support teachers in refining their teaching practices.

3. A Peek into One Mathematics Classroom

4. Shamrock Smile Mile
Put checks beside any of the representations that are accurate for our problem of 2/3 of 3/4.
Select any 2 of the representations and write an explanation for why it is accurate or why it is not an accurate representation.

5. A Passion for Fractions
Lesson Objective: Multiply a fraction by a fraction
Becky Pittard
Pathways Elementary School
Ormond Beach, FL
5th Grade

6. What did you notice in the video?

7. What to Look for in the K-12 Mathematics Classroom
Effective Mathematics Teaching Practices
& Classroom Norms

9. Effective 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.
Handout
Read and underline important phrases.
Turn to your Handout. Read and underline important phrases.
Then turn and share one important idea that stood out for you with a neighbor.
Allow about 7 minutes.

10. mathematical representations.
Use and connect
mathematical representations.
Math
Teaching
Practice 3
Strengthening the ability to move between and among these representations improves the growth of children’s concepts.
(Lesh, Post, & Behr, 1997)

11. mathematical representations
Use and connect
mathematical representations
Different representations should:
Be introduced, discussed, and connected.
Focus students’ attention on the structure of mathematical ideas by examining essential features.
Support students’ ability to justify and explain their reasoning.
(Lesh, Post, & Behr, 1987; Marshall, Superfine, & Canty, 2010; Tripathi, 2008; Webb, Boswinkel, & Dekker, 2008)

12. Use and Connect Mathematical Representations: Teacher and Student Actions

13. Facilitate meaningful mathematical discourse.
Teaching
Practice 4
Discussions that focus on cognitively challenging mathematical tasks, namely those that promote thinking, reasoning, and problem solving, are a primary mechanism for promoting conceptual understanding of mathematics.
(Hatano & Inagaki 1991; Michaels, O’Connor, & Resnick 2008)

14. Facilitate meaningful mathematical discourse
Mathematical discourse should:
Build on and honor students’ thinking.
Let students share ideas, clarify understandings, and develop convincing arguments.
Engage students in analyzing and comparing varied student approaches and strategies.
Advance the math learning of the whole class.
(Carpenter, Franke, & Levi, 2003; Fuson & Sherin, 2014; Smith & Stein, 2011)

15. Facilitate Meaningful Discourse: Teacher and Student Actions

16. Pose purposeful questions.
Math
Teaching
Practice 5
Teachers’ questions are crucial in helping students make connections and learn important mathematics concepts.
(Weiss & Pasley, 2004)

17. Pose purposeful questions
Effective Questions should:
Reveal students’ current understandings.
Encourage students to explain, elaborate, or clarify their thinking.
Make the targeted mathematical ideas more visible and accessible for student examination and discussion.
(Boaler & Brodie, 2004; Chapin & O’Connor, 2007; Herbel-Eisenmann & Breyfogle, 2005)

18. Pose Purposeful Questions: Teacher and Student Actions

19. Build procedural fluency from conceptual understanding.
Math
Teaching
Practice 6
Build procedural fluency from conceptual understanding.
A rush to fluency undermines students’
confidence and interest in mathematics and is considered a cause of mathematics anxiety.
(Ashcraft 2002; Ramirez Gunderson, Levine, & Beilock, 2013)

20. Build procedural fluency from conceptual understanding
Procedural Fluency should:
Build on a foundation of conceptual understanding.
Over time (months, years), result in known facts and generalized methods for solving problems.
Enable students to flexibly choose among methods to solve contextual and mathematical problems.
(Baroody, 2006; Fuson & Beckmann, 2012/2013; Fuson, Kalchman, & Bransford, 2005; Russell, 2006)

21. Fluency develops over time... and it builds from conceptual understanding.
Initial exploration and discussion
Informal reasoning strategies
Eventual use of general methods
Principles to Actions (NCTM, 2014, p. 42)

22. Build Procedural Fluency from Conceptual Understanding: Teacher and Student Actions

23. Support productive struggle in learning mathematics.
Teaching
Practice 7
Support productive struggle in learning mathematics.
The struggle we have in mind comes from solving problems that are within reach and grappling with key mathematical ideas that are comprehendible but not yet well formed.
(Hiebert, Carpenter, Fennema, Fuson, Human, Murray, Olivier, & Wearne, 1996)

24. Support productive struggle in learning mathematics
Productive Struggle should:
Be considered essential to learning mathematics with understanding.
Develop students’ capacity to persevere in the face of challenge.
Help students realize that they are capable of doing well in mathematics with effort in using appropriate strategies.
(Black, Trzesniewski, & Dweck, 2007; Dweck, 2008; Hiebert & Grouws, 2007; Kapur, 2010; Warshauer, 2011)

25. Support Productive Struggle in Learning Mathematics: Teacher and Student Actions

26. Tool 2.8 Effective Teaching “Look-Fors”

28. Classroom Norms

29. How to Support Teachers in Refining their Teaching Practices
Coaching-Cycle Tools
& Mathematics Teacher Leadership

30. Coaching-Cycle Tools
Planning
Data-Gathering
Reflection

31. 4.3 Planning Tool: Building Perseverance

32. 4.6 Data-Gathering Tool: Building Perseverance

33. 4.11 Reflection Tool: Building Perseverance

34. Mathematics Teacher Leadership
Mathematics teacher leaders are school-based teacher leaders who are responsible for supporting other teachers with mathematics teaching and learning.

35. Some Options for Mathematics Teacher Leadership
Team Learning
Individual LEARNING
Grade-Level Collaborative Planning
Analyzing Student Work
Lesson Study
Lesson Design
Instructional Rounds
Assessment Development
Engaging in Mathematics
Demonstration Lessons
Co-Planning and Co-Teaching
Collaborative Coaching
Pre-Observation Discussion
Observation
Post-Observation Discussion

36. Upcoming Events HAMTE Mathematics Teacher Leadership Conference
& Indiana Mathematics Leadership Academy

37. HAMTE Mathematics Teacher Leadership Conference
Friday, March 9, 2018, 8:30 am – 3:30 pm
Schwitzer Student Center, University of Indianapolis
Keynote speakers Shannon Larsen and Jenny Jorgensen, from the University of Maine, provide expertise in mathematics coaching
Morning and afternoon breakout sessions focus on specific issues related to mathematics teacher leadership in elementary and middle schools
$40 per participant if registration completed by February 23
Conference website:

38. Indiana Mathematics Leadership Academy

39. Teams of Grades K-8 principals & teacher leaders will —
Establish a clear and common vision for mathematics teaching learning in their schools.
Develop knowledge and use tools for supporting effective mathematics teaching and visionary professional learning.
Work collaboratively to develop and implement plans for activating their common vision.

40. Indiana Mathematics Leadership Academy
Summer Institute
Follow-Up Seminars
June 12-14, 2018
Plconnect.info/IMLA
October 3, 2018
February 6, 2019
April 10, 2019
$200/participant