1. Core Math Instruction
RtI Innovations in Education Conference, Milwaukee, WI
October 12-13, 2017

2. Who Am I?
Mathematics consultant and instructional coach at Kalamazoo RESA
Math specialist
Mathematics classroom teacher

3. Who are you? Share your name and role in education
Individually think for 1 minute about how you would complete the following statement…
“A Mathematically Powerful classroom is __________________.”
Share your thoughts at your tables.

4. Opening Exercise
Individually work on solving this problem
Share your strategy with a partner or small group
__________________________________________________________________________
John spent of his money on a sandwich. He spent 2 times as much on a gift for his brother as on some comic books. He had of his money left. What fraction of his money did he spend on comic books?

5. Opening Exercise (cont’d)
What did you find challenging?
How did you feel while solving this problem?
Anticipate where students might struggle with a problem like this.

6. Learning Objectives
Understand the Key Shifts brought about by the CCSSM
Understand the research and recommendations for improving core math instruction, specifically in the area of problem-solving
Practice utilizing the tape diagram as a visual representation and strategy for problem-solving
Participate in a problem-solving protocol as a classroom framework for problem solving

7. CCSSM- Key Shifts Focus Coherence Rigor
~ Key Shifts in Mathematics

8. Focus
Rather than racing to cover many topics in a mile-wide, inch-deep curriculum, the standards ask math teachers to significantly narrow and deepen the way time and energy are spent in the classroom. 
This focus will help students gain strong foundations, including a solid understanding of concepts, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the classroom.
~ Key Shifts in Mathematics

9. Coherence
Mathematics is not a list of disconnected topics, tricks, or mnemonics; it is a coherent body of knowledge made up of interconnected concepts.
The standards are designed around coherent progressions from grade to grade. 
Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years.
~ Key Shifts in Mathematics

10. Rigor
At your tables, discuss what you think is meant by the term “rigor.”

11. Rigor
Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades. To help students meet the standards, educators will need to pursue, with equal intensity, three aspects of rigor in the major work of each grade: conceptual understanding, procedural skills and fluency, and application.
~ Key Shifts in Mathematics

12. Rigor Conceptual Understanding Procedural Skills and Fluency
Application
~ Key Shifts in Mathematics

13. Rigor: Conceptual Understanding
“The standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives in order to see math as more than a set of mnemonics or discrete procedures.” ~ Key Shifts in Mathematics

14. Rigor: Procedural Skills and Fluency
“The standards call for speed and accuracy in calculation. Students must practice core functions, such as single-digit multiplication, in order to have access to more complex concepts and procedures. Fluency must be addressed in the classroom or through supporting materials, as some students might require more practice than others.” ~ Key Shifts in Mathematics

15. Rigor: Application
“The standards call for students to use math in situations that require mathematical knowledge. Correctly applying mathematical knowledge depends on students having a solid conceptual understanding and procedural fluency.” ~ Key Shifts in Mathematics

16. Standards for Mathematical Practice
The eight Standards for Mathematical Practice are:
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning

17. IES Practice Guide: Improving Mathematical Problem Solving

18. IES Practice Guide: Assisting Students Struggling with Mathematics: RtI for Elementary and Middle Schools

19. Connections
What connections do you see between the recommendations listed within the two IES Practice Guides?

20. How do we implement the recommendations?

21. IES Practice Guide: Visual Representations

22. CCSSM: Addition and Subtraction Problem Types

23. Visual Representation: The Tape Diagram
Bar model
Strip diagram
Demo how to create a tape diagram

24. Using tape diagrams Work on problems from Sets 1 and 2 only
Draw a tape diagram to represent the problem
Write an equation to represent your thinking
Find the solution (solve mathematically)
Write your answer including the units (or sentence form)

25. CCSSM: Multiplication and Division Problem Types

26. Using tape diagrams Work on problems from Sets 3 and 4 only
Draw a tape diagram to represent the problem
Write an equation to represent your thinking
Find the solution (solve mathematically)
Write your answer including the units (or sentence form)

27. Reflections: Tape Diagram
What are the benefits of using a tape diagram? Limitations?
How does using a tape diagram assist in solving problems?
Other thoughts or questions about the tape diagram?

28. A Problem-Solving Framework
3-Reads Protocol
A Problem-Solving Framework

31. IES Practice Guide: Improving Mathematical Problem Solving

32. Recommendation 1: Prepare problems and use them in whole-class instruction
How to carry out the recommendation…
Include both routine and non-routine problems in problem-solving activities
Ensure the students will understand the problem by addressing issues students might encounter with the problem’s context or language
Consider students’ knowledge of mathematical content when planning lessons

33. Connections
What connections can you make between the 3-Reads Protocol and Recommendation #1?

34. Recommendation #2: Assist students in monitoring and reflecting on the problem-solving process
How to carry out the recommendation…
Provide students with a list of prompts to help them monitor and reflect during the problem-solving process
Model how to monitor and reflect on the problem-solving process
Use student thinking about a problem to develop students’ ability to monitor and reflect

35. Connections
What connections can you make between the 3-Reads Protocol and Recommendation #2?

36. Recommendation #3: Teach students how to use visual representations
How to carry out this recommendation…
Select visual representations that are appropriate for students and the problems they are solving
Use think-alouds and discussions to teach students how to represent problems visually
Show students how to convert the visually represented information into mathematical notation

37. Connections
What connections can you make between the 3-Reads Protocol and Recommendation #3?

38. Recommendation #4: Expose students to multiple problem-solving strategies
How to carry out the recommendation…
Provide instruction in multiple strategies
Provide opportunities for students to compare multiple strategies in worked examples
Ask students to generate and share multiple strategies for solving a problem

39. Connections
What connections can you make between the 3-Reads Protocol and Recommendation #4?

40. Recommendation #5: Help students recognize and articulate mathematical concepts and notation
How to carry out this recommendation…
Describe relevant mathematical concepts and notation, and relate them to the problem-solving activity
Ask students to explain each step used to solve a problem in a worked example
Help students make sense of algebraic notation

41. Connections
What connections can you make between the 3-Reads Protocol and Recommendation #5?

42. Instructional coaching
At your tables, discuss the following…
How will this information impact student achievement in the area of problem solving?
How could this information be helpful for classroom teachers?
How do you envision this information being used by instructional coaches?
Additional questions?

43. Action Planning/Next Steps
As you think about your role in education, how will you use the information from today’s session?
What are some possible action steps for utilizing this information?
Fill out the provided Action Planning Template

44. Reflection… Front: 3 things I learned… 2 questions I have…
1 next step for implementation…
Back:
Other feedback or suggestions for improving the session
Math topics you would like to hear more about in the future

45. Thank You!
Amy Pratt K-12 Math Consultant Kalamazoo RESA