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

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

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.

Opening Exercise Individually work on solving this problem Share your strategy with a partner or small group __________________________________________________________________________ John spent 1 4 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 3 8 of his money left. What fraction of his money did he spend on comic books?

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.

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

CCSSM- Key Shifts Focus Coherence Rigor ~www.corestandards.org, Key Shifts in Mathematics

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. ~www.corestandards.org, Key Shifts in Mathematics

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. ~www.corestandards.org, Key Shifts in Mathematics

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

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. ~www.corestandards.org, Key Shifts in Mathematics

Rigor Conceptual Understanding Procedural Skills and Fluency Application ~www.corestandards.org, Key Shifts in Mathematics

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.” ~www.corestandards.org, Key Shifts in Mathematics

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.” ~www.corestandards.org, Key Shifts in Mathematics

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.” ~www.corestandards.org, Key Shifts in Mathematics

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

IES Practice Guide: Improving Mathematical Problem Solving

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

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

How do we implement the recommendations?

IES Practice Guide: Visual Representations https://youtu.be/hv3_S2ZLNHg

CCSSM: Addition and Subtraction Problem Types

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

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)

CCSSM: Multiplication and Division Problem Types

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)

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?

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

IES Practice Guide: Improving Mathematical Problem Solving

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

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

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

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

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

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

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

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

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

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

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?

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

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

Thank You! Amy Pratt K-12 Math Consultant Kalamazoo RESA amy.pratt@kresa.org 269.250.9343