Improving Math Achievement Through Engagement, Exploration, and Response Presented by:

Objectives/Outcomes Participants will deepen their understanding of mathematics discourse, including some background and rationale. Participants will experience Number Talks and consider how they might be used as part of a daily routine. Participants will deepen their understanding of how mental math, computation strategies and justification of their thinking will impact their student’s achievement. Go over the objectives/outcomes for this session

Targeted Audience K-5 mathematics teachers implementing mathematical discourse

Agenda Background and rationale Experience a variety of Number Talks Consider implications for implementation of mathematics discourse. Closing

Entrance Ticket What effective teaching strategies in mathematics have you implemented in your classroom that have had a positive impact on your students achievement? Participants will complete the entrance ticket upon entering and begin reading the article on How to Get Students Talking! Generating Math talk that supports Learning.

How to Get Students Talking Read the article excerpt when you complete your entrance ticket. “How to Get Students Talking! Generating Math Talk That Supports Math Learning” by: Lisa Ann de Garcia http://www.mathsolutions.com/documents/how_to_get_students_talking.pdf

Why Talk About Math? “ Our classrooms are filled with students and adults who think of mathematics as rules and procedures to memorize without understanding the numerical relationships that provide the foundation for these rules.” Introduction

Ice Breaker – Digit Place Guess my number! It’s a 3 digit number! There are no repeated digits! Explain your reasoning behind choosing your 3 digit number.

Understanding Math Discourse Talk Formats Whole-Class Discussion Small-Group Discussions Partner Talks Classroom Discussions: Using Math Talk to Help Students Learn -S. Chapin, C. O’Connor, N Anderson (2003)

What are Number Talks? Classroom conversations and discussions around purposefully crafted computation problems are at the very core of number talks. Number Talks incorporate: Accuracy: The ability to produce an accurate answer. Efficiency: The ability to choose an appropriate, expedient strategy for a specific computation problem. Flexibility: The ability to use number relationships with ease in computation.

Number Talks Number talks were developed for classroom teachers to engage students in “mental math” through grappling with interesting mathematics problems. Number talks is a pivotal vehicle for developing efficient, flexible and accurate computation strategies that build upon the key foundational ideas of mathematics such as composition and decomposition of numbers, our system of tens, and the application of properties. Accuracy denotes the ability to produce an accurate answer; efficiency refers to the ability to choose an appropriate, expedient strategy for a specific computation problem; and flexibility means the ability to use number relationships with ease in computation.

Key Components of Number Talks Classroom Environment and Community Building a cohesive classroom community is essential for creating a safe risk free environment for effective number talks. Classroom Discussions Students are given the opportunity to share their strategies and justifications with their peers. The Teacher’s Role Facilitator, questioner, listener, learner, and scriber. The Role of Mental Math Encourages students to build on number relationships to solve problems instead of relying on memorized procedures. Purposeful Computation Problems Guides students to focus on mathematical relationships to build mathematical understanding and knowledge.

Classroom Environment and Community Safe, risk-free environment Students comfortable and offer responses for discussion Classroom exhibits a culture of acceptance based on the common goal of learning and understanding Community of learners based on mutual respect

Benefits of Sharing and Discussing Computation Strategies Students have the opportunity to: Clarify their own thinking Consider and test other strategies to see if they are mathematically logical. Investigate and apply mathematical relationships. Build a repertoire of efficient strategies. Make decisions about choosing efficient strategies for specific problems.

The Teacher’s Role “Since the heart of number talks is classroom conversations, it is appropriate for the teacher to move into the role of facilitator.” Teachers must change their thinking from concentrating on the final correct answer, to listening and learning about students’ natural thinking through asking open ended questions. “What answer did you get?” “How did you get your answer?”

The Role of Mental Math Students need to approach problems without paper and pencil, and are encouraged to rely on what they know and understand about numbers and how they are related. Mental computation helps students strengthen their understanding of place value. Look at numbers as whole quantities and NOT JUST DIGITS! A problem such as, 199+199 written horizontally helps illustrate this reasoning.

Mathematical Thinking Counting All Counting On Known Facts Derived Facts Decomposing Recomposing Duality, Ambiguity, and Flexibility in Successful Mathematical Thinking Research by Eddie Gray and David Tall, 1994

Purposeful Computation Problems Careful planning BEFORE the number talk is necessary to design “just right” problems for students. This planning is important because we want to have a purposeful number talk with a common focus/specific skill in mind.

Establishing Procedures and Setting Expectations: The Four Essentials The number talk is designed to be only five to fifteen minutes of focused discussion. Select a designated location that allows you to maintain close proximity to your students for informal observations and interactions. Provide appropriate wait time for the majority of the students to access the problem. Accept, reject, and consider all answers. Encourage student communication throughout the number talk. Location of students is critical

Number Talks and Time Number Talks (about 10 minutes) Mini-Lesson (10 to 20 minutes) Lesson (more than 20 minutes)

Number Talk Examples Dot Patterns Mental Math Number Strings True/False Statements Dilemmas Spatial Reasoning What’s My Rule? Error Analysis and Coaching

Holding Students Accountable for their Learning Ask students to use finger signals to indicate the most efficient strategy. Keep records of problems posed in the corresponding student strategies. Hold small-group number talks every day. Create and post class strategy charts. (living document) Require students to solve an exit problem using the discussed strategies. (use an index card) Give a weekly computation assessment. ** When discussing #5, talk about index card using the purposeful strategy on the front and any other strategy the student wishes on the back. These exit cards are NEVER graded since they are used as a formative assessment only. This will help you direct the next day’s number talk.

Four Goals for K-2 Number Talks Developing Number Sense Developing fluency with small numbers Subitizing Making Fives and Tens Number Conservation Number Talks -Sherry Parrish

Five Goals for Number Talks 3-5 Number sense Place value Fluency Properties Connecting mathematical ideas Number Sense: Estimation of a reasonable answer Applying Place Value to Computation Fluency: Knowing how a number can be composed and decomposed and using that information to be flexible and efficient with solving problems. Connections: Not just real-world word problems but the relationship between addition, subtraction, multiplication and division

Curriculum Leadership Council 2011-2012 CLC December 6, 2011 Hand Signals Solution Strategy Question Comment I agree Integers Fractions

Number Talks in Action Video http://www.insidemathematics.org/classroom-videos/number-talks/5th-6th-grade-math-guess-my-rule/number-talk-part-1

Experience a Number Talk Now you will be participating in a number talk.

Exit Slip: Taking a Look at your Own Practice What changes might you make in your math instruction based on the information you learned in today’s session on Number Talks? Things to think about: Learning community in your classroom Your role as the teacher Questioning techniques Use of models, tools and mathematical reasoning games to support student thinking Addressing student wonderings.

Questions or Comments… Our goal as educators is to help students to become confident and competent in mathematics. We strive to create a classroom environment that encourages students to think critically about math in a variety of situations. As students explain their thinking to others, they self-correct and clarify their ideas leading to a deeper understanding of underlying mathematical concepts. Accuracy and the development of efficient problem-solving strategies are essential to student’s learning. The ability to solve problems many different ways and to understand the connections between mathematical ideas is equally important. As children learn to question, reconsider and justify solutions they become more confident in their own abilities as mathematicians.