Elementary Math Foundations Supporting CCSS-M & Mathematical Practices Dr. Tracy Goodson-Espy Dr. Diana Moss Appalachian State University Leadership Conference July 27-28, 2015

How do we help students build a sound mathematics foundation in grades K-8 that will support success in ninth grade and beyond?

Goal: Build a K-8 Teacher Cadre that- 1. Understands it is necessary for students to develop conceptual understanding; 2. Understands that students must develop procedural fluency without damaging their future attitudes toward doing mathematics; 3. Understands it is necessary to foster a sense of curiosity in investigating mathematical ideas.

How? We have to approach professional development for K-8 teachers in a manner that:  Is on-going and emphasizes developing both content and pedagogical expertise;  Promotes teachers’ autonomy and dignity.

How do we know this works?  For early career teachers, ASU graduates were judged to be the most effective teachers (in terms of student achievement on EOG or EOC tests) 1  For in-service teachers, we use teacher PD models that have been validated through extensive research 2 1.UNC Teacher Quality Research: 2013 Teacher Preparation Program Effectiveness Report: ( Designing Professional Development for Teachers of Science and Mathematics (Loucks-Horsley, Stiles, Mundry, Love, & Hewson)

Professional development approaches and resources Some Recent Professional Development Partnerships between ASU and Surrounding School Districts  North Carolina Elementary Math Specialist Network – (Z. Smith Reynolds Sponsored)  Avery County and ASU Partnership Project AAPP-Math (K-8)  Appalachian Elementary Leaders in in Mathematics APP-ELM (N.C. Quest Sponsored)

North Carolina Elementary Math Specialist Network —Z. Smith Reynolds Foundation awarded ASU an $100,000 grant for a set of math coaches from Alleghany, Avery, Burke, McDowell, and Wilkes Counties to be trained in the techniques of the Math Recovery program ( Teachers will receive training by Math Recovery specialists and implementation support from ASU Mathematics Education faculty from the Department of Curriculum & Instruction

Teaching Number in the Classroom with 4-8 year olds This book emphasizes strategies for teaching number recognition, counting and cardinality, and learning basic number facts

Developing Number Knowledge: Assessment, Teaching & Intervention with 7-11 year olds This book emphasizes strategies for teaching two-digit addition and subtraction, multiplication, and basic fraction concepts with upper elementary students.

Resources  U.S. Math Recovery Council  Numeracy Continuum Site from New South Wales  rces.wikispaces.net/ rces.wikispaces.net/

Avery County and ASU Partnership Project (AAPP~Math Avery County and ASU Partnership Project (AAPP~Math) —This partnership between Appalachian State University and Avery County Schools assisted teachers in Avery County with implementing the CCSS-M effectively in grades K-8.

AAPP~Math Project Deliverables:  Curriculum guide for each grade level  5 days of professional development  On-site visits (4) per each of the six university faculty to: a) demonstrate model lessons; b) provide coaching to teachers; c) assist with working with students.

How Children Learn Number Concepts This book shares information about the phases that children go through as they learn early number concepts and begin to learn basic facts and two-digit computation.

Cognitively Guided Instruction This book and collection of videos shows teachers how problems differ in terms of operations used, structure, and in sizes of numbers used. It also examines stages of problem- solving strategies that students apply in these settings, including direct modeling, counting strategies, and using derived number facts.

(Mathematical Tasks Framework) This classic text explains the mathematical tasks framework that describes the difference between high cognitive demand tasks and low cognitive demand tasks.

3-8 Emphases Content & Practice Standards Unified by Learning Trajectories Developed through Instruction

3-8 Emphases  Content & Practice Standards are unified through learning trajectories.  Central to the development of content & practice are:  Tasks  Questioning  Appropriate assessment

Lessons Learned 3-8 Teachers often ask for assistance with the following topics/pedagogies: 1. Fractions 2. Early algebra 3. Questioning strategies 4. Whole class discussions

Extending Children’s Mathematics: Fractions and Decimals This text is a follow-on volume to the seminal text, Children’s Mathematics (commonly known as CGI). It provides specific guidance for how to help students through the learning of fractions and proportional reasoning. These topics are common stumbling blocks for students as they learn mathematics.

Connecting Arithmetic to Algebra This book emphasizes how to develop children’s thinking to predispose them to be successful later in algebra. It describes how elementary teachers can shape their instruction so that students learn to: *notice and describe consistencies across problems *articulate generalizations about the behavior of the operations *develop mathematical arguments based on representations to explain why such generalizations are or are not true.

Whole Class Mathematics Discussions This book describes how to facilitate whole class math discussions and addresses how to set up a classroom, cultivate classroom routines, plan for instruction, facilitate discussions, and assess for future improvement. Reflective questions throughout the book enable teachers to develop professionally and support formal workshop or book study experiences.

Intentional Talk Intentional Talk provides teachers with a framework for planning and facilitating purposeful mathematics discussions that enrich and deepen student learning. According to Elham Kazemi and Allison Hintz, the critical first step is to identify a discussion’s goal and then understand how to structure and facilitate the conversation to meet that goal. Through detailed vignettes from both primary and upper elementary classrooms, the authors provide a window into what teachers are thinking as they lead discussions and make important pedagogical and mathematical decisions along the way.

Appalachian Elementary Leaders in Mathematics K-5 (APP-ELM)  Through a series of NC Quest Grants, we have worked with Wilkes County Schools, Alleghany County Schools, and Burke County Schools to help their teachers complete the Elementary School Mathematics Add-on License.  See brochure concerning the EMAoL at ASU.

Elementary Mathematics Add- on License- Graduate Certificate Courses 1. Number Systems and Operations: K-5 Mathematical Tasks 2. Rational Numbers and Operations: K-5 Learning Trajectories 3. Data Analysis and Measurement: K-5 Classroom Interactions 4. Algebra Reasoning: K-5 Discourse and Questioning 5. Geometry and Spatial Visualization: K-5 Assessment 6. Mathematical Modeling: K-5 Leadership

Mathematical Knowledge for Teaching Number Systems and Operations (Place Value) Rational Numbers and Operations Measurement and Data Analysis Geometry: Spatial Orientation and Visualization Algebraic Reasoning Mathematical Modeling

Six High Leverage Teaching Practices Helping Teachers Develop as School- based Leaders Understanding and Applying Knowledge of Learning Trajectories Orchestrating Classroom Interactions Fostering Reasoning through Discourse and Questioning Assessing Student Knowledge (Diagnosis and Intervention) Selecting, Designing, and Using Mathematical Tasks

What makes it work?  Teacher-centered professional development  Embedded PD experiences  Collaborative relationships  District-level discussions & vertical alignment 1. UNC Teacher Quality Research: 2013 Teacher Preparation Program Effectiveness Report 2. Designing Professional Development for Teachers of Science and Mathematics (Loucks-Horsley, Stiles, Mundry, Love, & Hewson)

Additional Elementary Collaborations  Pre-service teacher preparation  Field placements  Student teaching  Public School Partnership  Graduate programs

Questions and Suggestions? How can we assist your district? Contact: Tracy Goodson-Espy at Or Diana Moss at