Facilitator’s Guidebook
for Use of Mathematics Situations
in Professional Learning

Facilitator’s Guidebook
for Use of Mathematics Situations
in Professional Learning

Edited by

Rose Mary Zbiek

Glendon W. Blume

M. Kathleen Heid

INFORMATION AGE PUBLISHING, INC.
Charlotte, NC • www.infoagepub.com

Copublished by:
NCTM, NCSM
&

Library of Congress Cataloging-in-Publication Data

The CIP data for this book can be found on the Library of Congress website (loc.gov).

Paperback: 978-1-64113-079-0

Hardcover: 978-1-64113-080-6

eBook: 978-1-64113-081-3

NCSM is a mathematics education leadership organization that equips and empowers a diverse education community to engage in leadership that supports, sustains, and inspires high quality mathematics teaching and learning every day for each and every learner

Copyright © 2018 Information Age Publishing Inc., NCTM, and NCSM

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the publisher.

Printed in the United States of America

Contents

Preface vii

1. Introduction to Facilitating the Use of Situations 1

Rose Mary Zbiek

2. Facilitator’s Guide for Division Involving Zero: Situation 1 From the
MACMTL–CPTM Situations Project 7

Diane Briars, Rose Mary Zbiek, Glendon Blume, M. Kathleen Heid,
M. Suzanne Mitchell, Connie Schrock, Steven S. Viktora, and James W. Wilson

3. Facilitator’s Guide for Product of Two Negative Numbers: Situation 2 From the MACMTL-CPTM Situations Project 29

Glendon Blume and Connie Schrock

4. Facilitator’s Guide for Graphing Quadratic Functions: Situation 21 From the MACMTL–CPTM Situations Project 59

M. Kathleen Heid

5. Facilitator’s Guide for Circumscribing Polygons: Situation 34 From the
MACMTL–CPTM Situations Project 85

Patricia S. Wilson and M. Suzanne Mitchell

6. Facilitator’s Guide for Calculation of Sine: Situation 35 From the MACMTL–CPTM Situations Project 115

Steven S. Viktora and James W. Wilson

7. Facilitator’s Guide for Mean and Median: Situation 38 From the MACMTL–CPTM Situations Project 135

Rose Mary Zbiek with M. Suzanne Mitchell

8. Concluding Thoughts 157

Rose Mary Zbiek

Appendix: Standards for Mathematical Practice 165

v

Preface

Mathematics matters. It especially matters for teachers of mathematics and for those who work with teachers in in-service and pre-service settings. The purpose of this Guidebook is to be a tool for facilitators who help teachers to make connections among secondary school mathematics ideas and to value the relevance and power of their understanding of mathematics beyond that which they teach.

The Guidebook and the six Situation Guides it contains are for use in professional learning. Although the volume can be used by an individual teacher, the materials are designed for a facilitator to use with small groups or large groups of teachers. The group might be in a school setting, in a pre-service mathematics or mathematics education course, or in another venue in which teachers are working to enrich their understandings of mathematics and to improve their practice.

One unique feature of the Situations in this book, and the larger set of Situations in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations (Heid & Wilson, 2015), is their origin in the work of teachers. Rather than imagining the mathematics that teachers encounter, the Situations Project team drew from incidents they had witnessed in the daily work of teaching mathematics. These incidents become prompts to engage teachers in mathematics.

This book is for facilitators and for teachers who seek new mathematical experiences that reveal secondary mathematics as a connected and consistent subject that teachers and their students can enjoy.

ACKNOWLEDGEMENTS

The Situations Project (Principal Investigators and Senior Research Associates: M. Kathleen Heid, Patricia S. Wilson, James W. Wilson, Glendon Blume, Jeremy Kilpatrick, Rose Mary Zbiek) was supported in part by the National Science Foundation under Grant ESI-0426253 for the Mid-Atlantic Center for Mathematics Teaching and Learning (MAC-MTL) and Grant ESI-0227586 for the Center for Proficiency in Mathematics Teaching (CPTM). This publication arose from a collaboration of the National Council of Supervisors of Mathematics and the Situations Project Principal Investigators and Senior Research Associates. Any suggestions, opinions, findings, or conclusions expressed in this document are those of the authors and do not necessarily reflect the views of the National Science Foundation.

The MAC–CPTM Situations Project

M. Kathleen Heid, Distinguished Professor

The Pennsylvania State University

271 Chambers Building

University Park, PA 16803

(814) 865-2226

mkh2@psu.edu

Patricia S. Wilson, Professor Emerita

University of Georgia

Department of Mathematics and Science Education

105H Aderhold

Athens, GA 30602

(706) 542-4547

pswilson@uga.edu

The National Council of Supervisors of Mathematics

2851 S. Parker Rd. #1210

Aurora, Colorado 80014

(303) 317-6595

office@mathedleadership.org
mathedleadership.org