Lesson Play in Mathematics Education

Rina Zazkis • Nathalie SinclairPeter Liljedahl

Lesson Play in MathematicsEducation

A Tool for Research and ProfessionalDevelopment

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Rina ZazkisFaculty of EducationSimon Fraser UniversityBurnaby, BCCanada

Nathalie SinclairFaculty of EducationSimon Fraser UniversityBurnaby, BCCanada

Peter LiljedahlFaculty of EducationSimon Fraser UniversityBurnaby, BCCanada

ISBN 978-1-4614-3548-8 ISBN 978-1-4614-3549-5 (eBook)DOI 10.1007/978-1-4614-3549-5Springer New York Heidelberg Dordrecht London

Library of Congress Control Number: 2012951136

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Preface

Teacher education is currently receiving extensive attention in mathematics edu-cation research, as evidenced by the amount of research articles, books, as well asseries of books devoted to this theme. Anna Sfard, in her plenary address at theInternational Congress of Mathematics Education in Copenhagen in 2004, noted thatshe was ‘‘pleased to find out that the last few years have been the era of the teacher asthe almost uncontested focus of researchers’ attention’’ (Sfard, 2004, p. 90).She also described the last two decades of the twentieth century as ‘‘almostexclusively the era of the learner’’, and the several decades prior to that as the ‘‘eraof the curriculum’’ (ibid.). This research focus has been accompanied by a growinginterest in the education of prospective teachers.

Among a large variety of studies devoted to the education of future teachers ofmathematics, several directions are being pursued: a focus on teachers’ knowledgeand/or knowledge-in-use, a focus on teachers’ interpretation of student thinkingand classroom situations, and an examination of the tools that assist the devel-opment of teachers’ mathematical knowledge and pedagogical sensitivities. Ourresearch for this book fits within this latter focus: it introduces a novel tool—lessonplay—and discusses various examples of its implementation.

Lesson play is a novel construct in research on teachers’ professional devel-opment in mathematics education. Lesson play refers to a lesson or part of a lessonpresented, written—and sometimes performed!—in a script form, featuringimagined interactions between a teacher and her students. We have been using andrefining our use of this tool for a number of years in a variety of situationsinvolving mathematics thinking and learning. We have asked prospective teachersto write lesson plays on a variety of themes and following a variety of prompts.The goal of this book is to offer a comprehensive survey of the affordances of thetool, the results of our studies—particularly in the area of pre-service teachereducation—and the reasons for which the tool offers such productive possibilitiesfor both researchers and teacher educators.

Although we claim that lesson play is a novel method, its roots can be traced toSocratic dialogue, a genre of prose in which a ‘wise man’ leads a discussion, oftenpointing to flaws in the thinking of his interlocutor. Jumping to modern times,

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we are further influenced by the work of Sfard (2010) that focuses on communi-cation and, in particular, that describes thinking as communication. The task ofwriting a lesson play allows an individual to re-embody different selves—that of ateacher-character and of different student-characters. Moreover, elaborating on thetheatrical interpretation of the word ‘play’ in reference to a script to be potentiallyperformed on stage, we are influenced by research that focuses on improvisationand on the importance of role playing in education. Indeed, we consider teachingas an act of improvisation and we note, metaphorically, that every skillful jazzimproviser spent his or her youth practicing scales and chords. As such, creating ascript for a play can be considered as role playing in one’s thinking. It is practicedin a safe environment of one’s cubicle, without the need to ‘‘think on your feet’’.We see this role playing as a valuable part in preparing for ‘‘real teaching’’.

In teacher education we are constantly seeking methods that improve ourpractice and consequently the practice of teachers that are enrolled in the courseswe teach. We are not alone in this endeavor. Mason, Watson, and Zaslavskydevoted a special issue of the Journal of Mathematics Teacher Education (2007,volume 10) to the nature and role of tasks in teacher education. Following up onthis initiative, three edited books were published in these series: Tasks in PrimaryMathematics Teacher Education (2009), Teaching with Tasks for EffectiveMathematics Learning (2012), and Constructing Knowledge for TeachingSecondary Mathematics (2011). Although the latter book does not have ‘‘tasks’’ inits title, its focus is on illustrative tasks for use in teacher education at thesecondary level.

The lesson play task is a contribution to this endeavor. Although it focuses onone particular kind of task, it is flexible and can be adjusted to different populationsand different mathematical topics. As we demonstrate, it can be used in bothpre-service and in-service teacher education. It can also be used at any level ofmathematical curriculum, though our focus in this book is on the elementary schoolgrades. We further believe that the task can be extended beyond mathematics; wethus invite colleagues in teacher educators more broadly (in the sciences andhumanities) to adapt it to their contexts.

In Part I—Chaps. 1 to 3—we introduce the lesson play, describe our gradualdevelopment of this tool, and contrast it with other ways of planning forinstruction. Part II—Chaps. 4 to 9—is devoted to the analysis of the plays that arebased on particular prompts. In Part III—Chaps. 10 to 13—we present a crossanalysis of previous chapters and also discuss various uses of this tool in our workwith teachers.

Overall, we present a compelling argument for lesson play as a valuable tool forteachers preparing their lessons, for instructors/teacher educators who work withteachers in various professional development settings, and for mathematicseducation researchers who study teachers’ knowledge and development.

vi Preface

Contents

Part I

1 Planning for Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Legacy of the Tylerian Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . 3Lesson Plan: An Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Alternative Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Introducing Lesson Play . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Developing the ‘‘Lesson Play’’ . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Potential Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12A Sample Lesson Play . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Virtual Planning: What the Lesson Might Be . . . . . . . . . . . . . . . . . 20

3 Evolution of the Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Lesson Play: Iterative Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

First Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Next Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Final Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Lesson Play: Toward ‘Real Teaching’ . . . . . . . . . . . . . . . . . . . . . . 28

Part II

4 Linear Measurement: How Long is a Stick? . . . . . . . . . . . . . . . . 33Diverting Teacher–Student Interaction . . . . . . . . . . . . . . . . . . . . . . 35

‘‘Who else?’’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35‘‘Place blocks… and count them’’ . . . . . . . . . . . . . . . . . . . . . . 36

Funneling Through Telling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37‘‘Important rules for measuring’’ . . . . . . . . . . . . . . . . . . . . . . . 37‘‘When we are measuring we have to start at 0’’ . . . . . . . . . . . . 38

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‘‘There is a special trick that we use when we count!’’ . . . . . . . 41‘‘Place the stick upright on the table’’ . . . . . . . . . . . . . . . . . . . 41

Funneling Through Rerouting a Strategy. . . . . . . . . . . . . . . . . . . . . 42‘‘Count the spaces in between the numbers’’ . . . . . . . . . . . . . . . 42‘‘No matter where you start’’ . . . . . . . . . . . . . . . . . . . . . . . . . 44‘‘If you chose to start the measurement

of your stick at 5 cm…’’. . . . . . . . . . . . . . . . . . . . . . . . . . . 44‘‘You don’t count the first line’’ . . . . . . . . . . . . . . . . . . . . . . . 46‘‘Can you draw me a 1 cm long line’’ . . . . . . . . . . . . . . . . . . . 48

What Do We Learn About Prospective Teachers’Ideas of Measurement? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5 On Divisibility by 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Retrieving the Correct Divisibility Rule . . . . . . . . . . . . . . . . . . . . . 55

‘‘Who can remember?’’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55‘‘Look it up in my notes’’ or elsewhere . . . . . . . . . . . . . . . . . . 56‘‘We can look in the glossary of the textbook’’ . . . . . . . . . . . . . 58‘‘I think we are confusing…’’ . . . . . . . . . . . . . . . . . . . . . . . . . 60‘‘Some wonderful little tricks’’ . . . . . . . . . . . . . . . . . . . . . . . . 63‘‘You’ve won the concert tickets!’’ . . . . . . . . . . . . . . . . . . . . . 65‘‘How about 1000456814?’’ . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Moving Toward Student Reasoning . . . . . . . . . . . . . . . . . . . . . . . . 66‘‘See if you can find a rule that does work’’ . . . . . . . . . . . . . . . 67‘‘That’s easy, they’re all [16 ,20 and 24] divisible by four’’ . . . . 69‘‘Start looking’’… ‘‘after the break’’. . . . . . . . . . . . . . . . . . . . . 69‘‘How does it work?’’. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70‘‘Imagine that each one of these is a chocolate bar’’ . . . . . . . . . 71

Uses of Mathematical Language . . . . . . . . . . . . . . . . . . . . . . . . . . 74‘‘A number is divisible by 4 if…’’ . . . . . . . . . . . . . . . . . . . . . . 74‘‘Just look at the last two numbers’’. . . . . . . . . . . . . . . . . . . . . 75‘‘What about the number 6, what’s the rule for that one?’’ . . . . . 76More Troublesome Expressions . . . . . . . . . . . . . . . . . . . . . . . . 77

Because… Alternative Diagnoses and Remediation . . . . . . . . . . . . . 78‘‘Because 354 has 4 in the one’s place’’ . . . . . . . . . . . . . . . . . . 78‘‘Let’s try doing long division’’ . . . . . . . . . . . . . . . . . . . . . . . . 79‘‘Because 354 is an even number’’. . . . . . . . . . . . . . . . . . . . . . 82‘‘I worked through all the division steps’’ . . . . . . . . . . . . . . . . . 84‘‘4 goes into 354, 88.5 times’’ . . . . . . . . . . . . . . . . . . . . . . . . . 86

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

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6 On Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Following Prompt #1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

‘‘We could make the multiplication table bigger’’ . . . . . . . . . . . 90‘‘If I give you 12 blocks’’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91‘‘I will circle them and cross out all the multiples

of 5 and 7’’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93‘‘We should not be using the multiplication tables’’ . . . . . . . . . . 95

Following Prompt #2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96‘‘Can a number that is bigger than 9 be a factor

for a number?’’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96‘‘Does anyone know the divisibility rule for 11?’’ . . . . . . . . . . . 98

Following Prompt #3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101‘‘We only need to divide 37 by other primes’’ . . . . . . . . . . . . . 102‘‘That is not how a prime number is defined’’. . . . . . . . . . . . . . 103‘‘Let us use the blocks to find out’’ . . . . . . . . . . . . . . . . . . . . . 104‘‘Can there be an endless number of prime numbers’’ . . . . . . . . 105‘‘Find a number that is not a prime number and

is also not divisible by 2, …, 9’’ . . . . . . . . . . . . . . . . . . . . . 106Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

7 Repeating Patterns: Cars and Colours. . . . . . . . . . . . . . . . . . . . . 111From Multiples of 4 to Multiples of 3 . . . . . . . . . . . . . . . . . . . . . . 112

‘‘You should check with him’’ . . . . . . . . . . . . . . . . . . . . . . . . 112‘‘I think I know what Monica is doing’’ . . . . . . . . . . . . . . . . . . 114‘‘So the way we need to look at this problem…’’ . . . . . . . . . . . 115‘‘Let us draw out the train from cars 1 to 10’’. . . . . . . . . . . . . . 116‘‘All multiples of 4 should be red, right?’’ . . . . . . . . . . . . . . . . 117‘‘Why don’t you try re-writing the pattern’’ . . . . . . . . . . . . . . . 119

Alternative Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120‘‘Are there other numbers 80 is a multiple of ?’’ . . . . . . . . . . . . 120‘‘Are you thinking that the pattern will repeat

for each set of 10’’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121‘‘Let us look at the remainder to help us’’ . . . . . . . . . . . . . . . . 124‘‘What if we… add another group of 30?’’ . . . . . . . . . . . . . . . . 125

Some Troubles with Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127‘‘Pattern: what this word means?’’ . . . . . . . . . . . . . . . . . . . . . . 127‘‘Red would be number 81’’ . . . . . . . . . . . . . . . . . . . . . . . . . . 128‘‘Because 15 is a multiple of 3: lucky coincidence?’’ . . . . . . . . . 129

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

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8 On Comparing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133On Counterexamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

‘‘Which is the bigger fraction? 1/2 or 2/4?’’ . . . . . . . . . . . . . . . 135‘‘4/6 is bigger than 1/2. And that doesn’t

fit my hypothesis’’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136‘‘Maybe that one was a fluke’’ . . . . . . . . . . . . . . . . . . . . . . . . 137

On Domain of Applicability and Explanation . . . . . . . . . . . . . . . . . 138‘‘There might be something to my strategy’’ . . . . . . . . . . . . . . . 138‘‘Just because it was the same amount away’’ . . . . . . . . . . . . . . 139‘‘When the fractions are equivalent then it does not work’’. . . . . 140‘‘When the fractions have the same bottom number…’’ . . . . . . . 142‘‘You do it your way, but I like my trick better’’. . . . . . . . . . . . 145‘‘Why do you think that is?’’ . . . . . . . . . . . . . . . . . . . . . . . . . 147‘‘Just because it doesn’t work that doesn’t mean that

it doesn’t have value’’. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Revisiting Previous Strategies: Back to the Basics . . . . . . . . . . . . . . 150

Manipulatives, with a Caution. . . . . . . . . . . . . . . . . . . . . . . . . 150Common Denominators, Always the Best. . . . . . . . . . . . . . . . . 151Calculators to the Rescue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Cross-Play Themes ‘‘Met-Before’’ . . . . . . . . . . . . . . . . . . . . . . . . . 154‘‘Whichever numerator is closest to the denominator’’ . . . . . . . . 154‘‘1/10 = 9, 1/8 = 7, 2/5 = 3, 3/4 = 1’’ . . . . . . . . . . . . . . . . . . 155‘‘And if you can’t then this hypothesis is correct’’ . . . . . . . . . . . 156

On Counterexamples or on Disconfirming Evidence . . . . . . . . . . . . 157On Gap Thinking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

9 Area and Perimeter: Melon Farm . . . . . . . . . . . . . . . . . . . . . . . . 161Diagnoses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

Confusion Between the Two Formulas . . . . . . . . . . . . . . . . . . . 162Not Knowing the Formula for Area . . . . . . . . . . . . . . . . . . . . . 163Confusion Between the Two Concepts . . . . . . . . . . . . . . . . . . . 164Not Understanding the Concept of Area . . . . . . . . . . . . . . . . . . 165

Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166Macro-Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

‘‘What farm is bigger?’’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167‘‘How many cards to cover a student’s desk?’’ . . . . . . . . . . . . . 169‘‘How many blocks will cover the picture?’’ . . . . . . . . . . . . . . . 171‘‘Perimeter measures the outside and area

measures the inside’’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173‘‘But what does perimeter mean?’’. . . . . . . . . . . . . . . . . . . . . . 174

Micro-Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175‘‘‘By’ usually means multiply’’ . . . . . . . . . . . . . . . . . . . . . . . . 175‘‘Can you tell me what their formulas are?’’ . . . . . . . . . . . . . . . 176‘‘It says 9 so I could try to multiply’’ . . . . . . . . . . . . . . . . . . . 177

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‘‘What would happen if you used multiplication?’’ . . . . . . . . . . 178‘‘Because we used more tiles’’ . . . . . . . . . . . . . . . . . . . . . . . . 179‘‘Or we could just multiply, that would be faster’’ . . . . . . . . . . . 181

Errors, Inattention, and Oversights . . . . . . . . . . . . . . . . . . . . . . . . . 183‘‘Area is the amount of space an object occupies’’. . . . . . . . . . . 183‘‘You times the length by the width’’ . . . . . . . . . . . . . . . . . . . . 184‘‘Our classroom is 35 9 43 m’’ and other

unrealistic contexts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185‘‘John has 500 more square metres of land’’ . . . . . . . . . . . . . . . 186‘‘Because we measured the area in squares’’ . . . . . . . . . . . . . . . 187

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Part III

10 From Creation to Critique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193Lesson Play Written by a Prospective Teacher . . . . . . . . . . . . . . . . 194A Note on Noticing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195Lines 1–11, What We Noticed. . . . . . . . . . . . . . . . . . . . . . . . . . . . 196Lines 1–11, What Teachers Noticed . . . . . . . . . . . . . . . . . . . . . . . . 196Lines 11–20, What We Noticed. . . . . . . . . . . . . . . . . . . . . . . . . . . 200Lines 11–20, What Teachers Noticed . . . . . . . . . . . . . . . . . . . . . . . 200Lines 21–31, What We Noticed. . . . . . . . . . . . . . . . . . . . . . . . . . . 203Lines 21–31, What Teachers Noticed . . . . . . . . . . . . . . . . . . . . . . . 204What Was or Was Not Noticed: Summary . . . . . . . . . . . . . . . . . . . 207On Noticing Mathematics and Noticing Students . . . . . . . . . . . . . . . 208Noticing Through Lesson Plays . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

11 Focus on Language. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211Analyzing Lesson Play Discourse . . . . . . . . . . . . . . . . . . . . . . . . . 212

Modality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213Hedging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217Lexical Bundles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219Ambiguity in Personal Pronouns . . . . . . . . . . . . . . . . . . . . . . . 223

Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

12 Images of Teaching. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227Toward ‘Reform’ Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

Group Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228Manipulatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231Drawings and Other Visuals . . . . . . . . . . . . . . . . . . . . . . . . . . 235Realistic Situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

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Influences of ‘Traditional’ Approaches . . . . . . . . . . . . . . . . . . . . . . 240Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242Tricks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244Review and Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247Back-to-Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249Understanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250Calculators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

Pedagogical Moves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253Authority Transfer to a Student . . . . . . . . . . . . . . . . . . . . . . . . 253Paradox, Conflict, Counterexample . . . . . . . . . . . . . . . . . . . . . 254Leveling or Attention to the Collective . . . . . . . . . . . . . . . . . . 258

Emotional Support, Care and Praise . . . . . . . . . . . . . . . . . . . . . . . . 261Closing Scenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

General Advice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266More Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267Foreshadowing Future Activity . . . . . . . . . . . . . . . . . . . . . . . . 267Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268Extending/Varying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

In Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

13 Multiple Uses of Lesson Play . . . . . . . . . . . . . . . . . . . . . . . . . . . 271For Prospective Teachers: Lesson Play as a Simulator . . . . . . . . . . . 271For Researchers: Lesson Play as a Lens . . . . . . . . . . . . . . . . . . . . . 272For Teacher Educators: Lesson Play as a Tool . . . . . . . . . . . . . . . . 273

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

About the Authors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

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