Table Of ContentResearch in Mathematics Education
Series Editors: Jinfa Cai · James A. Middleton
Edna O. Schack
Molly H. Fisher
Jennifer A. Wilhelm Editors
Teacher Noticing:
Bridging and
Broadening
Perspectives,
Contexts, and
Frameworks
Research in Mathematics Education
Series editors
Jinfa Cai, Newark, DE, USA
James A. Middleton, Tempe, AZ, USA
Thisseriesisdesignedtoproducethematicvolumes,allowingresearcherstoaccess
numerous studies on a theme in a single, peer-reviewed source. Our intent for this
seriesistopublishthelatestresearchinthefieldinatimelyfashion.Thisdesignis
particularly geared toward highlighting the work of promising graduate students
and junior faculty working in conjunction with senior scholars. The audience for
thismonographseriesconsistsofthose intheintersection between researchersand
mathematics education leaders—people who need the highest quality research,
methodological rigor, and potentially transformative implications ready at hand to
helpthemmakedecisionsregardingtheimprovementofteaching,learning,policy,
and practice. With this vision, our mission of this book series is:
1. To support the sharing of critical research findings among members of the
mathematics education community;
2. To support graduate students and junior faculty and induct them into the
researchcommunitybypairingthemwithseniorfacultyintheproductionofthe
highest quality peer-reviewed research papers; and
3. To support the usefulness and widespread adoption of research-based
innovation.
More information about this series at http://www.springer.com/series/13030
Edna O. Schack Molly H. Fisher
(cid:129)
Jennifer A. Wilhelm
Editors
Teacher Noticing: Bridging
and Broadening Perspectives,
Contexts, and Frameworks
123
Editors
Edna O.Schack Jennifer A.Wilhelm
Morehead State University STEMEducation
Morehead, KY University of Kentucky
USA Lexington, KY
USA
MollyH.Fisher
University of Kentucky
Lexington, KY
USA
Research in MathematicsEducation
ISBN978-3-319-46752-8 ISBN978-3-319-46753-5 (eBook)
DOI 10.1007/978-3-319-46753-5
LibraryofCongressControlNumber:2017932118
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Foreword
Mathematics teachers are continually bombarded with information streaming from
many different sources. These streams are punctuated by time intervals (periods,
weeks, terms), by critical moments of student (mis)conceptualization, and by cur-
ricular packaging, each of which impact the others in the strange dance of their
professionallives.Thesubjectofnoticingisausefulperspectiveonthisdance.We
use this metaphor purposefully. First, we use it because John Mason, the
acknowledgedpioneerinthisareainmathematicseducation,issoeloquentwithhis
metaphors. Second, we use it because dance is always nuanced; involving actors,
music,tempo,partner(s),andoccasion,themetaphorcapturesmuchofamathematics
teacher’s experience, and these highly situated factors require the attention of the
dancer—theteacher—tounderstandtheminsuchamannerastoimprovethedance—
the lesson, the learning opportunity—and, importantly, future opportunities. Thus,
noticing in mathematics education research is more than just a technique—it is inter-
pretive,projectinganewpatternmoremeaningfullyengagingforstudentsaspartners.
Inthisvolume,theauthorsprovidenotonlyrigorousanalysesofcasesaswellas
large-scale studies, but also examples from practice that can serve as anchors for
discussion among teachers and researchers both intent upon the same goal:
improving mathematics teaching and learning. Its beauty is not that the authors
answer all of our questions about how teachers attend to information, interpret it
(multiple streams and all), and then decide what to do, but that it challenges the
reader to re-frame what is meant by attention, interpretation, and decision in the
context of improvement of one’s own teaching practice. Instead of a method of
noticing, the authors provide insight into a discipline of noticing (again, Mason’s
words) requiring mindfulness and decision as well as adaptation. After all, merely
reflecting on practice does not change it.
There are clearly different norms for what is considered pedagogically produc-
tiveandwhatisconsideredcounterproductive.Suchrelativismisdifficultwhenour
goalsaretodevelopcoherentmethodologicalframeworks.However,theadvantage
noticingasaperspectiveprovidesisjustthiskindofnuancedlookatwhatitmeans
v
vi Foreword
to improve practice and how local conditions, broader political aims, tools, and
resources contribute to local pedagogical innovation.
This volume is an excellent resource for both doctoral seminars in mathematics
teaching, and, we think, for teacher professional development programs. As we
indicated in the Foreword of other books in the series, we have designed the
solicitation, review, and revision process of volumes in the series to produce the-
matic volumes, allowing researchers to access numerous studies on a theme in a
single, peer-reviewed source. Our intent for this series is to publish the latest
research in the field in a timely fashion. This design is particularly geared towards
highlighting the work of promising graduate students and junior faculty working in
conjunction with senior scholars. The audience for this monograph series consists of
thoseattheintersectionbetweenresearchersandmathematicseducationleaders—those
who need the highest quality research, methodological rigor, and potentially transfor-
mative implications ready at hand to help them make decisions regarding the
improvementof teaching,learning,policy, andpractice.With this vision,ourmission
of this book series is:
1. To support the sharing of critical research findings among members of the
mathematics education community,
2. To support graduate students and junior faculty and induct them into the
researchcommunitybypairingthemwithseniorfacultyintheproductionofthe
highest quality peer-reviewed research papers, and
3. To support the usefulness and wide-spread adoption of research-based
innovation.
Likeothervolumesintheseries,thisvolumeservesthemissionwell.Wewould
like to thank the editors, Edna O. Schack, Molly H. Fisher, and Jennifer Wilhelm,
for their efforts in shepherding this volume. We also commend the authors of the
empirical articles and commentaries for providing such excellent examples of
research and reflection.
Jinfa Cai
James A. Middleton
Co-Editors in Chief, RME Book Series
Preface
Is it Noticing or is it . . .?
Whatisteachernoticing?Isteachernoticingdifferentthansimplygoodteaching?Is
teachernoticingonlyanin-the-momentoccurrencewithinawholeclasssettingoris
it also akin to a one-on-one clinical interview? Is the framing of this practice as
teachernoticingaffordingusanopportunitytoreexamine,ormoredeeplyexamine,
a crucial aspect of teaching? These questions continue to be discussed and pas-
sionately debated among our research team and colleagues. When one colleague
was discussing professional noticing within mathematics, another was interpreting
it asprofessionalvision, while stillanother was attemptingtoenvisionit beyond a
mathematicscontentperspective.Thesediscussionscauseduspauseandwehadto
ask ourselves, “How IS all of this different? Or, is it?” So, “is it noticing, or is
it….?”
InSherin,Jacobs,andPhilipp’s(2011)editedvolume,severalauthorsdescribed
the foundations of noticing. The roots are varied and the interpretations of the
construct are many. Foundational research in professional vision (Goodwin, 1994)
andthedisciplineofnoticing(Mason,2002)setthestageforadditionalresearchin
this field. Further frameworks of noticing have surfaced, such as noticing (van Es,
2011;Sherin&Star,2011),teachernoticing(Sherin,Jacobs,&Philipp,2011),and
professional noticing of children’s mathematical thinking (Jacobs, Lamb, &
Philipp,2010).Asaresult,onegoalofthismonographistoseekclarificationofthe
constructanditsrelatedbranches.Ourmonographexploresrecentdevelopmentsin
noticing and responds, in part, to the challenges Alan Schoenfeld put forth in the
final commentary of the aforementioned volume by Sherin et al.
In his commentary, Schoenfeld (2011) left us with multiple questions to pursue
withthegoalofapplyingourresearchedknowledgetothedevelopmentofeffective
teachers. Sherin et al.’s and Schoenfeld’s questions and our own successes and
vii
viii Preface
struggles with defining and measuring teacher noticing led us to propose this
monograph as a product of the 2013 Psychology of Mathematics Education-North
America and 2014 International Group of the Psychology of Mathematics
Education Working Groups, Teacher Noticing: A Hidden Skill of Teaching.
Many have contributed to its fulfillment. This work would not have been pos-
sible without the encouragement and guidance of Jinfa Cai, co-editor of the
ResearchinMathematicsEducationbookseries,thethoughtfulcontributionsofthe
commenting authors, the compilation of years of work by the many
researcher-authors whose work appears in this monograph, and the valuable feed-
backfromthereviewers.Eachproposalwassubmittedtoablindreviewprocessof
atleastthreereviewersandfullchaptersweresubsequentlyreviewedandeditedby
additional reviewers and the editors.
Inplanningthemonograph,wesoughttoaddressnotonlysomeofthequestions
raised by previous authors, (Sherin et al., 2011; Schoenfeld, 2011), but also those
questionsthatcontinuedtoemergeintheworkingsessionsattendedbyresearchers
worldwide. The question, “What are the key components of teacher noticing?” led
tothesection,ExploringtheBoundariesofTeacherNoticing.Arelatedquestionis,
“Can key components be isolated for study?” The chapters in the section,
Measuring Teacher Noticing, illustrate multiple methods used by researchers to
studythecomponents.Thesection,NoticinginVariousGradeBandsandContexts,
is in response to the question, “Is teacher professional noticing situation specific?”
Ofcourse,thestudyofteachernoticingisultimatelyfocusedonimprovingstudent
learning. The effects on student learning are addressed in the Examining Student
Thinking through Teacher Noticing section. Finally, the section, Extending
EquitablePracticesinProfessionalNoticing,developedafterthechapterproposals
were submitted and this new and exciting theme emerged that we had not antici-
pated. Interestingly, the addition of this section itself illustrates a point regarding
noticing that is raised by Mason in the introductory chapter herein, that of the
distinction between listening-to and listening-for. Had we limited ourselves to the
areas originally conceived for this monograph and only listened-for, we may have
missed this important addition to the teacher noticing dialog.
Whether noticing is its own new construct or whether it is a rose by another
name,thegoalistostudy,tolearn,andtocontributetotheincreasedeffectiveness
ofteachers.Ultimately,ifwearetoprepareeffectiveteachers,knowingwhatmakes
an effective teacher must guide this preparation. The research on teacher noticing
attempts to define, describe, and capture that which is essentially invisible to the
observer. In doing so, we hope to learn how to develop this ability in prospective
and practicing teachers in order to build robust learning environments for all
students.
Mostimportantly,thisbookistheresultofthethoughtandworkofmanybefore
us,includingthosewhomwehavenevermetbutwhosewritingindiverseareashas
Preface ix
influenced our work and the work of the author-researchers within. Like a good
conversation, good research builds upon the thinking of others to develop into a
deeperunderstandingbyall.Ourhopeisthatthechaptersinthisvolumecontribute
to the conversation.
Morehead, KY, USA Edna O. Schack
Lexington, KY, USA Molly H. Fisher
Lexington, KY, USA Jennifer A. Wilhelm
References
Goodwin,C.(1994).Professionalvision.AmericanAnthropologist,96,606–633.
Jacobs, V. R., Lamb, L.L.C., & Philipp, R. (2010). Professional noticing of children’s
mathematicalthinking.JournalforResearchinMathematicsEducation,41,168–202.
Mason, J. (2002). Researching your own practice: The discipline of noticing. London:
Routledge-Falmer.
Schoenfeld,A.(2011).Noticingmatters.Alot.Nowwhat?InM.G.Sherin,V.R.Jacobs,&R.
A.Philipp(Eds.),Mathematicsteachernoticing:Seeingthroughteachers’eyes(pp.223–238).
NewYork:Routledge.
Sherin,B.,&Star,J.R.(2011).Reflectionsonthestudyofteachernoticing.InM.G.Sherin,V.
R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’
eyes(pp.66–78).NewYork:Routledge.
Sherin,M.G.,Jacobs,V.R.,&Phillip,R.A.(2011).Situatingthestudyofteachernoticing.InM.
G.Sherin,V.R.Jacobs,&R.A.Philipp(Eds.),Mathematicsteachernoticing:Seeingthrough
teachers’eyes(pp.3–13).NewYork:Routledge.
van Es, E. (2011). A framework for learning to notice student thinking. In M. G. Sherin, V.
R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’
eyes(pp.134–151).NewYork:Routledge.
