implementing a reform-oriented pedagogy: challenges for novice secondary mathematics teachers

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ORIGINAL ARTICLE Implementing a reform-oriented pedagogy: challenges for novice secondary mathematics teachers Gary M. Lewis Received: 3 April 2012 /Revised: 27 May 2013 /Accepted: 9 December 2013 # Mathematics Education Research Group of Australasia, Inc. 2014 Abstract Novice secondary mathematics teachers attempting teaching consonant with the National Council of Teachers of Mathematics (1991, 2007) Professional Standards for Teaching Mathematics experience many stresses related to their attempts at student- centered instruction; prominent among those were novices' challenges when orches- trating whole-class mathematical discussions with students taking a central, substantive role. During such discussions, students offer conjectures, ideas, and solutions and use mathematical argumentation and verification processes. Such teaching can create uncertainty and stress as teachers occupy a revised teaching role. They avoid evaluating student ideas during class; instead, they ask questions to move students' thinking forward, pose problems that deepen students' mathematical understanding, and choose between competing directions the discussion may take. Ultimately, teachers decide whether to continue pursuing such teaching goals or revert back to more familiar, teacher-centered methods. Supportive networks showed promise at helping novices navigate their first few years of teaching; organized networks helped novices meet their teaching goals while limiting the impact of their challenges on their well-being and teaching goals. The results of this study may inform teacher educators, administrators, and colleagues on how to support novices in pursuing teaching better aligned with novices' teaching ideals and reformer's visions. Keywords NCTM Standards . Discourse . Educational reform . Teacher stress . Novice teachers Introduction Teaching is among the most stressful human service occupations (Travers and Cooper 1996). Proportions of teachers who identify their job as stressful at least fairly fre- quently generally range from one fifth (Travers and Cooper) to one third (Kyriacou 1998). Novices, in particular, report feeling highly stressed (Kyriacou and Kunc 2007; Math Ed Res J DOI 10.1007/s13394-013-0092-5 G. M. Lewis (*) Illinois State University, Campus Box 4520, Normal, IL 61790, USA e-mail: [email protected]

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Page 1: Implementing a reform-oriented pedagogy: challenges for novice secondary mathematics teachers

ORIGINAL ARTICLE

Implementing a reform-oriented pedagogy: challengesfor novice secondary mathematics teachers

Gary M. Lewis

Received: 3 April 2012 /Revised: 27 May 2013 /Accepted: 9 December 2013# Mathematics Education Research Group of Australasia, Inc. 2014

Abstract Novice secondary mathematics teachers attempting teaching consonant withthe National Council of Teachers of Mathematics (1991, 2007) Professional Standardsfor Teaching Mathematics experience many stresses related to their attempts at student-centered instruction; prominent among those were novices' challenges when orches-trating whole-class mathematical discussions with students taking a central, substantiverole. During such discussions, students offer conjectures, ideas, and solutions and usemathematical argumentation and verification processes. Such teaching can createuncertainty and stress as teachers occupy a revised teaching role. They avoid evaluatingstudent ideas during class; instead, they ask questions to move students' thinkingforward, pose problems that deepen students' mathematical understanding, and choosebetween competing directions the discussion may take. Ultimately, teachers decidewhether to continue pursuing such teaching goals or revert back to more familiar,teacher-centered methods. Supportive networks showed promise at helping novicesnavigate their first few years of teaching; organized networks helped novices meet theirteaching goals while limiting the impact of their challenges on their well-being andteaching goals. The results of this study may inform teacher educators, administrators,and colleagues on how to support novices in pursuing teaching better aligned withnovices' teaching ideals and reformer's visions.

Keywords NCTMStandards . Discourse . Educational reform . Teacher stress . Noviceteachers

Introduction

Teaching is among the most stressful human service occupations (Travers and Cooper1996). Proportions of teachers who identify their job as stressful at least fairly fre-quently generally range from one fifth (Travers and Cooper) to one third (Kyriacou1998). Novices, in particular, report feeling highly stressed (Kyriacou and Kunc 2007;

Math Ed Res JDOI 10.1007/s13394-013-0092-5

G. M. Lewis (*)Illinois State University, Campus Box 4520, Normal, IL 61790, USAe-mail: [email protected]

Page 2: Implementing a reform-oriented pedagogy: challenges for novice secondary mathematics teachers

Veenman 1984), probably too much so to learn effectively from their initial teachingexperiences (Borko and Putnam 1996).

It is not entirely clear how attempting to implement different types of educationalreforms may impact the stresses novices experience. In the case of government-mandated reforms, like the UK's 1988 Education Reform Act (Carlyle and Woods2002) and the US' No Child Left Behind policy (Davidson 2009), teachers reportedexperiencing greater stress and reduced job satisfaction.

What has been studied less is how reforms involving more student-centered math-ematical pedagogy have affected teachers. The approaches to mathematics teachingsuggested in the National Council of Teachers of Mathematics (NCTM) (1991, 2007)Professional Standards for Teaching Mathematics exemplify such teaching practices;hereafter, teaching that attempts to meaningfully implement these strategies will bereferred to as standards-based teaching (SBT). SBT will be defined more precisely inthe literature review.

In general, under SBT, teachers take a less central role than in lecture. They act asfacilitators for student-led explorations of mathematics, discussions, and development ofmathematical ideas (NCTM Standard 2). Students take a more active, central role in theirlearning. They develop methods to solve mathematical and real-life application problems,also known as problem solving. Students learn to take responsibility for their learning andtheir peers' learning by formulating conjectures, presenting partial and sometimes incorrectsolutions for peer feedback, and work to revise their and others' work to meet grade-appropriate standards of rigor (NCTM Standard 3). All of these activities occur in aclassroom environment created by the teacher and students requiring regular, active studentparticipation and the presentation of work for discussion in a socially and intellectuallyconstructive atmosphere (NCTMTeaching Standard 5). These teaching practices resemblethose observed (Jacobs, et al. 2006) in mathematically higher-achieving nations.

While the NCTM (1991, 2007) documents have existed for over two decades, USteachers have been slow to implement these voluntary teaching practices (Jacobs et al.2006). Spread of such teaching is likely hampered by teachers' hesitance to engage inactivities that may heighten anxiety (Smith 1996). Since few innovative teacherspractice in isolation (McLaughlin 1993), colleagues' choices also appear to affect thelikelihood of enacting such teaching.

Teacher education, professional development, and curricula in the USA (e.g., Borko,Eisenhart, Brown, Underhill, Jones, and Agard 1992; Wilcox, Schram, Lappan, andLanier 1991) and other countries (e.g., Niss 1996; Sembiring, Hadi, and Dolk 2008)encourage student teachers and novices to attempt student-centered teaching similar toSBT which may, in turn, shape beginning teachers' pedagogy. Novice teacher stress hasbeen studied much less than teacher stress in general, particularly when attempting suchteaching. As a result, this research explored many aspects of novice teachers' stresses andcoping. The current treatise primarily focuses on the following research questions:

1. Which sources of teacher stress do novice secondary mathematics teachers whohave exhibited some elements of NCTM (1991) SBT report as related to their SBTattempts?

2. What type of impact do each of the sources of teaching stress that novice teachersexperience have on them, i.e., which stresses do novices judge to be facilitative,neutral, or debilitative?

G. M. Lewis

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Review of the literature

The NCTM (1991, 2007) Professional Standards for Teaching Mathematics character-izes high-quality teaching through six standards. NCTM Standard 1, worthwhilemathematical tasks, describes choosing and/or creating tasks to deeply and effectivelyengage students in mathematical thought processes. Standard 2, teacher's role indiscourse, describes the orchestrative role and pedagogy used by teachers to enhancestudent understanding of mathematical ideas, notation, and language. Standard 3,students' role in discourse, identifies aspects of the active role students take in devel-oping lessons, in taking responsibility for their learning and work, in questioning otherstudents' work, and in determining the validity of their own and others' mathematicalarguments. NCTM Standard 4, tools for enhancing discourse, describes the effectiveuse of technology to facilitate discourse and deeper understanding of mathematicalconcepts. Standard 5, learning environment, describes how the teacher and studentswork together to create a safe, constructive environment with proper resources forstudents to take an active role in developing mathematical ideas and to hold all studentwork to high mathematical standards. NCTM Standard 6, analysis of teaching andlearning, described the process of reflecting on teaching, analyzing the impact ofteaching on students and their learning, and improving teaching and student under-standing in the next day's lesson and in future teaching years.

The effects of attempting such teaching on the stresses novice teachers experienceare unclear. Salient stresses for all teachers include managing student behaviors, lack ofstudent engagement, and lack of support for teaching (Chaplain 2008; Geving 2007;Davidson 2009). Veteran teachers report paperwork as more stressful, while novicesreport teaching-related activities as a top stress (Forgasz and Leder 2006). In particular,workload is reported as novices' top stress (Kyriacou and Kunc 2007).

Efforts to attempt SBT can further complicate challenges in the first few years ofteaching. Because novices are often most familiar with teaching as “telling,” settingaside “telling” to attempt more student- and discourse-centered practices may increasenovices' stress (Smith 1996). Discussions centrally involving students press on teachers'knowledge for teaching (Ball et al. 2008) as they choose among productive topics forcontinuing discussions; therefore, researchers suggest studying the extent to whichparticular educational reforms, such as SBT, are generating high levels of teacher stress(Kyriacou 2001).

After the UK government mandated the 1988 Education Reform Act, teachersreported an increase in teaching stresses. Students often responded negatively topressure teachers placed on them to achieve, becoming “combative and resistant”(Carlyle and Woods 2002). The UK's 1988 Education Reform Act was the inspirationbehind the US' No Child Left Behind (Davidson 2009) reform; teachers under thisreform reported similar stresses to those reported in the UK.

While researchers have not systematically studied SBT-related stresses, the literatureis peppered with examples of teachers struggling to implement such mathematicsteaching. In a pilot study of student teachers and novices attempting SBT Act(Author 2004), participants described similar but subtler student reactions to thoseunder the UK's 1988 Education Reform. They reported students behaved in lessproductive ways. Novices' relationships with teaching colleagues were also strainedat times when their pedagogical beliefs differed.

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For example, one novice who was teaching rate of change was deterred fromteaching this difficult concept in the way she wanted because her mentor stated thatshe must follow the textbook. In describing her approach, this novice teacher said shehad hoped to spend several days on slope and that she would cover more than onesection a day when teaching algebraic manipulation to make up time. When herdepartment chairperson and mentor heard of her plans, they demanded that she followthe textbook and spend only 1 day on each section in the textbook (including slope).The novice teacher described this event as very stressful and said she hoped to find ateaching position at another school.

Romagnano (1994) and his novice planning partner, Ms. Curry, experienced studentresistance to thinking more deeply about mathematical concepts. They mentioned howdifficult it was to plan engaging lessons centrally involving students when studentswere generally only interested in consumer mathematics. Chazan (2000) and hisplanning partner, Sandy Bethell, both veteran teachers, tried to implement an innova-tive pedagogy relying heavily on student participation. They reported challenges withstudent engagement similar to Romagnano, but they also reported frustrations due toinconsistent student engagement. For example, 1 day Mike was a group leader, finishedhis work early, and then helped peers throughout the classroom. A few days later, Mikedrew faces on his knees and had the drawn faces “talk” to each other throughout mostof the class, disrupting other students' learning.

Researchers not conducting case studies typically study teacher stress via surveys.This is of concern for two reasons. First, teacher self-reports about their implementedpedagogy are often inconsistent with researcher evaluations of their teaching (e.g.,Cohen 1990). In order to determine which stresses novices experience are related toSBT, it is first important to determine whether their SBT attempts are outwardlyobservable. Second, while surveys can yield important information, some researchersare concerned whether reported stresses would concur with researcher observations ofclassroom events (Manthei, Gilmore, Tuck, and Adair 1996). Few studies have beenpublished related to student-centered teaching methods, like SBT, and those that havebeen published relate primarily to single case studies (e.g., Van Zoest and Bohl 2002;Wilcox, et al. 1991; Borko, et al. 1992). Since novices are generally the most stressedteachers in educational systems, evaluating how student-centered goals often dissem-inated by teacher education programs affect their stress levels would seem important.

Teachers and researchers also report multiple resources that were central to copingwith the challenges involved in teaching stresses, particularly teacher work groups andstrong subject-matter departments. Weiss (1999) found novice teachers located incohesive departments were more likely to have high morale, stronger engagement intheir teaching, and plans to stay in the profession. Other studies (e.g., Ackerman 2011)describe the increased job satisfaction all teachers experience in such settings.McLaughlin (1993) found teachers located in departments supporting SBT were muchmore likely to observably implement innovative, student-centered teaching than theirpeers. Teacher communities can offer emotional support and help novices strive toattain their teaching goals.

In reviewing relevant literature, six major categories of environmental sources ofteacher stress are repeatedly cited (Phillips 1993; Kyriacou 1989): poor motivation ofstudents, poor student discipline, poor working conditions, time pressure and workoverload, low status and opportunities—including pay, promotion, and career

G. M. Lewis

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development, and poor school ethos—including conflict with colleagues and adminis-trators. These categories were a starting point for the categories developed in thisanalysis. Based on Kyriacou and Sutcliffe's (1978) definition, teacher stress in thisstudy was defined as a teacher's perception that an aspect of their job was demanding orinduced negative affect. This definition aligned with the research goals of this study andwith practical limitations (i.e., nonphysiological measurements) in identifying novices'stresses. For this study, teaching was defined broadly as the act of preparing for,engaging in, or reflecting on teaching.

Methods

To solicit participants, a senior-year undergraduate content instructor from a highlyranked, progressive university helped the researcher develop a list of recent graduateslikely attempting SBT. For this study, novices were defined as teachers with less thanthree full years of classroom teaching (Berliner 1988); therefore, the instructor identi-fied prospective participants from her last three cohorts based on three factors in thefollowing order of importance: the university supervisors' evaluations of SBT attemptsduring student teaching, the student–teacher mentor's pedagogical orientation towardsSBT, and SBT-related course participation.

The researcher observed 11 of the most promising prospective participants' teachinga class the teacher described as mathematically talkative for a “screening observation.”The researcher observed a sampling of each novice's teaching to lay a foundation fordiscussing aspects of the environment causing stress, particularly when related to SBT.The author used a protocol taken directly from NCTM (1991) Standards 2 (Teacher'srole in discourse), 3 (Students' role in discourse), and 5 (Learning environment) andtheir corresponding subcategories. These three standards were chosen because theyfocused on classroom interaction patterns which are elements of SBT that areoutwardly observable and within novices' control. The remaining standards werenot considered until analyzing teacher stress comments during formal participation. If aprospective participant made a meaningful attempt to enact at least one subcategory of aparticular standard, the novice was considered to have attempted that standard.Attempting two of the three chosen standards qualified the novice for participation inthis study.

Of the 11, 6 made visible attempts at SBT. Only one teacher, Mr. Jones, farsurpassed the criteria for qualifying during the screening observation, qualifying inseveral subcategories in all three standards; the other novices narrowly qualifiedmeeting only one or two criteria in two of the three different teaching standards.During participation, two participants, Ms. Boone and Ms. Grant, engaged in SBTfar more than during the screening observation, with scores on several days resemblingMr. Jones' on those three standards. The other participants' teaching during formalparticipation resembled their screening observation, including Mr. Jones'.

Of the six novices, five were female; one was male. Their years of teachingexperience ranged between 1 and 3 years (see Table 1). While the researcher attemptedto enroll first-year teachers, the only two who qualified, Ms. Riley and Ms. Wells, bothasked to delay formal participation for a year due to feeling overwhelmed by theirteaching workloads (Kyriacou and Kunc 2007).

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The six participants taught a variety of math courses in many different contexts (seeTable 1). Each taught five to six classes in total involving two to three differentmathematics courses. Most teachers used relatively traditional, teacher-centered UStextbooks, but teachers at Maple High School (where Ms. Boone and Mr. Jones taught)enacted a relatively student-centered, teacher-written curriculum. Ms. Wells self-identified as African American and the rest as non-Hispanic Caucasians. Three of thesix teachers (Ms. Boone, Mr. Jones, and Ms. Wells) belonged to what they described asa strong, cohesive department.

This study was partially situated in novices' classrooms to verify whether claimsabout novices' stresses (Manthei, et al. 1996) and pedagogy (Cohen 1990; Jacobs et al.2006) could be partially observed and verified. Because stress is defined as a self-perceived phenomenon (Abouserie 1994; Cox 1978) and because of the limited numberof observations performed, novices were also specifically asked to describe andevaluate their experiences to verify and extend researcher observations.

Participation consisted of a preliminary audiotaped interview comprised of generalquestions about teaching challenges each novice experienced prior to formal observa-tions. A sequence of three to five teaching observations were videotaped in a class eachnovice described as constructively talkative about mathematics [hereafter, “focusclass”] (see Table 1). A second class was videotaped once, where each novice describedtheir challenges as least like those in the focus class [hereafter, “contrast class”].Although not required, all contrast classes were in a different subject than the focusclass for each teacher. The researcher participated as an observer, rather than as anobserver-participant, to avoid influencing the novice teachers' stresses as much aspossible, while still generating a shared set of classroom events on which to base initialdiscussions of participants' teaching stresses. After completing the observations, nov-ices participated in a final audiotaped interview.

After each observed lesson, participants wrote notes in a teaching log about eventsthey perceived as surprising, unexpected, or challenging. After completing classroomobservations, the researcher reviewed the videotapes to create a list of events where theteacher showed observable signs of stress. The researcher also drew on participants'teaching logs to find additional events. The researcher created a list of all reportedly andapparently stressful events from the teaching log and researcher observations to discussat the final interview. Finally, the researcher selected three salient, representative, 1- to7-min clips from the focus class videotapes where each novice reported or appeared toexperience stress to review with the participant at the final interview. The researchergave priority in selecting those clips to stressful events that also related to novices' SBTattempts.

During the final interview, the researcher asked novices to discuss their thoughts onthe three specific classroom clips taken from the focus class, including what they werethinking and whether and why they perceived those events as challenging. Then, thenovice discussed other challenges mentioned in their teaching logs and from researcherobservations. The novices were then provided a list of specific teaching stress catego-ries from the author's pilot study (Author 2004) to see whether those categoriesresonated with their experiences and, if so, to describe those events. Finally, the noviceswere asked how representative the challenges discussed were of those they generallyexperienced, which challenges were atypical and which of all of the challenges theymentioned were salient to them. Novices did not negate the impact of any challenges

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Tab

le1

Participantdemographicdata

Nam

eMs.Boone

Mr.Jones

Ms.Grant

Ms.Price

Ms.Riley

Ms.Wells

Yearstaughta

2years,4months

1year,2

monthsb

2years,8months

2years,6months

1year,3

months

1year,4

months

School

name

Maple

Maple

Elm

Linden

Holly

(Oak

c )Redwood

School

context

Smallrural

Smallrural

Urban

Large

rural

Large

rural(urban

c )Urban

Class

observed

Integrated

3dIntegrated

2eAlgebra

1Geometry

Algebra

2Geometry

Contrastclass

Integrated

2eIntegrated

1Be

Algebra

1CAlgebra

1BGeometry

Algebra

1

Additionalclasses

APCalculus

None

Algebra

2CAlgebra

2None

None

SBTattempts

Moderate

Moderate

Moderate

Low

Low

(moderatec)

Low

Teachercommunity

Access(SBT)

Access(SBT)

None

None

None

Access(non-SBT)

aExperiencebasedon

a9-month

school

year

bMr.Jones'firstyearteaching

asaperm

anentsubstitu

teatMapleHighSchoolturned

intoafull-tim

eposition;hisexperience

includes

both

histim

eas

aperm

anentsubstituteandas

atenure-track

teacher

cMs.Riley'steaching

atherfirst-year

teaching

positio

n(inparentheses)was

quite

differentthan

athersecond

dIntegrated

3consistedprim

arily

topics

from

AdvancedAlgebra

eIntegrated

1,1A

,1B,and

2consistedprim

arily

oftopics

from

Geometry

andAlgebra

1

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they had already mentioned, unless they had already done so when initially mentioningthe challenge. They only added additional challenges or elaborated on those they hadpreviously mentioned.

The interview structure was created to uncover novices' general perceptions andstresses before discussing the particular stresses and events experienced during re-searcher observations or later probed due to the research agenda (Charmaz 2006). Theinterview also helped identify stresses that were particularly memorable, but possiblynot representative, of novices' common and ongoing experiences and stresses. In thisway, participants could discuss daily stresses and contrast them with stresses previouslymentioned so they could place stresses brought up by the researcher in perspective withothers they had mentioned. During both interviews, the researcher attempted to subtlyprobe, when necessary, whether participants' challenges related to their SBT attempts,without divulging to the participant that SBTwas part of the focus of the study prior tocompletion; this step helped avoid the strong, partisan feelings that such discussionscan produce that might skew study results.

Data analysis

For the analysis, the definition of teacher stress was operationalized as a teacherstatement that a situation or event was challenging or was accompanied by negativeaffect. Words indicating challenges included hard, difficult, stress, problem, etc. Wordsindicating negative affect included hate, frustrate, disappoint, bother, annoy, bad, etc.The researcher excluded neutral descriptions such as they are “not very organizedstudents” or “not really self-motivated,” which did not clearly convey a challenge ornegative affect.

After identifying stress statements in the transcript, the researcher found where thenovice started and finished talking about that topic and called each section a “passage.”A passage could last from one sentence to several pages. It could consist of a single turnto a long series of turns in the conversation between interviewer and participant. Theidentifying feature of a passage was that the teacher continued to talk about the samesituation or event.

The interview data were analyzed beginning with stress categories created during apilot study (Author 2004). The current and pilot study analyses were informed bycoding categories found in the literature (Kyriacou 1989). The analysis of both the pilotand current study data through a semi-open coding strategy proceeded in recursivefashion between the data and the coding categories to refine them to fit the data(Charmaz 2006). During the current study, the researcher worked to refine the catego-ries through theoretical sampling and, ultimately, saturation of the categories/codes. Forexample, during both analyses when some categories became too full, categories wereexamined to see if they could be split to better describe all aspects of the data. Ifparticipants described certain experiences as being qualitatively different than others, anew category was also created. If there were some categories that were either empty ornot clearly separate from other categories, categories were combined. And if categoriescontained data that no longer appeared to be a good fit for their heading and descrip-tion, the heading and description were revised and the categories split in new ways tointegrate the data into categories defined in ways that better matched trends in the data.

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The 21 pilot study categories were reworked, renamed, and refined into the 22categories of teacher stress that ultimately emerged from the interview data analysis(Author 2007, 2008) through the process of saturation (Charmaz 2006) using data fromthe current study into which the data were sorted. Although the number of categories issimilar, many changes were made in the category descriptions and headings to alignresults with the data analyzed in the current study. The remainder of the current analysisand discussion focuses on the four categories answering the given research questionsfor this treatise, namely managing classroom discussions, responding to unexpectedstudent ideas, directing student explorations of mathematics, and planning lessons.

Distinguishing between categories

There was initially modest overlap between the final 22 categories, even after codingand accommodation, but specific rules were created to sort each of the distinct phraseswithin the stress passages into a single category. For example, Ms. Grant had herstudents explore the effects on the graph of changing the coefficients (one at a time) ofthe quadratic equation y=ax2+bx+c. The subsequent discussion was labored becausethe students had not identified the patterns she wanted them to find. They had notentered the equations into their calculator one at a time, so they could not determine theeffect of incremental changes in the coefficient a, for example, in the quadraticequation.

Ms. G: Well, so then the bad thing about it is, when it's time to discuss—say wehad five groups of three. There were five people who had looked at how ‘a’affects the graph. There were five people who had looked at how ‘b’ affects thegraph. And five people who looked at how ‘c’ affected the graph. But noteveryone had had that time to look at it with each other, so only five peoplecould contribute. Those people that were really interested wanted to see itanyway. So they were spending time during the discussion trying to do whattheir partners should have done in the lab and explained with them and sharedwith them. So…it just didn’t go the way I wanted it to…

In the first italicized phrase, “the bad thing about it is,” Ms. Grant was referring tothe impact on the subsequent discussion of most of the students entering the equationsinto their calculators all at once, rather than one at a time, during the exploration. Sothis passage could have been coded into two different categories, directing studentexplorations of mathematics and managing classroom discussions. Because that stresswas judged to have primarily derived from the fact that students had not worked theactivity according to her plans, the passage was coded into the directing studentexplorations of mathematics stress category.

The second italicized phrase, “it just didn’t go the way I wanted it to,” referred to themathematical discussion that she had planned to have afterwards with her students ascentral participants in the discussion. Because of that phrase, the passage was alsocoded into the category, managing classroom discussions. This example illustrates thata passage could be coded into multiple categories, but there had to be a unique phrasethat qualified it into each category for any given passage.

There was also a lack of clarity in category descriptions, so those descriptions weremodified to create clear boundaries for the existing data (see Table 2). The rules for

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distinguishing placing codes in overlapping categories follow each category descriptionin Table 2 (in parentheses).

Finally, the researcher trained a second coder by giving definitions and examples ofeach of the 22 categories and coding rules in case of apparent overlaps. The secondcoder categorized all passages for one randomly chosen participant (Mr. Jones). Thesecond coder's judgments for Mr. Jones' interview matched the researcher's in 24 of 25passages for a reliability of 96 %. The category definition resulting in the single codingdisagreement was subsequently modified.

Finally, each of the passages was coded as to whether it related to SBT. The coderused all six NCTM (1991) Standards to code data. If the passage non-trivially met atleast one subcategory of one of the six NCTM (1991) Standards, then the stress passagewas coded as related to the participant's SBT attempts for that standard and couldreceive multiple codes.

Salience of stress categories

The next stage of the data analysis for this study was based on methodologyemployed by the Mathematical Transitions Project team (e.g., Star, Smith, andJansen 2008). Determining which stress categories appeared salient in eachnovice's experiences was achieved by considering five factors: repetition withinan interview, repetition between interviews, detail, magnitude words, and topstresses. If a stress category for a participant met the criteria for at least three ofthese five factors, the stress category was judged to be a “Main” (or salient)

Table 2 Table of select category descriptions

Code title Code definition

Managing classroom discussions Stresses deriving from teacher attempts to involve studentsactively in classroom discussions and contribute anticipatedideas or strategies. (If teacher has difficulty getting studentsto participate in conversation and shares responsibility orresponsibility is unclear, code here. If teacher characterizesstudents as resisting participation or lacking interest, codeas Lack of student interest/motivation.)

Responding to unexpectedstudent ideas

Stresses deriving from teachers' attempts to engage with andpursue unexpected student ideas offered during classroomdiscussions.

Directing students' explorationsof mathematics

Stresses deriving from engaging students in exploration activitiesalone or in small groups. (If teacher characterizes studentsas not participating and shares responsibility or responsibilityis unclear, code here; if teacher describes student lack of interestor resistance, code as Lack of student interest/motivation.)

Planning lessons Stresses deriving from teacher attempts to prepare individuallessons, sometimes involving creating or adapting existinglessons to curricular objectives. (If stress related to tailoringlessons for students of varying ability levels, code as Teachingstudents of varying ability levels category. If stress related tolack of student motivation, code as Lack of studentinterest/motivation)

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source of teaching stress for the participant. If a category met the criteria for twoor fewer factors, it was labeled as “Mentioned.”

In judging salience, first, the coder looked for “repetition within” a single interviewfor each category, meaning whether the stress category was mentioned in more than onepassage within a single interview. The coder also looked for “repetition between” thetwo interviews or whether a specific stress category was mentioned in both interviews.

The coder also looked for how much “detail” the participant used in describingevents as an indicator of emphasis on the challenge. The participant needed to use atleast three phrases detailing aspects of—not merely naming—a particular challenge tomeet this criterion. The coder also looked to see whether the participant used magnitudewords in describing each stress. Adjectives and adverbs participants used to emphasizethe magnitude of each stress like “very hard” or “really frustrating” also indicatedemphasis.

Lastly, the researcher looked for the participant's choice(s) of top stress(es) duringthe interviews. If a participant called an event or situation a “top stress,” “the worstthing,” etc., they also met the criterion for using magnitude words simultaneously. Thismethod gave more weight to such comments, further validating participants' percep-tions of their experiences. All top stresses were judged to be Main stresses using thesecriteria.

A frequency count alone would not have identified several arguably importantstresses as Main. For example, there were two Main stress categories that were onlymentioned once. The only way a stress category could be mentioned once and bejudged as Main is if the participant called it a top stress and described it in sufficientdetail. For example, Ms. Grant talked about being frustrated by how boring it was toteach to unengaged students that she sometimes considered leaving the profession toteach in her minor, English.

Ms. G: The biggest thing that might push me out of teaching math… [is that] Iknow what it's like to teach English… I want to make [the students], not likemath, but be successful at math when they maybe haven't in the past. And I'm justdiscouraged by how dull it is for me sometimes…

It would be difficult to argue that, because this challenge was only mentioned once,it was not a salient source of stress for Ms. Grant; indeed, this was the only point duringany interview that a participant mentioned leaving mathematics education. Without themultilayered analysis employed by this study, seven stress categories currently judgedas Main would have been merely Mentioned; four other stress categories currentlylabeled as Mentioned would have been Main. The more complex coding judgmentsappeared to better align with participant's voiced expectations of each stress category'ssignificance.

Results

Many of the 22 teacher stress categories (see Table 3) resulting from my analysis weresimilar to those already reported in the existing literature (Phillips 1993; Kyriacou 1989).For example, these novices reported the challenges of workload (Kyriacou and Kunc2007) and dealing with problematic student behaviors (Kyriacou 1989) or classroom

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management. Several stress categories were new to the literature (Author 2007, 2008). Inthis report, only categories with specific stresses that are new or partially new to theteacher stress literature are considered.

Stresses related to SBT attempts

Although 15 categories include stresses related to SBT, only eight are new orpartially new to the literature. Four categories containing primarily new teach-ing stresses are working with technology, teacher boredom, directing studentexplorations of mathematics, and responding to unexpected student ideas. Fourcategories of teacher stress differing partially and non-trivially from those in the currentteacher stress literature include managing classroom discussions, creating, aligning,modifying, or implementing curricula, assessing student understanding, and studentdiversity issues.

Table 3 lists the teacher stress categories for which at least 50 % of passages relatedto novices' SBT attempts. Table 3 also identifies (in italics) the categories that werementioned by more than one novice in the sample, namely managing classroomdiscussions, responding to unexpected student ideas, directing student explorations ofmathematics, and planning lessons; these categories appeared most important to nov-ices of those strongly related to their SBT attempts. Of these four stress categories,managing classroom discussions was by far the most commonly cited (see Table 3).And while all four categories were mentioned by two or more participants, onlymanaging classroom discussions was judged a Main stress category for any participant;the rest were Mentioned. Managing classroom discussions describes the challengesassociated with leading or orchestrating classroom discussions.

Responding to unexpected student ideas entailed challenges of responding to an idearaised by a student that the instructor had not anticipated. This required that the teacheractually attend to the idea and treat it as part of the mathematical content of the class.Directing student explorations of mathematics describes challenges experienced as theteacher orchestrates activities where students work to uncover mathematical conceptsfor themselves and share that work in their small groups. Planning lessons describesstresses teachers reported when trying to plan lessons that met their content andpedagogical goals.

Table 3 Teacher stress categories listed by proportion related to SBT

Teacher stress category SBT Total % SBT

Directing student explorations of mathematics 4 4 100

Planning lessons 3 3 100

Relationships and communications with colleagues 2 2 100

Responding to unexpected student ideas 2 2 100

Managing classroom discussion 10 17 58.8

Finding and utilizing resources 1 2 50.0

Student diversity issues 1 2 50.0

Italics indicate categories reported by more than one novice

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Managing classroom discussions

A large proportion and a relatively large number of passages in the managing classroomdiscussions category related to novices' attempts at SBT; moreover, this category was aMain category for two participants and Mentioned for two others.

While some of the stresses related to managing classroom discussions hadmore to do with generic concerns like wait time after the teacher askedquestions, most related to difficulties eliciting active, meaningful student participation.An example comes fromMr. Jones' interviews.When asked what was challenging abouta lesson he mentioned in his teaching log, Mr. Jones described frustration resulting fromthe discrepancy between the whole-class discussion he planned and what actuallyoccurred.

Mr. J: It's a combination of both the questions I ask them and how they respond tothem… Classroom discussions… [is] a big [challenge]. We talked about that asfar as who should be talking and how much work I should be doing… I really feellike I should be the facilitator in a discussion, but sometimes it just doesn'thappen. And I need to work on some different ways of having discussions.

Mr. Jones felt like he spent more time talking than he wanted during the whole-classdiscussion, rather than acting in a facilitative role (see Standard 2: Teacher's role indiscourse). He wanted more information to come from the students during the discus-sion (Standard 3: Students' role in discourse). So Mr. Jones' stress appeared to be asmuch about his teaching goals as it was about actual classroom events; this was acommon dimension of SBT-related stresses.

The reader may recall that Ms. Grant also reported frustration with thequality of the whole-class discussions she held about the effects of changingcoefficients of a quadratic function. She reported that most students failed tothink deeply about the problem or to participate in the discussion afterwards. Ms. Grantdescribed her challenges as structuring questions in the activity so students would reachher learning goals and preparing students to participate effectively in whole-classdiscussions.

From Mr. Jones' and Ms. Grant's reports, it appears that classroom discussions inwhich students play a central role can be challenging for novices to enact and mayrequire additional resources to successfully develop.

Responding to unexpected student ideas

Due to the emphasis participants placed on responding to unexpected student ideasduring a pilot study (Author 2004), those challenges were sorted into a separatecategory during this data analysis, even though this is clearly a subcategory ofmanaging classroom discussions. An example arose during Ms. Boone's interviewswhile discussing her videotaped classroom events. The class was working an introduc-tory activity on graph theory that asked students to find the minimum cost of con-structing roads to connect eight cities, given the known cost of connecting selectpairings of cities (see Fig. 1). While discussing the problem with the whole class, astudent without prompting conjectured “Since there are eight places, there must be atleast seven roads.”

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Ms. B: I was thinking… “Okay, I'd better figure out right now if this is true ornot.” …And I was thinking through a couple of examples really fast in my head.And I was like, “Okay, that would be true.” So then I gave them that as anassignment to think… “Why would that be true?”…

Int: Was there anything challenging about that?

Ms. B: Well, trying to figure it out within 30 s to see if it's right or not! And notletting them know that I'm trying to figure that out right [on] the spot.

Ms. Boone wrote on the whiteboard “With eight places, why must there be at leastseven roads to maintain connectivity?” Ms. Boone continued, “I want you to thinkabout that… If you had 10 places, would there be 9 roads? If you had 100 places,would there be 99? …For tomorrow, I'd like you to write up a little blurb, a couple ofsentences if you need to.” She also removed a few other homework problems to maketime for this activity.

In Ms. Boone's case, the challenge with responding to unexpected student ideas wasdirectly related to her mathematical content knowledge. In this case, the student made aconjecture relating to graph theory beyond the content of the course. Rather thandismissing the conjecture or postponing the discussion for later, Ms. Boone chose touse the comment as a springboard for investigation. Still, not knowing whether thedirection would be meaningful for her students caused her a stressful moment beforeshe mentally validated the assertion.

The events in Ms. Boone's class related to Standard 3, Students' role in discourse,since the student offered an unsolicited conjecture about a problem situation that theteacher posed. And because Ms. Boone treated the conjecture as a valid contribution tothe mathematical discussion, she attempted Standard 2: Teacher's role in discourse.

Another example of challenges with managing classroom discussions surfacedduring Ms. Grant's observations and post-observation interview. Ms. Grant was sur-prised by a student comment during a class discussion of how changing the ccoefficient in the equation y=ax2+bx+c changed the graph of that function.

Ms. G: I was interested that a couple of people pointed out that [“c”] moves [thegraph] up and down and [horizontally compresses] it. And I never would havethought of that. And then I was like, “Maybe they're right.” I really had to thinkon my feet, too, because I didn't know…

I: So then you're stuck kind of going, “Look, did it change width? I can't tell,because this part doesn't match with that”…

Ms. G: And then how to get them to believe that [it didn't].

So while it caused her a stressful moment, Ms. Grant determined and was able tohelp her students see that the graph shifted upwards, but did not shrink horizontallywhen c was added to the function y=x2, creating the function y=x2+c. This situationarose because the student made an unexpected conjecture about the data from theexploration, meeting Standard 3: Students' role in discourse. Ms. Grant lackedknowledge of the optical illusion that results when examining the effect of changingthe coefficient c on the graph of a quadratic function. That observation conflicted withher understanding that “c” only moves the graph vertically, causing her to pause and

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reevaluate her thinking in relation to this new idea. Similar to Ms. Boone, Ms. Granttreated the participation as mathematically valid by considering and addressing it,meeting Standard 2: Teacher's role in discourse.

Both situations demonstrated that students played a central role in classroomdiscussions. While one conjecture was correct and the other incorrect, both ideas caughtthe teachers off guard and made them think on their feet, which was uncomfortable forthem. And in both situations, the teachers treated these contributions as valid. Bothsituations were demanding for the same reason, an unexpected student conjecturepressed on the teachers' mathematical content knowledge.

Ms. Boone’s Introduction to Graph Theory: Problem Statement and Question 8

SITUATION: The United Nations is helping and underdeveloped country build roads

connecting 8 cities. The result should enable people in any city to travel to any other city

either directly or through other cities. The director wishes to minimize the total cost involved.

The cities will be designated A, B, C, D, E, F, G, and H. The estimated cost in millions of

dollars of constructing roads between certain pairs of cities is:

A and B: 7 A and C: 9 B and D: 14 C and D: 5

C and F: 3 D and F: 2 D and E: 1 E and G: 5

F and G: 4 G and H: 5

8. Your job: Remember that the director wants to minimize the cost of the roads building

project, while the United Nations insists that the cities remain connected. Focusing on

these two goals, minimizing cost while maintaining connectivity, make a

C

G

H

F

E

D

B

A

recommendation about which roads to build and what the cost of your plan is. (You will

probably need to try several different plans.)Fig. 1 Ms. Boone's introduction to graph theory: problem statement and question 8

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Directing student explorations of mathematics

When directing student explorations of mathematics, teachers created opportunities forstudents to explore problem situations on their own or in small groups. They tried toencourage students to think about mathematical problems and formulate conjecturesbased on their explorations.

Ms. Grant struggled to get students to meaningfully engage and thoughtfully reflecton the results of the task exploring how changing each of the coefficients in theequation y=ax2+bx+c affected the function's graph (see Standard 1: Worthwhilemathematical tasks). Ms. Grant felt that a lack of engagement limited students' abilityto meaningfully contribute to the whole-class discussion afterwards (see Standard 3:Students' role in discourse). Ms. Grant attributed this partially to the questions sheasked on the exploration sheet as students explored how changing parameters in anequation changes the form of its graph.

Another example of directing student explorations of mathematics comes from Mr.Jones' attempts to get his students to understand the intent of an activity he created. Heasked his students to try to draw two non-congruent triangles, using specific examplesof criteria representing specific cases of nine possible triangle congruence theorems(e.g., ASA, AAA, SSS, etc.). He hoped that this activity would convince them whethereach of the nine criteria was sufficient to ensure congruence of two triangles in general,but most students did not understand the reasoning behind his instructions. As a result,Mr. Jones spent a good deal of class time repeatedly explaining what they were tryingto do to the different pairs of students.

Mr. J: The challenging part was probably trying to get them to understand whatthey were doing, as far as why they were drawing two triangles, and telling themthat we're trying to draw two triangles that are not congruent… They didn't reallyunderstand why we cared about two congruent triangles. So maybe trying to do abetter job of explaining why we want to figure out about two congruent triangles,or even why it was important, why we came to say they're congruent. Why do wehave to have a minimum set of criteria? It would be very important to lay that outbefore we even tried to have any kind of activity where they had to figure outwhy the two triangles were congruent or not.

Mr. Jones found it so frustrating that his students did not understand the intent of theactivity that he considered throwing out the entire lesson. He clearly had specificinteractions in mind during the classroom exploration (Standard 1: Worthwhile math-ematical activities), namely creating justifications for why each prospective theoremwas or was not true which would involve student reasoning (Standard 3: Students' rolein discourse). He also envisioned himself in a facilitative role (Standard 2: Teacher'srole in discourse) which he felt he had not achieved.

Planning lessons

While planning lessons would not necessarily involve SBT, all stresses in this categorydirectly related to novices' SBTattempts. The lesson plans they described generally aimedto actively involve students in generating data, formulating mathematical conjecturesabout that data, and employing mathematical reasoning and justification to verify or prove

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their results that they often shared with the class. For example, Ms. Grant felt frustratedshe did not have time to create lessons each day reflecting her teaching values.

Ms. G: I don't necessarily have time to reflect on all of those lesson plans… Andthat is frustrating, but… since this [algebra class] is the highest level that Iteach… I'll try to work with the [lessons]… And it ends up being like a skeletonof a week and like filling things in the day before or the day of, just becausesometimes it's a little more natural when you're going with what the class isgiving you… It seems as if someone were to walk by or look at what was donedaily, it's so not structured compared to the way a traditional math classroom is.

Ms. Grant tried to be responsive to her students' needs while planning her lessons(Standard 6: Analysis of teaching and learning), but she did not always have time tocreate the types of lessons that she wanted (Standard 1: Worthwhile mathematicaltasks). She emphasized the importance of being flexible and using information thatstudents gave her to create lessons. She also talked about the varying format of herclasses which, in observing her teaching, involved investigations a few times a weekthat did not look “the way a traditional math classroom” would look.

Mr. Jones described a different type of challenge related to planning lessons. He set agoal to come up with one engaging activity for his students each week, but found thattask very time consuming.

Mr. J: I know that, as a newer teacher, I could probably burn myself out… I'vespent many hours… just trying to think of things that will get students tounderstand or help them have a discussion about different types of mathemat-ics…. And I've pretty much said that's what I'm going to do—one lesson a week.And usually I make it on Monday so I have the whole weekend to look at onelesson. And…depending on what we're doing, it's usually going to be my onemotivating, spectacular lesson that I give them that involves getting up andactually using the physical environment, or doing something in the hall, or doingsomething like a mini-project… It's hard to keep up with that, especially…how torelate something to the math that we're doing right now.

Mr. Jones found that he really had to pace himself in creating the types ofmathematics lessons that he wanted to have in his classroom. He felt like even creatingone student-centered, engaging, mathematically rich lesson per class per week was adifficult pace to keep up with, but chose to do so to meet his personal teaching goals.

Mr. Jones and Ms. Grant described how challenging it is to make time to plan lessonsthat meet their pedagogical goals. While both described their examples in differentterms, their teaching suggested that both wanted students to make personal investmentsin mathematically rich activities. The examples in this category all appeared to relatecentrally to Standard 1,Worthwhile mathematical tasks, since that is the area where suchlesson plans and activities are discussed in the NCTM (1991) Standards.

Overall stress levels

While participants were not directly asked about their overall stress levels, they wereasked which stresses they found to be facilitative (constructive) and which they foundto be debilitative (nonproductive). Only two teachers, Ms. Price and Ms. Riley, could

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name debilitative stresses when directly asked. Ms. Riley, in particular, said that allteaching challenges were negative. She struggled to think of even one positive teachingchallenge, even after the researcher shared a specific example from other teachers'experiences. Of the remaining teachers, only one talked during our interviews aboutoverwhelming stresses related to her teaching, Ms. Grant. She described how she wasthinking about leaving mathematics teaching to teach English instead because shecould have the kinds of conversations in English that she struggled to have inmathematics. Such comments seem to indicate that she was under a great deal of stressdue to her teaching experiences. These three novices' statements suggest that they wereexperiencing stress levels that may have been counterproductive to their professionallearning.

On the other hand, the three remaining participants (Mr. Jones, Ms. Boone, and Ms.Wells) described their stresses in more positive terms, as challenges and opportunitiesfor growth; all three were also part of what they described as strong, cohesivedepartments (see Table 1). Two of those three, Mr. Jones and Ms. Boone, describedtheir departments as teacher learning communities that helped them develop theirinnovative pedagogy and activities. Mr. Jones and Ms. Boone talked specifically abouta grant their school won that allowed them to begin working together one summer oninnovative pedagogy; their collaborative work had continued afterwards during theschool year and summers. They further described what each found helpful about theirdepartmental collaborations. For example, Ms. Boone said, “We generally are verycollaborative. So a lot of what we come up with comes from us talking it out andcreating our own problems. We create so much of our own, which is pretty nice… Thatis definitely one of my best resources is my co-workers.” Mr. Jones also elaborated onhis collaborations at Maple High School.

Mr. J: In these 3 days of professional development, we're going to sit down as…Integrated 2 [teachers], and we're going to go over everything and talk about…content, objectives. We're going to go over the projects. We're going to go overthe exact timeline for things. And we're going to talk about tests. We're going totalk about exactly what students should take away from this unit and how itrelates to the bigger picture.

Ms. Wells also described a very cohesive department that worked well together,although their teaching goals were not necessarily defined to align with the NCTMStandards. “We have a real good, tight community, a tight department. We eat lunchtogether every day, and we hash out all the stuff that we need to if there is anything. Itworks pretty good… We are very unified in terms of what we do.”

The remaining three novices mentioned a more piecemeal approach tofinding support for their teaching, generally relying on one or two colleagues.Ms. Price described going to look for another teacher to help her, if she couldcatch her after school before she left. Ms. Riley also described working withtwo other colleagues. Ms. Grant, on the other hand, talked about using considerablesocial skills to craft a large network of contacts with specific topics she felt comfortablediscussing with each person, such as pedagogy and lesson planning, student discipline,and technology.

In summary, these teachers' departments and social networking varied. While all ofthem had social resources, their access to those resources depended on many factors.

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Formally organized resources gave novices greater access to materials and ideas thatthey described as more effectively supported their teaching.

Discussion and conclusions

The six novices in this study struggled with implementing the types of teaching thataligned with their pedagogical goals. Specifically, they lacked some elements of thedeep, connected mathematical content required when attempting SBT (e.g., Ms.Boone), like novices in prior studies (e.g., Borko et al. 1992). They struggled withhow to effectively help students: work effectively on mathematical explorations,engage with content and peers in small groups, and participate in constructive, mean-ingful ways in whole-class discussions, like teachers in the literature (e.g., Romagnano1994; Chazan 2000). They found it difficult to know which of the many directions totake during whole-class discussions. Novices also found it difficult to plan effective,student-centered explorations and that such planning was time consuming (e.g., Mr.Jones). These challenges caused them increased teaching stresses that related to theirSBT teaching attempts.

These six novices implicitly and at times explicitly voiced strong alignment withSBT teaching practices during our interviews. For example, at one point during ourinterviews, Mr. Jones mentioned that he looked through the NCTM Standards (1991,2000) each week to make sure that he was enacting his teaching ideals. While somestresses related to novices' pedagogical goals and ideals, prior studies suggest thatteaching in enforced opposition to one's teaching beliefs heightens novices' teachingstress more than most other challenges they described (Author 2004). Abandoningthese attempts would likely increase, rather than alleviate, stress. Because SBT hasbeen shown to improve student achievement (Senk and Thompson 2003; Boaler 2002)and is practiced in mathematically higher-achieving nations, such changes could alsobe detrimental to students and educational equity.

Because three of the six novices in this study (Ms. Grant, Ms. Riley, and Ms. Price)identified their stresses as highly negative, they may have experienced too much stressto effectively learn from their early teaching experiences, as Borko and Putnam (1996)and Smith (1996) suggested; moreover, the three who talked about their stresses mostnegatively also had the least formally organized support systems (see Table 1).

Novices who most successfully navigated their overall stresses, Mr. Jones, Ms.Boone, and Ms. Wells, described their departments as unified and possessing well-organized supports for their teaching. These results demonstrate the importance of anorganized support network of colleagues to help novices reach their pedagogical goals(Ackerman 2011). Such networks show promise in alleviating teaching stresses tomaximize learning (McLaughlin 1993; Ackerman 2011) and to retain teachers (Weiss1999) particularly during the first few years of teaching. Even under the best circum-stances, beginning teaching is stressful. For example, Ms. Wells, who spoke verypositively about stresses during our interviews, initially delayed participation as afirst-year teacher due to feeling overwhelmed by her workload, in spite of being partof what she described as a very strong, supportive department. Such results suggest theimportance of having organized networks to support novice teachers, in particular, andsurely also benefit more veteran teachers.

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Half of the novices in this study were members of a teacher learning communitysituated within a strong, cohesive department; yet, innovators practicing in isolationwere rarely encountered in previous studies (McLaughlin 1993). On the other hand,two (Ms. Boone and Mr. Jones) of the three (Ms. Boone, Mr. Jones, and Ms. Grant)most student-centered teachers had strong, cohesive departments that focused time andresources on jointly developing shared pedagogical resources. This further underscoresthe important role of organized networks with a particular focus on helping novicesachieve their SBT-related pedagogical goals and alleviating their stress. Ms. Grant'schallenges and frustrations with maintaining her ideals without support in spite of herself-crafted, extensive, purposeful social network is evidence that even the mosttalented novices may struggle without these supportive, organized departments.

This study demonstrates the need for further research to increase understanding ofhow and why teachers' goals change over time by examining what leads novices topersevere in or abandon their SBT attempts. There were several instances in this studywhere novices devised means of dealing with their disappointments, as in the case ofMs. Grant who modified her quadratic activity for the following year. Ms. Riley saidshe would not teach an innovative lesson she had attempted the following year; she alsomentioned during our interviews that SBT was not as important at her new suburbanteaching position than at her prior urban teaching position “because these students arelike me—they learn the way I do.” Support for innovative teaching also appeared to bea contributing factor. But it was unclear in most cases why these novices chose toabandon or modify their lessons and whether those choices were the most productivefor their students' learning and for their own professional development. These areimportant questions that future studies may answer.

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