PRESERVICE FORMATIVE ASSESSMENT INTERVIEWS: THE DEVELOPMENT OF COMPETENT QUESTIONING

INGRID S. WEILAND, RICK A. HUDSON and JULIE M. AMADOR

PRESERVICE FORMATIVE ASSESSMENT INTERVIEWS:THE DEVELOPMENT OF COMPETENT QUESTIONING

Received: 13 June 2012; Accepted: 18 January 2013

ABSTRACT. Recent research and reform documents in mathematics and science educationhave highlighted the importance of preservice teacher education that focuses onunderstanding students’ reasoning and modifying instruction accordingly. Utilizing theconstructs of core practices and the professional noticing as lenses with which to examinethe development of preservice teachers’ questioning practice, we conducted a case studyof 1 pair of preservice teachers as they performed weekly formative assessment interviewsto elicit student thinking during 1 semester. Our study was driven by the followingresearch questions: (1) How do preservice teachers develop their questioning practice andability to notice students’ thinking about mathematical and science concepts? (2) How canthese questioning practices be further developed? Results suggest that with weeklypractice and reflection, preservice teachers can develop their questioning practice withinthe context of face-to-face interaction with students and that the ways they questionstudents can change when given opportunities to interact with them and analyze theirthinking. By having participants attend to what they were professionally noticing aboutstudents’ thinking, we contend that they learned to adapt their questioning techniques toask students more competent questions. Participants also exhibited 2 areas of questioningpractice ripe for improvement—asking leading questions and missed opportunities toprobe students’ thinking. While providing clinical field experiences to preservice teachersis not novel, we suggest the importance of foregrounding practices that elicit studentmathematical and scientific thinking through an iterative process of enactment andreflection to develop questioning practice and the ability to notice.

KEY WORDS: core practices, formative assessment, preservice teacher education,professional noticing, questioning

Recent research and reform documents in mathematics and scienceeducation have highlighted the importance of training preservice teachersto develop an understanding of students’ reasoning and to modify theirinstruction accordingly (NCTM, 2000; NSTA, 2000); however, coming tounderstand how students think requires that teachers pose problems andcompetently probe in ways that draw out and build on students’reasoning. Teachers can then make sense of the students’ language andactions by continually interpreting student behavior and thinking from

Electronic supplementary material The online version of this article (doi:10.1007/s10763-013-9402-3) contains supplementary material, which is available to authorized users.

International Journal of Science and Mathematics Education (2014) 12: 329Y352# National Science Council, Taiwan 2013

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students’ perspectives (Steffe & Thompson, 2000). With this understand-ing, the teacher can develop hypotheses about students’ cognition anddesign tasks to provoke creative activity (Hackenberg, 2005).

The act of interviewing students has been used in the mathematics andscience education communities to examine the thinking of studentsindividually or collectively in small groups. Piagetian “clinical inter-views” have been used to study students’ concepts (Posner & Gertzog,1982). “Diagnostic interviews” have been called “interviews aboutinstances” (Bell, Osborne, & Tasker, 1985). Steffe & Thompson (2000)have used multiple, sustained teaching interactions to examine students’longitudinal development and to test their teacher/researcher hypothesesabout how concepts develop. They refer to this longitudinal approach as ateaching experiment, which includes a number of teaching episodes,typically with pairs of children. They stated, “we have to accept thestudents’ mathematical reality as being distinct from ours…students’mathematics is indicated by what they say and do as they engage inmathematical activity, and a basic goal of the researchers in a teachingexperiment is to construct models of students’ mathematics” (p. 268).

This study documents how preservice teachers develop their question-ing practice and ability to professionally notice as a result of theirparticipation in an experimental field experience which focuses oneliciting students’ mathematical and scientific thinking. The fieldexperience is designed to provide preservice teachers with closeinteractions with elementary students and to allow them to developpersonal models of student reasoning. The preservice teachers engage informative assessment interviews—adapted from the teaching experimentmethodology (Steffe & Thompson, 2000)—to help them understandchildren’s mathematical and scientific reasoning through questioning. Inthis article, we address the following questions:

1. From participating in this field experience, how do preservice teachersdevelop their questioning practice and ability to notice students’thinking about mathematical and science concepts?

2. How can the preservice teachers’ questioning practices be furtherdeveloped?

THEORETICAL FRAMEWORK AND RELEVANT LITERATURE

Many educational researchers have noted that effective teacher prepara-tion programs provide preservice teacher clinical experiences in order to

INGRID WEILAND, RICK A. HUDSON AND JULIE AMADOR330

engage in specific research-based practices. Preservice teachers are thengiven opportunities to improve through repeated use and reflection(Darling-Hammond, 2010; Grossman, Hammerman, & McDonald, 2009;Lampert, 2010). These research-based practices, which have been called“core practices” (Grossman et al., 2009), “high-leverage practices” (Ball,Sleep, Boerst, & Bass, 2009), and “generative practices” (Franke &Kazemi, 2001), are considered key elements of teaching that canpotentially result in highly effective instruction. Common to these threeterms are the following criteria: (a) improve learning and achievement ofstudents, (b) are done frequently, (c) can be applied across content andcontexts, and (d) support the integrity of the teaching profession.

Lampert (2010) notes the various uses of the term “practice” and howdiffering definitions can affect approaches to teacher education. In thispaper, we aspire to the definition provided by Grossman and colleagues,which stipulates that practices are developed through social interaction (inthis case, with students) whereby preservice teachers engage in“pedagogies of enactment.” Pedagogies of enactment allow preserviceteachers to bridge the theory they learn in methods courses to interactionswith students in the classroom. Preservice teachers must engage inteaching practices with students and with subject matter in order todevelop understandings of the complexity of teaching as well aprofessional identity. Furthermore, teacher educators must focus on thetheoretical and practical aspects of any given practice.

Questioning meets the aforementioned criteria of core practices and isdriven by both theory and action. The theoretical underpinnings ofquestioning practice lie within cognitively guided instruction (Carpenter,Fennema, & Franke, 1996). Cognitively guided instruction approachesteaching with the notion that both teachers and students arrive in theclassroom with prior conceptions of phenomena and that teachers mustuncover this prior knowledge, interpret the knowledge with regard tomisconceptions or missing information, and modify instruction to buildon current understandings. Students bring “informal and intuitive”knowledge to the classroom, and it is the responsibility of the teacher toattend to these understandings during instruction. At the core of thisframework is focusing on what students know rather than what they donot know. In action, questioning is a core practice that can enhanceteachers’ understandings of what students know by uncovering students’prior conceptions of a mathematical or science topic. Questioning allowsteachers to elicit students’ thinking (Carpenter et al., 1996), interpret thisthinking, and modify instruction accordingly. In this study, we examinedhow preservice teachers develop the core practice of questioning to elicit

DEVELOPMENT OF COMPETENT QUESTIONING 331

students’ thinking about mathematical and science concepts. Ourparticipants engaged in weekly formative assessment interviews, whichprovided them opportunities to interact with students and engage inpedagogies of enactment to focus on particular students’ thinking.Utilizing questioning as a core practice that allows preservice teachersto focus on students’ thinking, we examined the development ofpreservice teachers’ ability to question students during weekly formativeassessment interviews that occurred over the course of one semester.

Teacher Questioning

Inquiry-based instruction requires teachers to be able to questionstudents in systematic ways that build on students’ knowledge andfocus students’ attention on important scientific and mathematicalcontent. The opportunities children have to learn are directlyimpacted by the questions they are asked. NCTM (2007) advocatesthat teachers pose “questions and tasks that elicit, engage, andchallenge each student’s thinking” and ask “students to clarify andjustify their ideas orally and in writing” (p. 45). Such questioningpractices provide a stark contrast to the Initiate–Respond–Evaluatediscourse patterns that have often characterized classroom discoursein traditional teaching settings (Mehan, 1979).

International comparisons of teachers’ classroom questioning practiceshave shown that the questioning practices of American teachers, inparticular, differ greatly from their peers in other countries. Kawanaka &Stigler (1999) found that American teachers are more likely to ask low-levelquestions (e.g. questions that can be answered with a response of yes/no)than teachers in Germany or Japan. They are also less likely than their peersto ask students to explain or describe their thinking, although the percentageof these higher-order questions asked in all three countries remained small.

Several research studies have investigated the modes and charac-teristics of teachers’ questions in classroom and small-group settings.These studies have shown that teachers’ questions can serve animportant role to guide students’ thinking (van Zee & Minstrell,1997) and to promote student justification and generalization(Martino & Maher, 1999). Sahin & Kulm (2008) characterizedteachers’ questions into three types: factual, probing, and guiding.These questions differ, respectively, by requiring students to providea predetermined response, by prompting students to explain or justifytheir thinking, and by scaffolding students’ thinking toward aparticular concept. In observing two mathematics teachers question-


ing practices, Sahin & Kulm (2008) found that the teachers, whowere using reform-based textbooks, tended to ask a preponderance offactual questions. Franke, Webb, Chan, Ing, Freund, & Battey (2009)reported on teacher questioning practices after participating inprofessional development sessions focused on algebraic reasoning.These teachers consistently asked questions to elicit student thinking(e.g. How did you get that?), but the ways they responded tostudents’ explanations varied widely, ranging from general questionsto responses specific to the students’ explanations. As Sahin & Kulm(2008) and Franke et al. (2009) have documented, even whenteachers have access to reform-based curriculum materials andprofessional development aimed at enhancing teacher knowledge,teachers still struggle to question students productively. Chin (2006)examined in-service teachers’ use of questioning in the scienceclassroom and proposed a framework for understanding “question-ing-based discourse.” She found that teachers responded to studentsin four ways: (a) affirm the answer and continue direct instruction,(b) affirm the answer and then ask probing questions, (c) correct thestudent, or (d) evaluate the response or provide neutral comments byasking follow-up questions. While these findings are interesting,Chin’s research did not focus on interviews specifically nor did herparticipants include preservice teachers, therefore highlighting a needfor continued study.

Although the importance of teachers’ questions has been docu-mented widely in educational research, very little research hasfocused on how teachers’ questioning practice develops. Moyer &Milewicz (2002) investigated preservice teachers’ use of interviewsthrough an examination of their abilities to ask students questionsabout their mathematical thinking. They examined questioningabilities during one interview session and found that preserviceteachers’ questions fell into three categories: checklisting (listingquestions off of the interview protocol), instructing rather thanassessing, and probing or follow-up questions. Although this studyprovides insight about the types of questioning that preserviceteachers employ, it does not address how preservice teachers’questioning changes over time. Using two data points throughout apracticum experience, Ralph (1999) argued that preservice teachersimproved the clarity of their questions, increased wait time forstudent responses, and posed questions to a wider variety ofstudents. However, one of the limitations of Ralph’s study is anoverreliance on self-assessment of questioning abilities. These studies


suggest that there is still much to understand about how noviceteachers learn to develop their questioning practices.

Professional Noticing

A strong relationship exists between teachers’ monitoring of students’thinking and the ability to pose timely questions to deepen studentunderstanding (Martino & Maher, 1999). To do so, teachers must first cometo professionally notice and understand the methods of reasoning studentsare using in the act of problem solving and scientific inquiry (Jacobs, Lamb,Philipp, & Schappelle, 2011). The construct of professional noticing is a“way to understand how teachers make sense of complex classrooms”(Jacobs et al., 2011, p. 98) and encompasses where teachers focus attentionand how they interpret and reflect on their discoveries about studentthinking. Van Es & Sherin (2002, 2008) describe professional noticing inmathematics as what teachers attend to during instruction; for the purposes ofthis paper, we apply the construct of professional noticing to the contentareas of both mathematics and science as we examine the core practice ofquestioning because of its applicability across disciplines (Sherin, Russ, &Colestock, 2011). (Further use of the term “noticing” in this paper refers tothis construct, unless otherwise specified).

Van Es& Sherin (2002, 2008) claim that the act of noticing involves threerelated aspects: (a) identifying what is noteworthy about classroominteractions, (b) connecting classroom events to broader principles ofteaching and learning, and (c) using what one knows about a situation’scontext to reason about the situation. In van Es and Sherin’s view, teachereducation has not traditionally focused on helping teachers learn to interpretclassroom interactions in the midst of instruction. Recent work by Jacobs etal. (2011) has found that deciding how to respond while teaching requiresexpertise in attending to children’s strategies and interpreting their thinkingand that learning how to engage in professional noticing can be learnedthrough support.

Researchers have begun to investigate what supports are necessary to helpteachers focus their professional noticing on aspects of teaching that areinherent to reform initiatives, such as the classroom discourse required tobuild conceptual understanding. Such interventions are intended to moveteachers past noticing superficial aspects of reform teaching like classroommanagement or use of manipulatives. For example, Scherrer & Stein (2012)and van Es & Sherin (2008) found that teacher participants improved in theirability to recognize and interpret children’s mathematical thinking when theyshifted the focus of what they notice.


Van Es (2011) argues that professional noticing during discourseencourages the interpretation of student thinking and formulation ofevidence that serves as a catalyst for future teaching decisions.

Like Jacobs, Lamb, & Philipp (2010), our interest lies in what teachers’notice about children’s thinking, which includes three interrelated skills:(a) attending to children’s strategies, (b) interpreting children’s mathe-matical understandings, and (c) deciding how to respond to students onthe basis on their understandings. Their results align with Jacobs et al.(2011) and suggest that the ability to notice is not routine for noviceteachers, but is more prevalent among emerging teacher leaders. Researchby Star, Lynch, & Perova (2011) found that teacher preparation programscan positively impact preservice teachers’ abilities to attend to thinkingstrategies and interpret understandings. Such findings suggest that theability to professionally notice can be learned even early on, and teachingexperience coupled with continuous professional development thatfocuses on children’s thinking has the potential to support furtherdevelopment.

METHOD

Context

At the university where the study took place, all preservice teachersmajoring in elementary education enroll concurrently in a mathematicsmethods course, a science methods course, and a field experience focusedon both mathematics and science instruction during one semester. As apart of a larger research project, preservice teachers in the experimentalsection of the field experience engage in an iterative weekly processthroughout the semester which consists of conducting formative assess-ment interviews, building sharable models of student thinking, planningand teaching whole-class lessons, and collectively reflecting via amodified version of lesson study (Lewis, 2000). This paper focusessolely on the formative assessment interview component of theexperimental field experience approach.

During the first 2 weeks of the field experience, preservice teachersbecome oriented with the experimental approach and the school setting.Next, they spend 6 weeks focusing on mathematics and 5 weeks focusingon science. Each week, a pair of preservice teachers conducts a formativeassessment interview (FAI) with two elementary students from their hostclassroom. The FAIs, modeled after Steffe & Thompson’s (2000)


teaching experiments, are intended to help preservice teachers gain anunderstanding of how individual students think and reason about specificcontent. The purpose is also formative in that the findings influenceinstructional decisions regarding planning and teaching of the whole-classlessons taught the following week. As a part of this process, thepreservice teachers develop weekly interview protocols based on amathematics or science topic.

Research Design and Data Collection

To investigate the preservice teachers’ questioning, we conducted a casestudy, following the same pair of preservice teachers over the course of asemester. We considered the pair as a single case as they worked togetherclosely to develop and conduct FAIs. Case studies are best used when“how” questions are being asked about a contemporary set of events overwhich the researcher has little or no control (Yin, 2009). We thereforeemployed a case study methodology to understand how two preserviceteachers questioned elementary students within the context of FAIs andhow their questioning techniques evolved over time.

The FAIs with elementary students were video-recorded for 10 weeksthroughout the semester; during this time, the two preservice teachersrotated between the two roles as lead and witnessing interviewer. The firstsix interviews focused on mathematics content, while the final fourinterviews addressed science content. Each video was transcribedverbatim, and student and preservice teacher actions were included toconstruct a rich record of each interview. To triangulate data and supportthe construct validity of our results, we analyzed the FAI protocolswritten by the preservice teachers and the videos and transcripts offormative assessment interviews. We provide thick description of the casestudy using these data to support the validity of our findings. Preserviceteachers completed a Formative Assessment Interview Reflection andPlanning form (see Electronic Supplementary Material (ESM), AppendixA) immediately following each interview as part of the class. Weanalyzed these to understand the preservice teachers’ noticing of studentthinking. Finally, we engaged in peer debriefing of our findings withcolleagues to ensure that our work resonates with other mathematics andscience education researchers (Creswell, 2002).

Participants

Our case study includes two participants, Kelly and Caleb, who were bothelementary education majors in their junior year at a large, American


university. At the time of the study, Kelly and Caleb were workingwith four peers in a first-grade classroom as part of their fieldexperience course. We selected this pair to study because their fieldinstructor indicated that their professional dispositions would likely bereceptive to our examination of their questioning practices. Inaddition, based on the results of a survey designed to measureteachers’ beliefs Hudson, Kloosterman, & Galindo (2012), Kellyindicated she felt more confident to teach mathematics than science.Caleb, on the other hand, felt confident to teach both mathematicsand science.

Data Analysis

The purpose of this study was to examine the change in questioningtechniques used by preservice teachers over time and in depth. Wedocumented the types of questions posed by preservice teachers overthe course of the semester in which they participated in theexperimental field experience, striving to understand how they werequestioning students during FAIs and seeking to explicate changes intheir questioning over time.

To analyze the data, we created a framework based on recentstudies focused on questioning. Reliability of case study methodologycan be addressed by following a case study protocol (Yin, 2009); wetherefore utilized research procedures similar to those described byMoyer & Milewicz (2002). We began with the codes created byMoyer & Milewicz (2002) because they provided a way to categorizeand label preservice teachers’ questions during interviews withstudents. To identify questioning types, we first considered twocategories presented by Moyer & Milewicz (2002): instructing ratherthan assessing and probing or follow-up questions. We did notinclude their third category, “checklisting,” which signifies instanceswhen questions are posed as a list from the protocol, because weconsidered such questions as instances of posing problems andtherefore coded it as such. We used this framework to arrive at thefollowing three major types of questions: instructing rather thanassessing, probing or follow-up questions, and problem-posingquestions. We then subcategorized these three question types asdescribed below.

To begin, an initial set of interview data was coded by each of the threeauthors independently. Only questions posed in the interrogative formwere coded; thus, imperative statements that merely implied the asking of


a question were not included in the analysis. To promote inter-raterreliability and consistent coding, the authors met to reconcile codingdifferences and to refine the questioning coding framework. Based onthese initial discussions, “instructing rather than assessing questions”were subcategorized into leading questions or teaching/telling.“Probing or follow-up questions” were subcategorized into incorrectresponse, nonspecific, and competent questions. “Problem-posingquestions” were subcategorized into framing questions, protocolquestions, and new questions. The prevalence of various prompts inthe initial analysis also led to one additional code: repeated questions.Further descriptions and examples of these codes are provided inTable 1 and a summary of codes is depicted in Fig. 1.

Following the initial analyses, all subsequent interview transcriptswere coded by two of the authors and differences in codes weremutually discussed and reconciled until agreement was reached onhow the question should be coded. After coding all questions, thenumber of each type of question for each FAI was counted andpercentages were calculated for the question types.

To investigate the relationship between Kelly and Caleb’squestioning practices and their abilities to notice, we analyzed theFAI Reflection and Planning forms. We created a rubric containingfive dimensions (see ESM Appendix B) to analyze the interpretationof student thinking and inferences about student understanding.Following Jacobs et al. (2010), the rubric was structured aroundthree categories of professional noticing: robust (three points),limited (two points), and lacking (one point). Therefore, combinedscores for each form ranged from a high score of 15 to a low scoreof 3. Once the rubric was refined, each author independently codedthe forms with 90.2 % scoring agreement and the scores werereconciled so that there was a single score for each dimension. Afterall the codes were reconciled, we found a summative score andquantitatively analyzed the data to examine changes in Kelly andCaleb’s noticing patterns over the course of the semester.

FINDINGS

Kelly and Caleb engaged in a variety of questioning techniquesthroughout the semester. From the nine types of questions outlined inTable 1, a total of 539 questions were coded over ten FAIs. Each questiontype is elaborated below.


TABLE1

Cod

esandexam

ples

from

data

Cod

eDescriptio

n(ada

pted

from

Moyer

&Milewicz,20

02)

Example

Frequ

ency

(%)

Problem

-posing:

protocol

Task/qu

estio

nisdirectly

read

orslightly

mod

ified

from

thetask/questionthat

appeared

intheFAI

protocol

Kelly:So,

Mr.Caleb

…haseleven

stud

ents

inhisclass,ok

ay?Hehasbo

thbo

ysandgirls

inhisclass.How

manydifferentcombinatio

nsof

boys

andgirlscouldhe

have

inhisclass?

105(19.5)

Problem

-posing:

fram

ing

Task/qu

estio

nthat

does

notappear

ontheFAI

protocol,bu

tthat

thePSTuses

tointrod

uce

orfram

ethetask/questionthat

appears

ontheprotocol.

Protocolstates:“IfIstartedwith

10cubes,

howman

yareun

derthecup?

17(3.2)

Kelly:I’m

goingto

take

someandI’m

going

topu

tthem

underacup,

okay.Sopay

attentionhere.Why

don’tyo

ugu

yscoun

tho

wmanyareno

tin

thecuprigh

tno

w?

Problem

-posing:

new

Task/qu

estio

nthat

does

notappear

ontheFAI

protocol,bu

tthat

thepreservice

teacherpo

ses

tostud

ents

Protocolstates:Havethestud

entmovemag

nets

over

theiron

filings.Ask

stud

entswha

tthey

noticean

dseeifthey

canexplainwha

tisha

ppening.

21(3.9)

Caleb

askedhadaskedthestud

entsto

dotheabov

etask.Hepo

sedanew

prob

lem

whenstating:

Okay,

sono

wyo

uusemagnetsandyo

ucantry

tomakethismov

e,seewhatyo

ufind

.Problem-posing:repeat

Task/qu

estio

nthat

hasalreadybeen

asked,

but

theteacherrepeatsin

orderto

refocusthe

stud

ents’attentionor

reactto

stud

entqu

estio

nsabou

ttheinitial

prob

lem

posed

Caleb:Sowhatdo

youno

ticeabou

tthecolors?

See

righ

tthereyo

u’re

touching

white.Whatdo

youno

ticeabou

tthat?[problem

-posing:

protocol]Student:Ido

n’tkn

ow.It’s

very

sticky

.Caleb:Doyo

uno

ticeanything

abou

tthecolors?

[problem

-posing:

repeat]

80(14.8)


Instructing:

teaching

andtelling

Questionmov

esaw

ayfrom

assessing

stud

entthinking

toteaching

thestud

ent

bytelling

them

afact

orconcept

Caleb:Well,ifyo

ulook

atthis,whatitdo

es,

well,itissupp

osed

tokind

ofbalanceitou

t.…

Okay?

So,

seeifIpu

shreally,really

hard,

thisisn’tlin

edup

.

27(5.0)

Instructing:

leading

questio

nQuestionintend

edto

focusstud

ents’attention

toaparticular

aspect

orprov

ides

prom

pting

hintsor

clues

Kelly:So,

that,that

[problem

]uses

this

symbo

l,(pointsto

additio

nsign

)righ

t?Ifwe

wereto

write

that

out.

28(5.2)

Follow-up:nonspecific

Questionin

reactio

nto

stud

entrespon

se,bu

tlacksspecificity

ordo

esno

treactto

stud

ent

words

oractio

ns

Caleb:Why

doyo

uthinkso?

105(19.5)

Follow-up:

competent

Questionin

reactio

nto

stud

entrespon

se,bu

tin

which

thepreservice

teacherattempted

tobu

ildon

thestud

ents’thinking

tocausethestud

ent

tojustifythinking

,explorereason

ing,

orcreate

acognitive

conflictto

reorganize

thinking

Caleb:Doyo

uno

ticeanything

abou

tthe

colors?[problem

-posingrepeat]

70(13.0)

Student:Yeah,

thedifferentcolors

Caleb:Sowhenyo

umov

ethemagnets,do

you

noticeanything

abou

tho

wthedifferentcolors

affect

each

other?

[follow-up:

competent]

Follow-up:

incorrect

Questionin

reactio

nto

stud

entrespon

sethat

issolely

presentedto

tellthestud

entthat

they

are

incorrect.In

theseinstances,thePSTdo

esno

tfollo

wingup

questio

nsthat

they

perceive

the

stud

enthasrespon

dedto

correctly

.

Caleb:(Lon

gpause)

So,

sinceyo

uare

blow

ing,

doyo

uthinkyo

ualwayshave

totouchan

object

tomakeitmov

e?[problem

-po

sing

:protocol]Student:Yeah.

Caleb:You

do?[follow-up:

incorrect]

12(2.2)

Total

questio

ns53

9

TABLE1

(con

tinued)

Cod

eDescription(adapted

from

Moyer&Milewicz,2002)

Example

Frequ

ency

(%)


Problem-Posing Questions

Kelly and Caleb asked problem-posing: framing questions 17 times(3.2 % of questions asked). During an FAI focusing on the concept ofbalance using a triple beam balance, Kelly asked the following problem-posing: framing question:

Kelly: What happens is if these two [sides of the balance] have the same amount in them,then this stick is going to match this in the middle. So, see if I push really, really hard, thisisn’t lined up. Okay?Does this remind you of something?Maybe something you have seen?Student: Yeah.Kelly: Yeah, do you know what I am talking about?Student: Yeah.Kelly: Yeah, a see saw, or a teeter totter or something. Yeah. Have you ever played onone of those before?

Kelly familiarized the student with the concept of balance by referring to ateeter totter. She made the assumption that the student had prior knowledgeof balance through experiences on a teeter totter and utilized this assumedprior knowledge to frame the following protocol question, “What do younotice happens when I put one of these blocks on one side?”

In addition to framing questions, Kelly and Caleb asked questions fromthe protocols they had prepared prior to the FAI. Problem-posing:protocol (19.5 %) and problem-posing: repeat (14.8 %) questions were

NonSpecific 19%

Protocol 20%

Repeat 15%

Clarifying 14%

Competent 13%

IRTA 10%

Other 9%

Fig. 1. Summary of overall questioning codes. IRTA=instructing-rather-than-assessing(teaching and telling or leading questions)


those that were taken directly from the written protocol or changed onlyslightly so that the intent of the question remained the same.

New problems were asked 21 times (3.9 %) and consisted ofquestions that deviated from the protocol in terms of conceptualcontent rather than minor wording. For example, during FAI 2, Calebsought to find out what his students thought about composing anddecomposing the number “eight.” In the FAI protocol, Caleb plannedto ask the following questions:

� If I have 4 chips and 4 cubes, how many chips and cubes do I haveall together?

� Do I have to use 4 chips and 4 cubes to get 8 or is there maybeanother way to get 8 total objects?

� Are there any other combinations of chips and cubes I can use so thatthere are still 8 total items on the table?

During the FAI, the students presented different combinations ofchips and cubes so there were a total of eight items. For example,one student showed two chips and six cubes to demonstrate 2+608.The student used a strategy of replacing a cube for each chip. As thestudent did this, Caleb posed a new question, “Can you take away allof them?” This question was not originally in the protocol, but wasasked as a new task based on the student–teacher interaction. In thiscase, the student was able to represent the situation and exclaimedthat it represented, “Eight plus zero.”

Often after asking questions, Kelly and Caleb would clarify theresponse, asking the student to repeat his or her answer or repeatingthe response in the form of a question (i.e. Student: Eleven. Kelly:Eleven?). Approximately 13.0 % of all questions Kelly and Calebasked were focused on clarifying student responses.

Instructing-Rather-Than-Assessing Questions

We also identified instances when Kelly and Caleb instructed ratherthan assessed when asking questions. At times, they told the studentthe answer within their question (5.0 %) or incorporated leadingquestions (5.2 %) that suggested to the students a solution path. Forexample, in FAI 5, Kelly guided the student in solving to the pointthat it was difficult to determine the student’s thinking. The studentwas given the following problem: “Bill had five donuts, George gavehim some more and now Bill’s total is eighteen. How many didGeorge give him?” The following ensued:


Student: I don’t know. I think it is eight.Kelly: Keep working, you can use the cubes if you need to, Erica.Student: That is nineteen.Kelly: Nineteen. How did you get that? He gave him nineteen to get to eighteen?Student: Eighteen, nineteen.Kelly: Okay, here, think about this. So, he had five, right? You can use the counters[counts out five counters for him]. He had five and he got some, we don’t know howmany though, and he ended with eighteen. How many do you think he gave him?

Kelly told the student to keep working, implying that the answer was incorrect.Kelly led the student to use cubes to solve the problem, which hindered herability to uncover how the student was solving the problem. Rather thaneliciting the student’s thinking, Kelly continued to guide the student to usecounters. In fact, she even counted out the five counters. This extensiveguidance hindered the potential for the student to represent and solve theproblem. This incident was therefore coded as instructing: teaching and telling.

Follow-Up Questions

The most notable trends in the data were evident in the follow-upquestioning that took place after a problem had been posed and thestudent had responded. As described above, follow-up questions wereseparated into three main categories: follow-up: incorrect, follow-up:nonspecific, and follow-up: competent. Questions that indicated to thestudent an incorrect answer were deemed follow-up incorrect (2.2 % of allquestions). Of particular interest to our first research question is that19.5 % of all questions asked were coded as follow-up: nonspecific and13.0 % were coded as follow-up: competent. Examples of these findingsare described in detail below.

Development of Competent Questioning

Follow-up: nonspecific questions were those that were general in nature,meaning they focused on exposing student thinking and reasoning, butdid not necessarily cause the student to reorganize or conceptualizemathematical or scientific processes or draw directly on the actions andutterances of the student. For example, Kelly interviewed a student abouther understanding of balance. When the student was able to add weight toone side of a triple beam balance so that both sides were equal, shefollowed up with a nonspecific probe: “So, why do you think thathappened?” Rather than pose a general question, Kelly could have askeda more detailed question that incorporated the student’s action such as,“What do you think made the two sides balanced?” or, “What did adding


more weight to one side do?” Table 2 shows the decrease in percentage ofthe use of these types of questions over the course of the semester.

During FAI 1, Kelly and Caleb primarily asked questions from the protocol(23.5 %) or asked clarification (17.6 %) or follow-up: nonspecific questions(15.7 %). However, over the course of the semester, Kelly and Caleb’s use offollow-up: nonspecific questions decreased and their use of competent follow-up questions increased. Questions coded as competent were directly related tohow the student responded and competent questions were indicated by thosecausing some type of disequilibrium within the student’s thinking or thoseattempting to draw students’ attention to conceptual meaning. These sorts ofquestions asked the students to consider how the new information would makesense given their existing schema. This question type is exemplified by Kellywhen asking the student about balancing a ruler.

Kelly: …Let me see you balance it with just your finger. (Student balanced the ruleron her finger)Student: Easy.Kelly: How do you know to put your finger there?Student: It’s the very middle.Kelly: It’s the very middle. Well, why does the very middle work, Amy? (Paused)Why does it work on the very middle?

In this excerpt, Kelly asked the student questions that would cause her tospeculate beyond her initial conjectures and reflect more deeply. Kelly’squestions focused on the actions and responses of the student andencouraged the student to understand the action within the concept of

TABLE 2

Percentage of follow-up: nonspecific questions

FAI 1 2 3 4 5 6 7 8 9 10% NS 15.7 26.8 25.6 43.2 23.9 8.1 12.2 18.0 11.5 14.9

% NS: percentage of questions coded as “follow up: nonspecific” by FAI

TABLE 3

Percentage of follow-up: competent questions

FAI 1 2 3 4 5 6 7 8 9 10% C 3.9 8.9 5.1 4.5 6.2 10.8 26.5 14.0 22.1 17.0

% C: percentage of questions coded as “follow up: competent” by FAI


balance. Table 3 shows the increasing percentage of competent follow-upquestions Kelly and Caleb asked throughout the ten FAIs.

Kelly and Caleb both developed more competent questioning practicethroughout the course of the semester. The percentage of competentfollow-up questions during FAI 1 was 3.9 % of questions, the minimumfor the entire semester. However, the percentage of competent questionswas as high as 26.5 % and ended with 16.7 %.

Noticing

Kelly and Caleb’s ability to professionally notice their students’ thinkingwasmeasured by their responses on the FAI Reflection and Planning forms. Intheir abilities to detail the students’ strategies, interpret the students’understanding, and decide how to respond based on the students’understanding, Kelly gradually improved while Caleb fluctuated throughoutthe semester. Recall that the FAI Reflection and Planning forms were codedas robust (three points), limited (two points), and lacking (one point) on fivedimensions, resulting in a maximum score of 15 (see Fig. 2).

Caleb steadily improved from FAI 1 to 4, but exhibited a dramatic dipby FAI 6, the last of the mathematics FAI Reflection and Planning forms.The sixth reflection lacked the detail and rigor he provided in previousforms. Caleb improved again during the science FAIs, yet never exceededhis scores on the third and fourth mathematics FAI Reflection andPlanning forms. Kelly, on the other hand, showed a steady improvementover time up to FAI Reflection and Planning form 8.

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 10

No

tici

ng

Sco

re

Interview Number

Caleb

Kelly

Fig. 2. Kelly and Caleb’s noticing scores based on FAI Reflection and Planning formanalysis


Areas for Further Development

Data analysis revealed growth in Kelly and Caleb’s questioningpractice (i.e. competent follow-up questions); however, both preser-vice teachers exhibited areas that could be further developed toenhance their abilities to elicit student thinking. Analysis of FAIvideo and transcripts to explore research question 2 suggested manyopportunities Kelly and Caleb missed to ask further questions toexplore student thinking more deeply. Leading questions resulted inthe preservice teacher not gaining an accurate understanding of thestudents’ thinking by foregrounding their own solution strategiesbecause in these cases, the student tended to agree with thepreservice teacher rather than provide their own rationale. Forexample, in FAI 3, Kelly asked the student how many differentcombinations of boys and girls one could have in a class with 11total students. The following conversation ensued.

Student: Nine girls and one boy.Kelly: If there’s eleven kids in the class...Student: I’m kidding, two boys.Kelly: Okay, so write out what you had. So you had nine girls, right?Student: And two boys.Kelly: And two boys? And together that makes?

In this example, Kelly provided the student prompting and failed toadequately gauge the student’s reasoning. She began by reminding thestudent that there were 11 total students. While this may have beenappropriate to clarify for the student, Kelly focused on the incorrectresponse rather than on how the student solved the problem. Furthermore,Kelly failed to uncover the student’s thinking as she continued to supporthim by telling him to write down what he is thinking. This may haveguided him to solve the problem in a certain way instead of using otherstrategies such as manipulatives or mental mathematics. Finally, Kellysaid to the student, “And together that makes,” providing him with a clueto sum the two numbers. Perhaps the student would not have added thetwo numbers had Kelly not lead him with that prompt. Had Kelly focusedmore on the student’s reasoning, she may have discovered how thestudent was thinking about the decomposition of the number 11.Therefore, Kelly and Caleb needed to learn that allowing students toattempt their own methods and assessing their reasons for this method canoften uncover misconceptions that the student may hold.


In addition to asking leading questions, there were several instanceswhere Kelly and Caleb could have asked follow-up questions, but missedthe opportunity to do so. In FAI 7, Kelly explored the concept of balancewith the student. She had the student place dried beans and woodenblocks on a scale and observed what happened as they placed variousobjects on each side of the scale. Once the scale was balanced with ablock on one side and beans on the other, Kelly asked the student to placetwo more blocks on the scale and balance it again. The followingconversation ensued:

Kelly: Can you find a way to balance this, using one block on this side and one blockon this side and some beans in there?(Student places a block on one side. She begins placing another block on the same side.)Student: Here?Kelly: Well, you already got the one here, so what if you put another one over here?(Kelly puts block on the other side). What do you think is going to happen?

In this episode, Kelly missed an important opportunity to allow the student toexplore the concept of balance on her own. The student may have sharedinformation related to her understanding of balance if Kelly had allowed the studentto place the block on the same side of the scale and asked, “What happened whenyou put the block on that side?” Instead, Kelly instructed the student where tocorrectly place the block and asked herwhat she thought was going to happen afterthe student had already placed the block on the correct side.

Both Kelly and Caleb demonstrated questioning practice that suggestedareas for improvement. They asked questions that led students to solveproblems in a certain way rather than allowing students to solve theproblem in their own way regardless of the accuracy of the response. Thisresulted in their inability to capture the full thought processes of thestudents. In addition, Kelly and Caleb missed a number of opportunitiesto ask follow-up questions to probe the students’ thinking further, whichmay have elicited a deeper level of the students’ thinking.

DISCUSSION

Educators have suggested that that the ability to competently question is akey component of teaching (Bell et al., 1985; Harlen, 2001). The types ofquestions teachers ask can influence the opportunities that students haveto learn about content (Hackenberg, 2005) and what, in turn, teachers canlearn about students. The core practice of questioning contributes torevealing student thinking, allowing teachers to modify their instruction


based on student needs. Although some researchers suggest thatpreservice teachers are not developmentally ready to engage in advancedpractices (Kagen, 1992), similar to Levin, Hammer, & Coffey (2009), webelieve that preservice teachers can develop core practices that foregroundstudent thinking. The many aspects of professional noticing—attending tostrategies, interpreting understandings, and deciding how to respond—play an important role in student-centered teaching (Jacobs et al., 2010;Scherrer & Stein, 2012; van Es & Sherin, 2002, 2008). We believe thatthe ability to competently question students is a core practice that must bedeveloped through continued practice and support and that developmentof this practice is influenced by one’s ability to notice.

As stated by Darling-Hammond (2010), the results of this study suggestthat with weekly practice and reflection, preservice teachers can developtheir questioning practice within the context of face-to-face interaction withstudents and that the ways they question students can change when givenopportunities to interact with them and analyze their thinking. Theimportance of placing student thinking at the center of instruction is notnovel (Carpenter et al., 1996); however, we believe that preservice teachereducation could place greater emphasis on preparing teachers to uncoverstudent thinking. We believe that a focus on questioning practice and theability to notice is one way to do so. In this study, Kelly and Caleb improvedtheir ability to competently pose follow-up questions based on students’responses to delve deeper into the students’ understanding. Although allteachers engage in the act of noticing during instruction (Jacobs et al., 2010;Sherin, Jacobs & Philipp, 2011a; Sherin, et al., 2011b), what they notice andchoose to attend to may differ. Through weekly field experiences andreflection, Kelly and Caleb were not only able to practice their abilities toquestion through weekly FAIs but also received feedback from their fieldinstructor (via grading of FAI protocols) and from the students themselvesthrough their responses. We postulate that the reflection forms providedKelly and Caleb are an important scaffold to think critically about theirprofessional noticing of student thinking, and in Kelly’s case, we sawcontinual growth. We contrast this to the experiences of many preserviceteachers who may never have the opportunity to dissect the mentalconstructions of children.

We posit that the experimental field experience approach provided richopportunities for Kelly and Caleb to develop the core practice ofquestioning and their abilities to notice. Our analyses suggest that thisdevelopment occurred simultaneously, particularly with regard to Kelly.Although one might suggest that any engagement in consistent practicewould contribute to improved performance, another explanation for the


change we observed is the development of Kelly and Caleb’s abilityto notice. In this study, Kelly and Caleb demonstrated progress intheir ability to competently question students to reveal componentsof their mathematical and scientific reasoning. By reflecting on whatthey professionally noticed about students’ thinking, we contend thatKelly and Caleb learned to adapt their questioning practice to offermore competent questions in their interactions with students. Wepostulate that they were attending to their students’ thinking (asdemonstrated by increasingly foregrounding student thinking withintheir follow-up questions), interpreting their students’ responses (asdemonstrated by responding with meaningful follow-up questions andreflect on student responses in the FAI Reflection and Planning form), anddeciding how to respond (as demonstrated by their increased propensity toask relevant follow-up questions not included in the FAI protocol and tomake suggestions for further lessons in their FAI Reflection and Planningforms). By building their knowledge of each student’s thinking fromweek toweek, they were formulating an understanding of the individual students’thinking as well building broader models of how students engage in specificcontent.

Our study builds on the prior work of Moyer & Milewicz (2002)by considering how preservice teachers’ questioning practices changeover time. Like others (Franke et al., 2009; Kawanaka & Stigler,1999; Ralph, 1999; Sahin & Kulm, 2008), we have documented thestruggles that teachers face in asking students provocative questions,but we also have shown that given appropriate scaffolds, preserviceteachers can make changes in their questioning throughout the course of asemester. While providing clinical field experiences to preservice teachers isnot novel, we suggest the importance of foregrounding student mathematicaland scientific thinking through an iterative process of enactment andreflection to develop questioning practice and the ability to notice. In thispaper, we note areas for further development that could potentially improvepreservice teachers’ questioning practice. These areas could be specificallytargeted in a field experience course, such as the one described in this study.

ACKNOWLEDGMENTS

We would like to thank Anderson Norton III, Meredith Park Rogers,Enrique Galindo, and Valarie Akerson. Support for this project wasfunded by the National Science Foundation (project no. 0732143).


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Ingrid S. WeilandCollege of Education and Human DevelopmentUniversity of Louisville1905 S. 1st Street, #273, Louisville, KY, 40292, USAE-mail: [email protected]

Rick A. Hudson

University of Southern IndianaEvansville, IN, USAE-mail: [email protected]

Julie M. Amador

University of IdahoCoeur d’Alene, ID, USAE-mail: [email protected]


Documents

PRESERVICE FORMATIVE ASSESSMENT INTERVIEWS: THE DEVELOPMENT OF COMPETENT QUESTIONING