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Exploring the links between pre-service teachers’ beliefs and video-based reflection in wikis Young Hoan Cho a,, Yemin Huang b a Department of Education, Seoul National University, South Korea b School of Information Science and Learning Technologies, University of Missouri, Columbia, MO, USA article info Article history: Available online 16 March 2014 Keywords: Teacher education Beliefs Mathematics Video-based reflection Wikis abstract In teacher education, video has been used frequently for the development of competencies for effective teaching. However, few empirical studies have investigated reciprocal relationships between pre-service teachers’ beliefs and video-based reflection activities. The present study investigated the influences of epistemological beliefs about mathematics on video-based reflection in wikis. Elementary school pre-ser- vice teachers had carried out reflective writing and questioning activities after watching a video clip about mathematics learning or instruction in wikis for six weeks. This study also explored the relation- ships between video-based reflection activities and the change of mathematical beliefs for teaching (MBT). Both quantitative and qualitative data were collected to examine the links between beliefs and reflection activities. This study found that epistemological beliefs partially influenced reflective writing and questioning activities in wikis. In addition, video-based reflection activities were beneficial for the beliefs of mathematical knowledge and students. This study also identified a few reflection and question categories that were closely related to the change of MBT. Lastly, implications of this study were dis- cussed in regard to video-based reflection practices in teacher education. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Video has been used effectively to support professional devel- opment and reflection on teaching practices (Pryor & Bitter, 2008; Sherin & van Es, 2009; Stockero, 2008). Video allows pre- service teachers to observe an important or problematic event repeatedly and negotiate the meanings of the event with their peers for in-depth reflection. Recently, a growing number of studies have shown that video-based reflection is much beneficial for the improvement of pre-service teachers’ competencies to no- tice key features of classroom activities and make sense of them on the basis of professional knowledge (Star & Strickland, 2008; Stockero, 2008). The effectiveness of video-based reflection may depend on indi- vidual differences like pedagogical content knowledge (Hill, Ball, & Schilling, 2008; Shulman, 1986), learning and teaching styles (Felder & Silverman, 1988), and beliefs about knowledge, students, and pedagogy (Hofer & Pintrich, 1997; Philipp, 2007). Pre-service teachers who favor sensing over intuition, for instance, may observe carefully and memorize details of a lesson in a video clip, whereas those who prefer intuition to sensing are likely to reflect on concepts and principles related to the video (Felder & Silverman, 1988). Although there are a variety of factors that influ- ence reflection on a video, the current study focuses on pre-service teachers’ beliefs. Literature of teacher education shows that indi- viduals selectively pay attention to the events relevant to their be- liefs and interpret the events in a way to confirm their existing beliefs (Ambrose, 2004; Borko, Mayfield, Marion, Flexer, & Cumbo, 1997; Cooney, Shealy, & Arvold, 1998; Pajares, 1992; Philipp, 2007; Yadav & Koehler, 2007). Nevertheless, few studies were carried out to investigate what kinds of beliefs influence video-based reflec- tion in teacher education. In addition, video-based reflection can help pre-service teachers to change their naive beliefs. Reflection has been emphasized in teacher education because teachers need to recognize problems in their classroom practices and change their beliefs through continuous reflection activities (Dewey, 1933; Mewborn, 1999; Philipp et al., 2007; Schön, 1987). Particularly for pre-service teachers with little teaching experience, video-based reflection can be much helpful because video provides authentic and vivid classroom situations. In addition, pre-service teachers may experi- ence expectation failure, which is necessary for belief change (Ambrose, 2004), when they view novel teaching practices or http://dx.doi.org/10.1016/j.chb.2014.02.022 0747-5632/Ó 2014 Elsevier Ltd. All rights reserved. Corresponding author. Address: 1 Gwanak-ro, Gwanak-gu, Department of Education, College of Education, Seoul National University, Seoul 151-748, South Korea. Tel.: +82 2 880 8937; fax: +82 2 878 1665. E-mail address: [email protected] (Y.H. Cho). Computers in Human Behavior 35 (2014) 39–53 Contents lists available at ScienceDirect Computers in Human Behavior journal homepage: www.elsevier.com/locate/comphumbeh

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Page 1: Exploring the links between pre-service teachers’ beliefs and video-based reflection in wikis

Computers in Human Behavior 35 (2014) 39–53

Contents lists available at ScienceDirect

Computers in Human Behavior

journal homepage: www.elsevier .com/locate /comphumbeh

Exploring the links between pre-service teachers’ beliefsand video-based reflection in wikis

http://dx.doi.org/10.1016/j.chb.2014.02.0220747-5632/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Address: 1 Gwanak-ro, Gwanak-gu, Department ofEducation, College of Education, Seoul National University, Seoul 151-748, SouthKorea. Tel.: +82 2 880 8937; fax: +82 2 878 1665.

E-mail address: [email protected] (Y.H. Cho).

Young Hoan Cho a,⇑, Yemin Huang b

a Department of Education, Seoul National University, South Koreab School of Information Science and Learning Technologies, University of Missouri, Columbia, MO, USA

a r t i c l e i n f o

Article history:Available online 16 March 2014

Keywords:Teacher educationBeliefsMathematicsVideo-based reflectionWikis

a b s t r a c t

In teacher education, video has been used frequently for the development of competencies for effectiveteaching. However, few empirical studies have investigated reciprocal relationships between pre-serviceteachers’ beliefs and video-based reflection activities. The present study investigated the influences ofepistemological beliefs about mathematics on video-based reflection in wikis. Elementary school pre-ser-vice teachers had carried out reflective writing and questioning activities after watching a video clipabout mathematics learning or instruction in wikis for six weeks. This study also explored the relation-ships between video-based reflection activities and the change of mathematical beliefs for teaching(MBT). Both quantitative and qualitative data were collected to examine the links between beliefs andreflection activities. This study found that epistemological beliefs partially influenced reflective writingand questioning activities in wikis. In addition, video-based reflection activities were beneficial for thebeliefs of mathematical knowledge and students. This study also identified a few reflection and questioncategories that were closely related to the change of MBT. Lastly, implications of this study were dis-cussed in regard to video-based reflection practices in teacher education.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Video has been used effectively to support professional devel-opment and reflection on teaching practices (Pryor & Bitter,2008; Sherin & van Es, 2009; Stockero, 2008). Video allows pre-service teachers to observe an important or problematic eventrepeatedly and negotiate the meanings of the event with theirpeers for in-depth reflection. Recently, a growing number ofstudies have shown that video-based reflection is much beneficialfor the improvement of pre-service teachers’ competencies to no-tice key features of classroom activities and make sense of themon the basis of professional knowledge (Star & Strickland, 2008;Stockero, 2008).

The effectiveness of video-based reflection may depend on indi-vidual differences like pedagogical content knowledge (Hill, Ball, &Schilling, 2008; Shulman, 1986), learning and teaching styles(Felder & Silverman, 1988), and beliefs about knowledge, students,and pedagogy (Hofer & Pintrich, 1997; Philipp, 2007). Pre-serviceteachers who favor sensing over intuition, for instance, may

observe carefully and memorize details of a lesson in a video clip,whereas those who prefer intuition to sensing are likely to reflecton concepts and principles related to the video (Felder &Silverman, 1988). Although there are a variety of factors that influ-ence reflection on a video, the current study focuses on pre-serviceteachers’ beliefs. Literature of teacher education shows that indi-viduals selectively pay attention to the events relevant to their be-liefs and interpret the events in a way to confirm their existingbeliefs (Ambrose, 2004; Borko, Mayfield, Marion, Flexer, & Cumbo,1997; Cooney, Shealy, & Arvold, 1998; Pajares, 1992; Philipp, 2007;Yadav & Koehler, 2007). Nevertheless, few studies were carried outto investigate what kinds of beliefs influence video-based reflec-tion in teacher education.

In addition, video-based reflection can help pre-service teachersto change their naive beliefs. Reflection has been emphasized inteacher education because teachers need to recognize problemsin their classroom practices and change their beliefs throughcontinuous reflection activities (Dewey, 1933; Mewborn, 1999;Philipp et al., 2007; Schön, 1987). Particularly for pre-serviceteachers with little teaching experience, video-based reflectioncan be much helpful because video provides authentic and vividclassroom situations. In addition, pre-service teachers may experi-ence expectation failure, which is necessary for belief change(Ambrose, 2004), when they view novel teaching practices or

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40 Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53

unexpected students’ learning behaviors in video. In-depth reflec-tion on the events conflicting with existing beliefs can help pre-service teachers to change their naive beliefs about learning andteaching. More research is necessary to explore what kinds of vi-deo-based reflection activities are associated with the change ofpre-service teachers’ beliefs.

The current study aims to explore reciprocal relationships be-tween pre-service teachers’ beliefs and video-based reflectionactivities in the domain of elementary school mathematics. It isimportant to understand what kinds of beliefs make differencesin noticing and reflecting on an event in video. Based on literaturereviews, we predicted that epistemological beliefs (i.e., beliefsabout knowledge and knowing) would influence what pre-serviceteachers notice in video and how they reflect on the event. In addi-tion, this study intends to explore how video-based reflectionactivities are related to the change of pre-service teachers’ beliefsabout mathematical knowledge, students, and pedagogy. Althoughthese beliefs have been considered as important goals in teachereducation (Cooney et al., 1998), few empirical studies were carriedout to improve the beliefs, particularly through video-based reflec-tion. The current study can provide an implication about whatkinds of video-based reflection activities should be fostered forthe change of pre-service teachers’ beliefs. To promote in-depthreflection on video, this study used wikis that enable pre-serviceteachers to easily create, revise, organize, and share their reflectivewriting and questions in the Internet.

2. Role of epistemological beliefs in video-based reflection

Literature of educational psychology and teacher education hasshown that epistemological beliefs are influential in teaching andlearning practice (Hofer & Pintrich, 1997; Kang, 2008; Schommer,Crouse, & Rhodes, 1992). Epistemological beliefs are defined as‘‘individuals’ beliefs about the nature of knowledge and the pro-cesses of knowing’’ (Hofer & Pintrich, 1997, p. 117). Previous stud-ies have suggested multiple dimensions of epistemological beliefsincluding beliefs about the structure, stability, and source ofknowledge (Buehl & Alexander, 2005; Hofer & Pintrich, 1997). Peo-ple with more advanced epistemological beliefs tend to believethat knowledge consists of highly interrelated concepts and facts(structure of knowledge); knowledge is evolving and changeable(stability of knowledge); and people construct their own knowl-edge (source of knowledge). By contrast, people with less advancedepistemological beliefs are likely to believe that knowledge in-volves isolated facts (structure of knowledge); knowledge is abso-lute and fixed (stability of knowledge); knowledge comes from anexternal authority (source of knowledge).

However, these epistemological beliefs are not fixed indepen-dently from domains or contexts (Buehl, Alexander, & Murphy,2002; Hofer, 2000). Buehl and Alexander (2005) found that collegestudents had different epistemological beliefs in two domains:mathematics and history. Students tended to believe that knowl-edge in mathematics is more certain than knowledge in history;knowing mathematics depends on an authority more than know-ing history. In addition, Kuhn, Cheney, and Weinstock (2000) foundthat the development of epistemological beliefs varied across thedomains of personal taste, aesthetic, value, social truth, and phys-ical truth. The transition from multiplists to evaluativists tended tobe more difficult in the domains of personal taste and aestheticthan truth domains. Multiplists believe that all opinions areequally right, whereas evaluativists tend to judge the value ofopinions by analyzing and comparing their rationale and evidence.

Epistemological beliefs may play a critical role in video-basedreflection when it comes to the quality of reflective thinking.

Pre-service teachers with the belief that knowing is to memorizeinformation given by an authority may not be spontaneously en-gaged in analyzing events noticed in a video. Mewborn (1999)found that pre-service teachers were more engaged in reflectivethinking when the locus of authority was internal to themselves.By contrast, when pre-service teachers believed that teacher educa-tors had the authority of evaluating classroom practice, they merelyrecalled classroom events without generating hypotheses on theevents that they observed. In addition, Mason, Ariasi, and Boldrin(2011) assumed that epistemological beliefs are activated in theform of reflective thinking when students carry out a specific tasklike searching for information in the Internet. They identified twopatterns of epistemic reflections by asking high school students tothink aloud during navigation in the Internet. Students in the firstpattern not only evaluated the credibility of web sources but alsoexamined scientific evidence to support claims. On the other hand,students in the second pattern merely evaluated the credibility ofwebsites without reflection on the justification of knowledge. Theformer outperformed the latter in learning from web resources.This study indicates that epistemological beliefs influence learninggains through reflection about knowledge and knowing.

In addition, epistemological beliefs can influence the motiva-tion of students on video-based reflection. Buehl and Alexander(2005) found that students with more advanced domain-specificepistemological beliefs had higher motivation in studying historyand mathematics than those with less advanced ones. Literatureof epistemological beliefs also indicates that students are moremotivated when they conduct tasks consistent with theirepistemological beliefs (Cho, Lee, & Jonassen, 2011; Tsai, 2000;Windschitl & Andre, 1998). Students with more advancedepistemological beliefs are motivated by open-ended tasks andinquiry-based learning, whereas students with less advancedepistemological beliefs prefer close-ended tasks and didacticinstruction. Windschitl and Andre (1998) found that studentswith more advanced epistemological beliefs gained more concep-tual knowledge by exploring and testing their own hypotheseswith a computer simulation of the human body. In contrast,confirmatory tasks in which students follow a step-by-stepinstruction in the simulation were more beneficial for studentswith less advanced epistemological beliefs.

Lastly, epistemological beliefs can influence what pre-serviceteachers notice in video. Pre-service teachers with the belief thatknowledge comes from an authority may pay more attention toteaching practices in video (Yadav & Koehler, 2007). By contrast,pre-service teachers with the belief that students construct theirown knowledge may have more interests in student activities,which determine what students learn. A number of researchers ar-gue that beliefs have a filtering effect, which allows selective atten-tion to the event closely related to their beliefs (Ambrose, 2004;Borko et al., 1997; Cooney et al., 1998; Pajares, 1992; Philipp,2007). Grant, Hiebert, and Wearne (1998) investigated the rela-tionships between teachers’ observation of reform-oriented les-sons and their beliefs of mathematical learning and teaching.Teachers, who believed that they should have much of responsibil-ity in teaching mathematical problem solving skills and algo-rithms, tended to pay little attention to students’ discussionabout alternative problem solving strategies. The teachers also per-ceived discussion as a confusing and detrimental activity. In addi-tion, Yadav and Koehler (2007) found that pre-service teachersselected different video cases as the best teaching practices and de-scribed a very similar situation in very different ways according totheir beliefs about knowledge and learning. Thus, epistemologicalbeliefs may play an important role in video-based reflection. Nev-ertheless, this assertion has been seldom examined empirically inteacher education contexts.

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Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53 41

3. Change of mathematical beliefs for teaching

Literature of teacher education shows that teachers’ beliefshave close relationships with their instructional practices and stu-dents’ achievements (Peterson, Fennema, Carpenter, & Loef, 1989;Philipp, 2007; Staub & Stern, 2002). Staub and Stern (2002) foundthat teachers with a stronger cognitive constructivist belief ofmathematics learning were more likely to select tasks that en-hance conceptual understanding. Staub and Stern also examinedwhether teachers’ beliefs influenced between-classroom differ-ences in Grade 3 mathematics achievement gains, using hierar-chical linear modeling (HLM). Elementary school teachers’beliefs explained 27% of the between-classroom variance in addi-tion–subtraction word problem scores and 50% of the between-classroom variance in multiplication–division word problemscores. In teacher education, thus, it is an important goal tochange naive beliefs of pre-service teachers. Particularly, thisstudy is interested in pre-service teachers’ beliefs in elementaryschool mathematics.

In the current study, beliefs closely related to mathematicalteaching practice are defined as mathematical beliefs for teaching(MBT). This concept is closely related to recent discussions aboutsubject matter knowledge and pedagogical content knowledge(PCK). Shulman (1986) emphasized that PCK is essential for effec-tive teaching as much as subject matter knowledge. Mathemati-cians, experts in their research areas, may not be successful inteaching mathematics unless they have sufficient knowledge aboutstudents, instructional strategies, and learning tasks pertaining tomathematical topics. A growing number of researchers have madeefforts to improve and assess PCK in teacher education (Hill et al.,2008; Krauss et al., 2008). In addition, the concept of technologicalpedagogical content knowledge (TPCK) emerged in order to de-scribe teachers’ knowledge required for effective technology inte-gration for learning and instruction (Mishra & Koehler, 2006).

Hill et al. (2008) conceptualized mathematical knowledge forteaching that includes both subject matter knowledge and PCK inorder to describe knowledge necessary for teaching mathematics.They argue that mathematics teachers need to have not onlyknowledge of mathematics but also knowledge of how studentslearn a mathematical topic (content and students), how the con-tent can be effectively taught (content and teaching), and howmathematical tasks or topics should be selected and organized(curriculum). Based on previous studies, this study assumes thatpre-service teachers need to improve MBT including not onlybeliefs of mathematical knowledge but also pedagogical contentbeliefs in mathematics.

Previous studies show that many pre-service teachers have na-ive MBT. For instance, pre-service teachers tend to believe thatthey have enough knowledge to teach elementary school students;doing mathematics is to solve problems by following step-by-stepprocedures; teaching is telling and caring about students; and goodteachers have quiet classrooms (Ambrose, 2004; Ball, 1990; Ng,Nicholas, & Williams, 2010). Pre-service teachers develop the naivebeliefs through previous experiences they had as students in K-12schools.

For the change of MBT, many teacher educators have empha-sized reflection on teaching and learning activities in school.Ambrose (2004) argued that pre-service teachers should reflecton their beliefs that are implicit but influential in guiding theirbehaviors. After making hidden beliefs overt, pre-service teachersneed to discuss or reflect on the beliefs from multiple perspectivesand principles. In the study by Ambrose (2004), an instructor hadpairs of pre-service teachers work with 6 to 10-year-old childrenusing mathematical problem solving tasks. They observed chil-dren’s behaviors, exchanged their ideas about mathematical tasks,

and discussed issues pertaining to children’s mathematical think-ing. These activities were helpful in changing pre-service teachers’existing beliefs, particularly when they reflected on the events thatconflicted with their expectation about mathematical teaching andlearning.

Video-based reflection activities can be influential for thechange of MBT. Mewborn (1999) found that pre-service teacherswere much engaged in identifying curious phenomena in video-tapes of children’s mathematics problem solving (e.g., third gradersdiscussing which one was larger between 4/4 and 5/5) and seekingfor explanations about the phenomena. Pre-service teachers werelikely to reflect on what they watched in a video by comparing itwith their beliefs and experiences. In addition, Philipp et al.(2007) investigated the effectiveness of video-based reflection forthe change of MBT by comparing the treatment with the othertreatment in which pre-service teachers observed classroom prac-tices in local elementary schools. In the video-based reflection, pre-service teachers discussed children’s mathematical thinking afterwatching videos about how children solved mathematics problemsand how they understood mathematical concepts. Philipp et al.found that pre-service teachers who reflected on the videos chan-ged their MBT more than those who visited elementary schoolsnear their campus. It was plausible that video-based reflectionhelped pre-service teachers to pay more attention on children’smathematical thinking than classroom observation.

For the design of effective video-based reflection activities,more research is necessary to explore what reflection activitiesare crucial for the change of MBT. First of all, pre-service teachersmay need to notice important events closely related to their naivebeliefs while watching a video. Pre-service teachers who pay atten-tion only to classroom management practices in a video might nothave opportunities to change their beliefs about student mathe-matical thinking. In addition, in-depth reflection may be necessaryfor the change of MBT. Even if pre-service teachers identify anevent that significantly conflicts with their existing beliefs, theymay not learn from the event without analyzing and explainingit (Chinn & Brewer, 1993; Grant et al., 1998). Pre-service teacherswho interpret the meanings of what they noticed in a video frommultiple perspectives and principles would change their beliefsmore than those who merely describe what happened in a video.

4. Quality of video-based reflection

Literature of video-based reflection emphasizes selective atten-tion and knowledge-based reasoning while or after watching a vi-deo (Star & Strickland, 2008; Stockero, 2008; van Es & Sherin,2008). Previous studies investigated what teachers notice in a vi-deo and how they describe, explain, or evaluate the events noticed.These two questions are important in understanding reciprocalrelationships between beliefs and video-based reflection. Thisstudy investigates the quality of video-based reflection in termsof topics, stances, and complexity of reflective writing (seeTable 1).

The topic dimension examines what is noticed in a video interms of four categories: mathematics, student mathematicalthinking, mathematical pedagogy, and general pedagogy. The cat-egory of mathematics refers to statements about mathematicalconcepts and problem solving strategies, whereas student mathe-matical thinking involves students’ understanding, difficulties,and misconceptions. In addition, mathematical pedagogy refersto tasks, tools, and strategies for teaching mathematics, but generalpedagogy including classroom management can be applied toteaching practices regardless of subjects. Sherin and van Es(2009) found that discussions about videos of classroom practices

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Table 1Topics, stances, and complexity of video-based reflection.

Dimension Categories Description Example

Topic Mathematics Mathematical concepts and problemsolving strategies

I personally think using blocks is helpful because then you can see how it visually worksalong with the problem

Studentmathematicalthinking

Students’ knowledge and problemsolving process

This child is struggling making sense out of the blocks but she thinks that she can easilysubtract it on paper

Mathematicalpedagogy

Mathematical tasks, tools, and teachingstrategies

I do like, however, how the teacher who asked her the question kept making her referback to visual items that she is familiar with

Generalpedagogy

General teaching strategies andclassroom management

When the teacher was interrupted, she glanced at each child and continued talkingwithout making it disrupt the whole class

Stance Describing Stating what happened in video withoutany judgment and analysis

The main event that I found interesting was the first child who used subtracting usingthree different methods. She used the stack, then manipulatives, then a hundreds chart

Explaining Interpreting the meaning of an event andmaking inferences

I am assuming that the traditional method was probably what was taught as the‘‘appropriate’’ way to solve the problem, and that is why she strongly believed that thefirst answer was correct

Evaluating Judging the value of an activity andproviding a suggestion

I believe it was a good idea to use a manipulative for first grade students because it allowsthem to count the squares rather then do the math in their heads

Confronting Recognizing a cognitive conflict andquestioning his or her own assumption

After watching the video, I couldn’t help but wonder how would I attempt to explain thesubtraction problem to the first little girl

Complexity Simple Statements without any explanation andjustification

In episode two the student knows the algorithm but doesn’t know why she uses it or howit works

Elaborated Statements with details, examples,explanations, rationales, and suggestions

I think showing the first little girl that the number she came up with originally wasincorrect with the blocks and the number chart was a great thought provoker for thestudent. She really could see that there was something she was missing, something wrongwith what she came up with. Piaget says that students have to be in the stage ofdisequilibrium first for real learning to occur

42 Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53

helped teachers to pay more attention on student mathematicalthinking in a video. The authors interpreted the increased focuson student mathematical thinking as the development of selectiveattention skills.

The stance and complexity dimensions can be used to examinehow pre-service teachers make sense of the events noticed in a vi-deo. The stance dimension includes describing, explaining, evalu-ating, and confronting (Sherin & van Es, 2009; Stockero, 2008).Describing refers to stating what happened in a video withoutany judgment and explanation, whereas explaining refers to inter-preting the meaning of an event and making inferences aboutcause and effect relationships (Stockero, 2008). Evaluating is de-fined as judging the value of an activity and providing a suggestionto improve the activity. Sherin and van Es (2009) found that teach-ers initially discussed classroom practices in a video by describingor evaluating them. Video-based discussions helped teachers tomake sense of the event noticed in a video by explaining the mean-ing of student behaviors or synthesizing different events within orbetween videos. In addition, confronting indicates identifyinganomalous events in a video and considering alternative view-points (Stockero, 2008). Confronting can promote critical reflectionon existing beliefs that conflict with the video.

The complexity dimension examines whether pre-serviceteachers describe, explain, evaluate, or confront an event withelaboration and justification (Hmelo-Silver & Barrows, 2008). Elab-orated reflection is supported by other statements like examples,rationales, evidence, and suggestions. Literature of constructivelearning indicates that elaboration helps to integrate new knowl-edge with existing knowledge in a meaningful way (Chi, 2009;Levin, 1988). In addition, elaborated reflection may be closelyrelated to epistemological beliefs. Pre-service teachers with the be-lief that knowledge comes from an external source may not makean effort to justify and elaborate their own opinions (King &Kitchener, 2004; Kuhn, 1991; Weinstock & Cronin, 2003). There-fore, the complexity dimension can play a key role in explainingreciprocal relationships between video-based reflection and beliefsof pre-service teachers.

5. The present study

The current study used wikis to support video-based reflec-tion activities. Wikis allow individuals to create and sharewebpages quickly and flexibly without knowledge of markuplanguage (HTML) and web editing software. It is easy to inserthyperlinks to other webpages and various files (e.g., images,videos, documents) within wikis. In addition, users can easilyidentify the change of webpages using a history function thatprovides different versions of a wiki in order of time. As a typeof Web 2.0, wikis encourage individuals to become an activeparticipant in collaborative work in the Internet rather than apassive receiver of online information created by others (Hew& Cheung, 2013). Donnelly and Boniface (2013) indicate thatwikis have five positive attributes for meaningful learning:collaboration, organization, operation, cognition, and emotion.Wikis can support shared knowledge creation through collabora-tive writing, organization of information and resources withhyperlinks, easy operation leading to cost effective education,cognitive engagement through peer interaction, and emotionalsupport from other participants (Donnelly & Boniface, 2013).Due to these advantages of wikis, they have been effectivelyused for collaborative knowledge building in teacher education(Biasutti & EL-Deghaidy, 2012; Wheeler & Wheeler, 2009). In thisstudy, wikis are used to help pre-service teachers to create,share, and modify their reflective writings and to ask and answerquestions reciprocally.

The current study seeks for empirical evidence about thefollowing research questions:

1. Do epistemological beliefs in mathematics influence video-based reflection activities in wikis?

2. Do mathematical beliefs for teaching change through video-based reflection activities in wikis?

3. What kinds of video-based reflection activities in wikis areclosely related to the change of mathematical beliefs forteaching?

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Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53 43

Based on the literature review, we hypothesized that epistemo-logical beliefs in mathematics would influence the quality of video-based reflection activities in wikis (Hypothesis 1). This study alsopredicted that pre-service teachers would change their MBTthrough video-based reflection activities in wikis (Hypothesis 2).In addition, reflection on mathematics, student mathematicalthinking, and mathematical pedagogy would be beneficial for thechange of MBT (Hypothesis 3-1). Reflection on general pedagogy,which is not domain-specific, may not be closely related to thechange of MBT. Lastly, in-depth reflection (e.g., explaining, con-fronting, elaborated reflection, deep-reasoning questions) wouldbe positively related to the change of MBT (Hypothesis 3-2).

6. Research methods

6.1. Participants

In an elementary school mathematics education course, 26 pre-service teachers initially participated in the current study as part oftheir coursework at a state university located in the United States.However, two participants were excluded from further data analy-sis because they did not complete reflection tasks. One more par-ticipant was excluded for data analysis pertaining to researchquestions 2 and 3 because she did not complete a post-survey.As a result, 23 pre-service teachers (22 females and 1 male) com-pleted all tasks and surveys in this study. The participants wereCaucasian, and their age ranged from 19 to 22 (M = 20.43, SD = .73).

For interviews, volunteers were recruited when participantsfilled in a consent form. The volunteers (n = 15) were categorizedinto two groups based on epistemological belief survey results,and then three interviewees were randomly sampled from eachgroup. There were three interviewees (M1, M2, and M3) with moreadvanced epistemological beliefs and three interviewees (L1, L2,and L3) with less advanced epistemological beliefs. Both groupsof interviewees believed that mathematical knowledge was closelyrelated to other subjects and everyday lives (i.e. advanced beliefabout the structure of mathematical knowledge). However, L1,L2, and L3 believed that mathematical knowledge, which usuallycame from an external authority, was certain and fixed. By con-trast, M2 and M3 had more advanced beliefs about both stabilityand source of mathematical knowledge. Although M1 believed thatmathematics principles were rarely changeable, she believed thatindividuals actively constructed their own mathematical knowl-edge. All interviewees were female pre-service teachers.

6.2. Procedure

There was a training session (60 min) in which a researcherdemonstrated the use of wikis and explained high-quality reflec-tion and deep-reasoning questions. After the training session, par-ticipants carried out video-based reflection activities in wikis forsix weeks. Before and after the video-based reflection activities,participants took a pre-survey and a post-survey respectively viathe Internet. The surveys examined domain-specific epistemologi-cal beliefs and MBT. In addition, interviews pertaining to researchquestions were conducted with six participants before and afterthe video-based reflection activities.

The video-based reflection was carried out as an assignment outof the classroom. The activity involved reflective writing and ques-tioning. First, pre-service teachers watched a video of whole num-ber operations and wrote reflection on the most important event inthe video. A prompt was provided to help pre-service teachers towrite their own ideas rather than to summarize the event ob-served. Next, pre-service teachers posed at least one questionbased on their reflection on the video. Questioning has been

considered as a key metacognitive strategy to monitor an under-standing of new information and to process its meanings deeply(Graesser & Olde, 2003; King, 1991). Pre-service teachers answeredtheir own or other group members’ questions two days after askinga question in wikis. Pre-service teachers were requested to think oftheir questions for two days rather than answer them immediatelyin order to prevent posing a simple question to which they alreadyhad an answer. The reflective writing and questioning activitieswere carried out individually for three weeks and collaborativelyfor three weeks in order to help pre-service teachers to reflect onlearning and teaching activities independently as well as collabora-tively with others. In the individual reflection session, pre-serviceteachers reflected on videos without the help of others and soughtfor answers to their own questions. In the collaborative reflectionsession, pre-service teachers shared their reflective writing andquestions with 3 or 4 group members and answered the questionsof other group members in wikis. In both sessions, all wikis for vi-deo-based reflection were shared with other participants in theInternet.

6.3. Learning environment and materials

All video-based reflection activities were carried out in wikis. Inthis study, the wiki site (http://www.pbworks.com) included theinstruction of reflection activities and guidelines about high-quality reflective writing and questioning. As shown in Fig. 1, therewere reflection wikis in which pre-service teachers wrote and pub-lished their reflective writings, questions, and answers. To preventtechnical issues, researchers created basic reflection wikis includ-ing instructions and links of guidelines about reflective writingand questioning before participants carried out video-based reflec-tion activities. The titles of reflection wikis included a participant’s(or a group’s) name and a starting date of the reflection activity inorder to help pre-service teachers to find their reflection wikis eas-ily. After moving to their reflection wikis by clicking on hyperlinksin a home page (or a side bar), participants clicked on the Edit but-ton at the top of a wiki in order to write their reflection and ques-tions about a video clip. Participants published their writing onlineby clicking on the Save button at the bottom of a wiki, and it waspossible to modify their reflection wikis whenever they want byclicking on the Edit button again. The wiki site showed recentactivities of users, so participants were able to monitor what washappening in the wiki site. They were also able to visit others’reflection wikis quickly and easily by clicking on the links in theNavigator, Side Bar, and Recent Activity menus. In addition, thePage History function allowed participants to track the changesof a wiki and return back to the previous version of the wiki. Thewiki site was helpful particularly for collaborative reflection activ-ities in which participants needed to coordinate their group perfor-mance and respond to the questions of other group members.

For reflection activities, videos were carefully selected fromthree sources: IMAP Select Videos of Children’s Reasoning CD(Philipp, Schappelle, & Cabral, 2002), Children’s Mathematics:Cognitively Guided Instruction (Carpenter, Fennema, Franke, Levi,& Empson, 1999) and Teaching Mathematics: A Video Library, K-4(WGBH Boston, 1997). The researchers in this study collaborativelyselected videos to support the change of MBT and grouped theminto three topics: classroom lessons, student errors, and studentproblem solving strategies. These videos were closely related topre-service teachers’ naive beliefs about mathematical knowledge,students, and pedagogy in elementary school mathematics class.For instance, a video clip showed that a child, who correctly solveda multiple digit subtraction problem using the standard algorithm,did not conceptually understand meanings of the hundreds, tens,and ones digits. The selected videos were reviewed by the courseinstructor and an associate professor in mathematics education.

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Fig. 1. Wiki for video-based reflection activities.

44 Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53

They rated the quality of videos and provided comments in termsof whether they would be helpful for the belief change of pre-service teachers. Based on their comments, videos were finallyselected and edited into two video clips for each of three topics.The video clips were all about whole number operations.

Two videos of classroom lessons (8–9 min) showed student-centered lessons in which children explored their own problemsolving strategies or created their mathematics problems in smallgroups. Two videos of student errors (8–9 min) showed interviewswith two children who made errors in mathematical problem solv-ing due to the lack of their conceptual understanding about wholenumber operations. Lastly, two videos of student problem solvingstrategies (4–5 min) showed interviews with five children whosolved multi-digit addition and subtraction problems in novelways (e.g., direct modeling, counting, and derived facts) that weredifferent from typical problem solving strategies in a mathematicstextbook. These videos were selected and edited in order to helppre-service teachers to identify and reflect on an event conflictingwith their existing beliefs.

6.4. Data collection and analysis

Pre- and post-surveys included a domain-specific epistemolog-ical belief survey (Buehl & Alexander, 2005) and the IMAP (Inte-grating Mathematics and Pedagogy) web-based belief survey(Philipp et al., 2007). The domain-specific epistemological beliefsurvey included 12 items about beliefs of the structure, stability,and source of mathematical knowledge with a 10-point Likert scalefrom 0 (strongly disagree) to 9 (strongly agree). Through confirma-tory factor analyses, Buehl (2003) showed three distinct factors inepistemological beliefs of mathematics, which were also differentfrom three epistemological belief factors in the domain of history.

Responses to eight survey items (e.g., ‘‘truth is unchanging inmathematics’’) were reverse coded so that participants with moreadvanced epistemological beliefs got higher points than the others.The reliability coefficients (Cronbach’s alpha) were .72 for thestructure of mathematical knowledge, .65 for the stability of math-ematical knowledge, and .72 for the source of mathematicalknowledge.

Philipp et al. (2007) developed the IMAP belief survey based onthe assumption that beliefs are context specific and must be in-ferred from the dispositions to act in specific situations. In the do-mains of whole number operations and fractions, pre-serviceteachers were asked to interpret specific learning and teaching sce-narios and to make a decision within the situation. The responsesof pre-service teachers were assessed with rubrics of MBT. Fromthe IMAP survey, 12 questions about whole number operationswere selected in regards to beliefs of mathematical knowledge(BMK), beliefs of mathematics and students (BMS), and beliefs ofmathematics and teaching (BMT). As shown in Table 2, six beliefs(i.e., BMK1, BMK2, BMS1, BMS2, BMS3, and BMT1) were examinedin the situations of teaching whole number operations to elemen-tary students. Rubrics developed by the IMAP research team (2003)were used to rate belief levels from 0 (no evidence for a belief) to 3(strong evidence for a belief). Two raters independently evaluatedresponses to survey questions, and disagreements between thetwo raters were all resolved through discussions. The inter-raterreliabilities (Cohen’s kappa) ranged from .74 to .9.

Data of reflective writing and questioning were collected fromthe wiki site after the video-based reflection activities were com-pleted. The messages were segmented into idea units includingone or more phrases that are all related to a single idea. Tworesearchers analyzed the data with coding schemes that weremodified from previous studies (Graesser & Person, 1994;

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Table 2Mathematical beliefs for teaching survey (modified from Philipp et al., 2007).

Categories Beliefs

Belief of Mathematical Knowledge (BMK) � Mathematics is a web of interrelated concepts and procedures (BMK1)� One’s knowledge of how to apply mathematical procedures does not necessarily go with understanding of theunderlying concepts (BMK2)

Belief of Mathematics and Student (BMS) � If students learn mathematical concepts before they learn procedures, they are more likely to understand theprocedures when they learn them (BMS1)� Children can solve problems in novel ways before being taught how to solve such problems (BMS2)� The ways children think about mathematics are generally different from the ways adults would expect them to thinkabout mathematics (BMS3)

Belief of Mathematics and Teaching (BMT) � During interactions related to the learning of mathematics, the teacher should allow the children to do as much ofthe thinking as possible (BMT1)

Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53 45

Nussbaum & Schraw, 2007; Sherin & van Es, 2009). As shown inTable 1, the quality of reflective writing was analyzed in terms oftopics, stances, and complexity. In addition, the quality of ques-tions was analyzed regarding functions and topics (see AppendixA). In the dimension of functions, questions were categorized intocomprehension, deep-reasoning, and judgmental questions, andthe deep-reasoning questions included subcategories of reasons,consequences, and methods (Graesser & Person, 1994). The topiccategories of questions were consistent with those of reflectivewriting, including mathematics, student mathematical thinking,mathematical pedagogy, and general pedagogy. The quality of an-swers was rated from 0 to 4 points (see Appendix B for the rubric).A highest score was given when an answer was supported by well-elaborated examples and reasons and considered multiple view-points on one issue (Nussbaum & Schraw, 2007). Inter-rater reli-abilities (Cohen’s kappa) ranged from .73 to .94 in the contentanalysis.

Table 3 shows the summary of quantitative data analyses alongwith research questions. For statistical analyses, this study usedmean values of epistemological belief survey items for the threefactors (i.e., structure, stability, and source). MBT included six be-liefs measured with the IMAP survey (see Table 2), and the levelsof six beliefs were used for statistical analyses. The changes ofsix MBT were calculated by subtracting belief levels of the pre-survey from those of the post-survey. In addition, video-basedreflection activities included reflective writing (ten categories)and questioning activities (nine question categories and answerquality). Across six weeks, mean frequencies of reflective writingand question categories were calculated for statistical analysesalong with mean values of answer quality.

Multiple regression analyses were carried out to examine theinfluence of epistemological beliefs about mathematics on video-based reflection activities including reflective writing andquestioning activities. In addition, paired t-tests were used for

Table 3Quantitative data analysis.

Research question

1. Do epistemological beliefs in mathematics influence video-based reflection activiti

2. Do mathematical beliefs for teaching change through video-based reflection activi

3. What kinds of video-based reflection activities in wikis are closely related to the cbeliefs for teaching?

examining the changes of MBT from the pre-survey to the post-survey. For the last research question, partial correlation analyseswere conducted to examine the relationships between video-basedreflection activities (i.e., reflective writing and questioning activi-ties) and the change of MBT after controlling for initial MBT inthe pre-survey. It was possible that initial MBT were correlatedto both video-based reflection activities and the change of MBT.The assumptions of quantitative data analyses were checkedthrough examination of scatterplots, histograms, partial regressionplots, residual plots, and VIF values.

Pre- and post-interviews were carried out individually for 40–50 min in regards to MBT and perceptions on video-based reflec-tion. This study applied embedded design in which interview datawere collected to foster quantitative findings and provide addi-tional information (Creswell, 2012). An interviewer asked ques-tions about teaching and learning whole number operations inelementary school. To facilitate interviews in specific contexts,the interviewer showed mathematics problems, student errors(e.g., 61–13 = 52), and a classroom lesson video. The video, whichwas not used for video-based reflection activities, showed a tea-cher-directed instruction about whole number operations. In thevideo, a teacher explained the steps of mathematical problem solv-ing along with worked examples in an elementary school class-room, while children were passively engaged in the lesson. Thevideo showed real classroom practices near the university in whichparticipants were enrolled. After watching the video (8–9 min),participants were asked to describe what they noticed in the videoand what they thought of the event noticed. Follow-up questionswere asked to help participants to elaborate their thoughts. Inaddition, the interviewer asked questions about the perceptionsof video-based reflection in wikis, helpfulness of the activity forMBT, and suggestions to improve the activity.

Two researchers analyzed interview transcripts to createthemes that supplemented quantitative findings about research

n Variables Data analysis

es in wikis? 24 Epistemological beliefs Multiple regressionReflective writingQuestioning activities

ties in wikis? 23 Pre-MBT Paired t-testPost-MBT

hange of mathematical 23 Reflective writing Partial correlation

Questioning activitiesChange of MBT(Control: Pre-MBT)

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46 Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53

questions. According to the steps suggested by Creswell (2012), theresearchers initially read and divided the transcripts into segmentsof ideas. They coded the interview segments with a word or phraseindicating what the segments meant, particularly focusing onresearch questions in this study. After making a list of codes, theresearchers grouped similar codes and excluded redundantones. Next, similar codes were aggregated into a few themes thatwere closely related to the research questions and frequentlystated by interviewees. The themes were refined through constantcomparison with codes and raw data. Interview findings describedrelationships between beliefs and video-based reflection with spe-cific examples and provided additional information about beliefchanges, of which some were not found in statistical analyses.

7. Findings

7.1. Influence of epistemological beliefs for video-based reflection inwikis

Participants tended to have advanced beliefs about the knowl-edge structure (M = 7.34, SD = 1.33) while they had moderate be-liefs about the stability (M = 5.2, SD = 1.8) and source (M = 4.2,SD = 1.46) of knowledge. There was no significant relationshipamong these epistemological beliefs (ps > .05). Reflective writingsin average included 3.79 idea units, of which 67% were simply sta-ted without any explanation and justification (M = 2.52, SD = .66).Participants tended to reflect on student mathematical thinking(M = 2.18, SD = .76) and mathematical pedagogy (M = 1.19,SD = .4) by explaining (M = 1.52, SD = .61), describing (M = 1.03,SD = .46), and evaluating (M = .96, SD = .34) what they observedin a video clip. As shown in Table 4, a few reflection topics wereclosely related to reflection stances and complexities. Particularly,student mathematical thinking was significantly related to thereflection stances of describing, r = .55, p = .005, and explaining,r = .66, p < .001. This topic was also positively related to both sim-ple, r = .54, p = .007, and elaborated, r = .57, p = .004, reflective writ-ings. Simple reflection was positively related to describing an eventin a video clip, r = .68, p < .001, whereas elaborated reflection waspositively related to explaining an event, r = .63, p = .001. In addi-tion, the topic of mathematics was significantly related to con-fronting, r = .46, p = .024, which was also positively related toevaluating, r = .55, p = .005.

For questioning activities, participants in average asked 1.23questions (SD = .26) and generated .98 answers (SD = .18) everyweek. Participants were likely to ask questions about mathemati-cal pedagogy (M = .84, SD = .35) rather than other topics. When itcame to the function of questions, participants tended to ask ques-tions about a method to achieve a goal or solve a problem (M = .42,SD = .29). Table 5 shows correlations between questioning

Table 4Correlations between reflective writing categories.

Reflection M(SD) 1 2 3

1. Mathematics .18(.22) � �.03 .062. Student mathematical thinking 2.18(.76) � �.183. Mathematical pedagogy 1.19(.4) �4. General pedagogy .23(.24)5. Describing 1.03(.46)6. Explaining 1.52(.61)7. Evaluating .96(.34)8. Confronting .28(.19)9. Simple 2.52(.66)10. Elaborated 1.27(.57)

* p < .05.** p < .01.

categories. Participants who asked more questions about studentmathematical thinking were less likely to ask questions aboutmathematical pedagogy, r = �.67, p = .001. Questions of reasonswere positively related to questions about mathematics, r = .44,p = .038, and student mathematical thinking, r = .6, p = .003. Inaddition, questions of methods were negatively related to studentmathematical thinking, r = �.5, p = .016, but positively related tomathematical pedagogy, r = .5, p = .014. Lastly, the quality of an-swers was in average 2.24 (SD = .61), and it was not significantlycorrelated to any question category.

Multiple regression analyses were carried out to examine theinfluence of epistemological beliefs for reflective writing and ques-tioning activities. Epistemological beliefs significantly influencedreflection on student mathematical thinking, F(3,20) = 4.2,p = .019, R2 = .39, and elaborated reflection, F(3,20) = 4.9, p = .01,R2 = .42. As shown in Table 6, participants with more advanced be-liefs about the source of knowledge (i.e., learners constructing theirown knowledge) reflected more on student mathematical thinking,b = .55, t = 3.14, p = .005, and generated more elaborated reflection,b = .6, t = 3.55, p = .002. In the questioning activities, epistemologi-cal beliefs in mathematics significantly influenced the quality ofanswers, F(3,20) = 4.45, p = .015, R2 = .4, although there was no sig-nificant effect of epistemological beliefs for question categories(p > .05). Participants with a more advanced belief about the struc-ture of mathematical knowledge (i.e., a series of interrelatedknowledge) generated higher quality answers to questions,b = .52, t = 2.97, p = .008.

From the interviews with six participants, this study also iden-tified the connection between epistemological beliefs and video-based reflection activities. During the interviews, participantsviewed a video presenting teacher-directed instruction. Threeinterviewees with more advanced epistemological beliefs paidattention mainly to student behaviors when describing what theynoticed in the video. For instance, M3 described what she noticedin the video clip as follows:

I think also maybe students are more willing to help out theirpeers rather than their teacher. A lot of times students are afraidof their teacher. I don’t know what the case was in this, but Ithink if the students had gone up and shown their work onthe smart board, that could have been additional help.

This interviewee paid much attention to student behaviors andtheir mathematical thinking, although the video of teacher-directed instruction did not focus on students. She also noticedan event in which two students left the classroom, althoughother interviewees did not notice the event. By contrast, threeparticipants with less advanced epistemological beliefs paid much

4 5 6 7 8 9 10

�.05 �.17 .19 .25 .46* .19 .15.07 .55* .66** .02 .11 .54** .57**

�.22 .14 .01 .37 .19 .28 .07� �.02 .27 .05 .15 .2 .13

� .11 �.2 �.2 .68** �.06� �.2 .03 .37 .63**

� .55** .12 .27� .19 .32

� �.09�

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Table 5Correlation between questioning categories.

Question M(SD) 1 2 3 4 5 6 7 8 9

1. Mathematics .04(.09) � .07 �.1 �.14 .11 .44* �.07 �.06 �.22. Student mathematical thinking .18(.2) � �.67** .01 .18 .6** .26 �.5* �.323. Mathematical pedagogy .84(.35) � �.22 .05 �.41� �.01 .5* .4�

4. General pedagogy .16(.17) � �.11 .26 .07 .29 �.135. Comprehension .27(.18) � �.01 .15 �.19 �.41�

6. Reason .18(.21) � �.17 �.31 �.197. Consequence .1(.12) � �.16 �.068. Method .42(.29) � �.249. Judgment .26(.21) �

* p < .05.** p < .01.� p < .1.

Table 6Standard coefficients of epistemological beliefs in mathematics on the mean frequencies of reflective writing categories.

Reflection categories Epistemological beliefs in mathematics Model significance

Structure Stability Source

TopicMathematics .11 �.15 .03 F(3,20) = .2, p = .895Student mathematical thinking �.15 �.25 .55** F(3,20) = 4.2, p = .019Mathematical pedagogy .28 �.01 �.28 F(3,20) = 1.26, p = .314General pedagogy .15 �.22 .15 F(3,20) = .58, p = .637

StanceDescribing �.01 �.31 .15 F(3,20) = .87, p = .472Explaining .05 �.14 .46 F(3,20) = 1.92, p = .159Evaluating �.04 �.11 �.14 F(3,20) = .23, p = .873Confronting .29 �.13 .2 F(3,20) = .94, p = .441

ComplexitySimple �.05 �.25 �.01 F(3,20) = .48, p = .701Elaborated .2 �.23 .6** F(3,20) = 4.9, p = .01

** p < .01.

Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53 47

attention to teaching practices in the video. They rarely describedstudents’ classroom activities and mathematical thinking. For in-stance, L1 described in details what a teacher did in the video:

The teacher picked up a different example. Like she brought inthe example of money. Like if I have 75 cents how much moredo I need to equal 100? The students were able to subtractthe number 75 from 100 and get 25 cents. She kind of relatedit back to the formulas that one of the students answered, andshe was like to say, ‘‘So, what do we need to do with this prob-lem to get it to equal 100?’’

This finding was consistent with the result in multiple regres-sion analyses. That is, epistemological beliefs played an importantrole in noticing student mathematical thinking in video. In addi-tion, epistemological beliefs made differences in interpreting tea-cher-directed instruction in a video. The three participants withmore advanced epistemological beliefs gave negative commentsto the teaching practice, such as ‘‘it [instruction] puts people tosleep it’s not very engaging,’’ ‘‘I don’t think they [students] wereable to do much with it,’’ ‘‘some of those students seemed prettybored,’’ and ‘‘not all of the kids were focused.’’ In addition, theysuggested that the lesson should be more student-centered; theteacher should engage students in class activities; the teachershould relate mathematics problems to real world contexts; andstudents need to explain answers to each other. By contrast, thethree participants with less advanced epistemological beliefs pos-itively perceived the teaching practice: ‘‘she did an excellent wayof teaching,’’ ‘‘I don’t think she really had any weaknesses,’’ ‘‘Ididn’t really see anything wrong,’’ and ‘‘there weren’t any weak-nesses that really stood out.’’ Thus, epistemological beliefs wereinfluential in determining the content of video-based reflection.

7.2. Change of mathematical beliefs for teaching

Paired t-tests were carried out to examine the changes of math-ematical beliefs for teaching. As shown in Table 7, significantchanges in mathematical beliefs for teaching were found in regardsto BMK1, t(22) = 2.21, p = .038, BMS1, t(22) = 4.41, p < .001, andBMS2, t(22) = 2.26, p = .034. The video-based reflection in wikishelped participants to develop the beliefs that mathematics is aweb of interrelated concepts and procedures (BMK1); if studentslearn mathematical concepts before they learn procedures, theyare more likely to understand the procedures when they learnthem (BMS1); and children can solve problems in novel ways be-fore being taught how to solve such problems (BMS2). There wereno other significant changes in MBT (ps > .05).

The change of MBT was also found in the interviews with the sixparticipants. Consistently with the t-test results, participants im-proved their beliefs about students’ ability to solve mathematicsproblems in novel ways. For example, before the video-basedreflection activities, L3 thought that first graders could not learnto solve two-digit subtraction problems:

They [first graders] are learning subtraction with one digitmaybe up to like 20 minus something. They would have thegeneral idea of how to do it, but maybe not be able to imple-ment what they are thinking. I don’t think first graders everlearn how to borrow.

She believed that children could not solve a multiple digit sub-traction problem because they did not learn standard algorithmsyet. After the reflection activities, by contrast, she believed thatfirst graders had competencies to explore new methods for solving

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Table 7Means (standard deviations) of mathematical beliefs for teaching in the pre-survey and post-survey.

Mathematical beliefs for teaching Pre-survey Post-survey Paired t-test

Belief of Mathematical Knowledge 1 (BMK1) .87 (1.1) 1.3 (.97) t(22) = 2.21, p = .038Belief of Mathematical Knowledge 2 (BMK2) .57 (.59) .91 (1.04) t(22) = 1.4, p = .175Belief of Mathematics and Student 1 (BMS1) .91 (1.16) 1.91 (1.04) t(22) = 4.41, p < .001Belief of Mathematics and Student 2 (BMS2) .96 (1.19) 1.52 (.9) t(22) = 2.26, p = .034Belief of Mathematics and Student 3 (BMS3) 1.04 (.93) 1.22 (.9) t(22) = .89, p = .383Belief of Mathematics and Teaching 1 (BMT1) 1.52 (.79) 1.61 (.94) t(22) = .4, p = .692

48 Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53

mathematics problems before being taught by a teacher. The inter-viewee also suggested that students should try to solve two-digitproblems by themselves.

Although the change of BMT1 was not significant in quantita-tive results, this study identified the change of beliefs about math-ematical pedagogy from four of six participants (L1, L2, L3, andM2). Before the reflection activities, they believed that teachersshould demonstrate mathematical problem solving proceduresclearly to students. However, after the reflection activities, they be-lieved that teachers should provide students with more opportuni-ties to think on their own. The interviewees also defined the role ofteachers as facilitators. For instance, L1 initially believed thatteachers should clearly demonstrate step-by-step problem solvingprocedures, supporting teacher-directed instruction. After thereflection activities, however, she showed a strong belief aboutthe importance of student participation: ‘‘I think it is importantto allow students to catch up. Maybe make up their own discover-ies of the problem rather than just listening to the teacher thewhole time.’’ These findings support the prediction that video-based reflection in wikis would be helpful for the change of MBT.

7.3. Relationship between video-based reflection and belief change

Partial correlation analyses were carried out to explore the rela-tionships between reflective writings and the changes of MBT aftercontrolling for initial MBT in the pre-survey. As shown in Table 8,all control variables were negatively correlated to the change ofMBT variables. That is, participants with lower MBT were morelikely to improve their MBT through video-based reflection in wi-kis. After controlling for initial MBT, reflection about mathematicswas positively related to the changes of BMK1, r = .5, p = .019, andBMS1, r = .45, p = .037. Reflection on mathematical pedagogy waspositively related to the change of BMT1, r = .45, p = .037, whilethe belief change was negatively related to reflection on generalpedagogy, r = �.48, p = .024. In addition, elaborated reflection waspositively related to the change of BMS1, r = .46, p = .03. Otherreflective writing variables were not significantly correlated tothe change of MBT (ps > .05).

The study also examined the relationships between questioningactivities and MBT changes after controlling for initial MBT (seeTable 9). Participants who asked more questions about student

Table 8Partial correlation between reflective writing and MBT changes.

MBT change M(SD) Reflective writing

Mathematics Mathematical pedago

BMK1 change .43(.95) .5* .02BMK2 change .35(1.19) �.04 �.3BMS1 change 1(1.09) .45* �.08BMS2 change .57(1.2) .31 .2BMS3 change .17(.94) .24 �.2BMT1 change .09(1.04) �.34 .45*

* p < .05.

mathematical thinking were less likely to change BMT1, r = �.44,p = .041, but more likely to change BMK2, r = .42, p = .053. In con-trast, participants who asked more questions about mathematicalpedagogy were more likely to change BMT1, r = .41, p = .06,although the correlation was marginally significant. In addition,the question of general pedagogy was positively associated withthe change of BMS2, r = .49, p = .022. In regard to the functiondimension, consequence questions were positively related to thechange of BMS1, r = .53, p = .01, and marginally positively relatedto the change of BMK1, r = .42, p = .053. In addition, this studyfound negative correlations between method questions andBMK2 changes, r = �.44, p = .041, and between judgment questionsand BMK1 changes, r = �.45, p = .035. There were no other questioncategories significantly correlated to the change of MBT. The qual-ity of answers was not significantly related to the change of MBT(ps > .05).

Consistently with the quantitative results, all interviewees per-ceived that reflection on mathematical pedagogy was beneficial fortheir belief change. For example, M2 changed her belief about astudent-centered learning strategy: ‘‘I think, in the beginning, atfirst, I didn’t really know if the idea of having students solve a prob-lem before they were taught was a good idea, but now I think it is.’’In addition, L1 perceived that she gained new knowledge of math-ematical pedagogy from a video: ‘‘I think it [video] did an excellentway of providing future teacher strategies that can be used.’’ Bypaying attention to student-centered mathematical pedagogy, par-ticipants were able to gain new knowledge and change their exist-ing beliefs.

Although reflective writing on student mathematical thinkingwas not significantly related to the change of MBT in quantitativeresults, five interviewees (L2, L3, M1, M2, and M3) perceived thatreflection on student mathematical thinking was helpful for theirMBT. The interviewees mentioned that videos about student math-ematical thinking helped them to realize that students’ thinking isdifferent from the expectation of adults. For example, M1 said, ‘‘Itwas interesting to see that students could . . . like I never would’vethought of it that way.’’ The expectation failure on student mathe-matical thinking might motivate participants to reflect on the vi-deo deeply: ‘‘it was interesting to see all the different strategiesstudents were coming up with. There were things I had never seenbefore.’’

Control variable

gy General pedagogy Elaborated (Initial MBT)

�.38 .05 Pre-BMK1 (r = �.56��)�.17 �.06 Pre-BMK2 (r = �.49*)�.13 .46* Pre-BMS1 (r = �.58��)�.22 .26 Pre-BMS2 (r = �.72��)

.15 �.1 Pre-BMS3 (r = �.53��)�.48* .08 Pre-BMT1 (r = �.5*)

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Table 9Partial correlation between questions and MBT changes.

MBT change Question Control variable

Student mathematical thinking Mathematical pedagogy General pedagogy Consequence Method Judgment (Initial MBT)

BMK1 change .32 �.06 .24 .42� .29 �.45* Pre-BMK1 (r = �.56��)BMK2 change .42� �.31 .09 .33 �.44* .05 Pre-BMK2 (r = �.49*)BMS1 change .21 .09 �.08 .53* �.04 .11 Pre-BMS1 (r = �.58��)BMS2 change .11 .06 .49* .24 .3 �.35 Pre-BMS2 (r = �.72��)BMS3 change .11 �.14 .28 .01 .18 �.26 Pre-BMS3 (r = �.53��)BMT1 change �.44* .41� .08 �.06 .33 .06 Pre-BMT1 (r = �.5*)

* p < .05.� p < .1.

Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53 49

8. Discussion

The current study aimed to explore reciprocal relationships be-tween beliefs of pre-service teachers and video-based reflectionactivities in wikis. To serve the purpose, this study investigatedthe role of epistemological beliefs in video-based reflection activi-ties including reflective writing and questioning. The current studypartially supported the hypothesis that epistemological beliefsinfluence the quality of video-based reflection activities in wikis(Hypothesis 1). Participants with more advanced beliefs aboutthe source of knowledge were more likely to reflect on studentmathematical thinking after watching videos. Literature of video-based reflection (e.g., Sherin & van Es, 2009; Stockero, 2008) indi-cates that it is an important competency for teachers to notice andreflect on student mathematical thinking in video. Kersting, Givvin,Thompson, Santagata, and Stigler (2012) found that teachers’ anal-ysis of student mathematical thinking from classroom videos wasclosely related to their teaching practices. The current study showsthat the important competency of noticing and analyzing studentmathematical thinking is closely related to pre-service teachers’beliefs about the source of knowledge.

Consistently, interviews revealed that participants with moreadvanced epistemological beliefs mainly noticed student-relevantevents and had negative attitudes toward teacher-directed instruc-tion in a video. By contrast, interviewees with less advanced epis-temological beliefs largely paid attention to a teacher’s behaviorsin the video and positively perceived the teacher-directed instruc-tion. These findings support the assertion that people selectivelypay attention to an event relevant to their beliefs and interpretthe event in a way to strengthen their existing beliefs (Cooneyet al., 1998; Grant et al., 1998; Pajares, 1992; Philipp, 2007).

In addition, the more pre-service teachers believed that knowl-edge is constructed by learners, the more they elaborated reflectivewriting with examples, reasons, and suggestions. This finding isconsistent with the study by Mewborn (1999) in which pre-serviceteachers’ locus of authority was closely related to reflective think-ing during field experiences. Pre-service teachers with the beliefthat knowledge is given by an external authority might not feelthe necessity of justifying their thoughts with evidence (Kuhn,1991; Weinstock & Cronin, 2003) during video-based reflectionactivities.

This study also showed that the belief about the structure ofknowledge significantly influenced the quality of answers in reflec-tive questioning activities. When pre-service teachers believed thatknowledge is a series of interrelated ideas, they were more likely tosupport their opinion with examples and reasons, consideringalternative viewpoints. Schommer et al. (1992) found that studentswith less advanced beliefs about the structure of knowledge wereless likely to understand the content of a mathematical text be-cause they tried to memorize isolated facts in the text rather thanintegrate contents for an in-depth understanding. In this study,pre-service teachers with less advanced beliefs about the

knowledge structure did not make sufficient efforts to integratetheir opinion with reasons, examples, and alternative viewpoints.

However, epistemological beliefs did not have any significanteffect when it came to question categories. This finding is differentfrom the assertion that epistemological beliefs influence metacog-nitive processes (Hofer, 2004; Mason et al., 2011), which in turninfluence questioning. Epistemic metacognition (i.e., knowingabout knowing) may play an important role in identifying the lackof knowledge and anomalous events for questioning. The influenceof epistemological beliefs for questioning might be limited in thecurrent study because participants posed only one question everysession, although they could pose more than one. Pre-serviceteachers might select one of the questions that they generatedwhile or after watching a video, so the number of questions mightnot be sufficient in examining the influence of epistemologicalbeliefs.

In the current study, video-based reflection in wikis was bene-ficial for the change of MBT (Hypothesis 2). Particularly, BMK1,BMS1, and BMS2 were significantly changed through the reflectionactivities. Although quantitative results did not reveal a significantchange in BMT1, four of six interviewees perceived the change oftheir belief about mathematical pedagogy. While the intervieweesinitially believed that a teacher should clearly demonstrate step-by-step problem solving procedures, they claimed that a teachershould allow students to explore mathematical problems by them-selves after video-based reflection activities.

Despite the difficulty in changing beliefs of pre-service teachers(Cooney et al., 1998), video-based reflection in wikis promotedchanging MBT in a short time period. Consistently, Philipp et al.(2007) found that observing and analyzing videos about children’smathematical problem solving processes were influential for thechange of MBT. In the current study, videos including unexpectedstudent behaviors and novel teaching practices might be helpfulfor the change of MBT because they challenged naive beliefs ofpre-service teachers in authentic contexts.

This study also found what kinds of reflection activities wereclosely related to the belief change. Pre-service teachers withlower MBT were more likely to improve their beliefs throughthe video-based reflection activities in wikis. As predicted, reflec-tive writing on mathematics was positively associated with thechanges of BMK1 and BMS1, and reflective writing on mathemat-ical pedagogy was positively related to the change of BMT1(Hypothesis 3-1). Questions about mathematical pedagogy werealso beneficial for the change of BMT1, although the relationwas marginally significant. In addition, elaborated reflective writ-ing was positively related to the change of BMS1, which was alsopositively related to deep-reasoning questions about conse-quences (Hypothesis 3-2). For the change of MBT, teacher educa-tors need to encourage pre-service teachers to pay more attentionto the topics of mathematics and mathematical pedagogy and tocarry out in-depth reflection by elaborating thoughts and askingdeep-reasoning questions.

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50 Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53

The hypothesis that reflection on student mathematical think-ing would be beneficial for the change of MBT was not well sup-ported in statistical analyses. There was no significant correlationbetween reflective writing on student mathematical thinking andthe change of MBT. Although questions about student mathemati-cal thinking were marginally positively related to the change ofBMK2, the questions were negatively correlated to the change ofBMT1. Nevertheless, five interviewees perceived that video clipshelped them to recognize and change their naive beliefs throughreflection on student mathematical thinking. Further research isnecessary to examine the role of reflection on student mathemat-ical thinking for improving MBT.

Reflection stances have been considered important in the liter-ature of video-based reflection and professional vision (Sherin &van Es, 2009; Stockero, 2008). However, this study did not findany significant correlations between reflection stances (describing,explaining, evaluating, and confronting) and the change of MBT.Although confronting (i.e., recognizing a cognitive conflict andquestioning his or her own assumption) could be closely relatedto the belief change, this relationship was not supported in the cur-rent study. It was possible that pre-service teachers ignored orinappropriately interpreted anomalous events contradicting withtheir beliefs (Grant et al., 1998). Chinn and Brewer (1993) argued,‘‘Anomalous data do not always lead to belief change. Students of-ten find ways to discredit anomalous data and protect their prein-structional beliefs against the data’’ (p. 3). In the current study, forinstance, a few pre-service teachers interpreted a novel problemsolving strategy developed by a student as a new strategy taughtby a teacher. Teacher educators need to plan and implement vi-deo-based reflection activities, considering how pre-service teach-ers interpret anomalous events in video with their existing beliefs.

Although the literature of interactive learning showed theimportant role of deep-reasoning questions for knowledge con-struction (Graesser & Person, 1994; King, 1991; Roscoe & Chi,2008), the questions were seldom related to the change of MBTin this study. Questions of consequences were positively relatedto the change of BMS1, but there was no significant correlation be-tween questions about reasons and the change of MBT. Moreover,questions about methods were negatively correlated to the changeof BMK2. While previous studies of deep-reasoning questions werecarried out in face-to-face settings, the current study was carriedout in the online learning environment, wikis. Because many pre-service teachers waited responses of other group members fortwo or more days after posing a question in a wiki, interactivelearning might not be effectively promoted through deep-reason-ing questions in the current study. This limitation might make ithard to find significant relationships between deep-reasoningquestions and the change of MBT.

The current study found reciprocal relationships betweenpre-service teachers’ beliefs and video-based reflection in wikis.For instance, beliefs about the source of mathematical knowledgesignificantly influenced elaborated reflection in wikis, which was inturn closely related to the change of BMS1. However, the findings ofthis research should be carefully applied to different contexts. Allparticipants in the current study were elementary school pre-serviceteachers, and there was only one male participant. If video-basedreflection activities are conducted for experienced teachers, theymay more frequently integrate events in a video with their experi-ence and classroom practice than participants in the current study.In addition, experienced teachers tend to have stronger beliefsabout mathematical learning and teaching than pre-serviceteachers. It may take more time and effort to change the MBT ofexperienced teachers through video-based reflection activities.Future research is recommended to examine the effectiveness ofvideo-based reflection activities in different contexts and explore

adaptive instructional strategies for changing MBT of differentindividuals.

In addition to the limitation in generalizing the findings to othercontexts, this study has a few limitations that should be consideredin the future research. First of all, the number of participants wasrelatively small, which might make it difficult to find statisticallysignificant relationships between beliefs and video-based reflec-tion activities. Future research is needed to test the hypothesesof this study with a larger sample size. In addition, the currentstudy found significant changes of MBT through video-basedreflection in wikis. However, this study did not examine whetherthe new beliefs would be sustained in a longer time period. Inthe future research, it is recommended to conduct delayed post-surveys and interviews because pre-service teachers may returnback to their naive beliefs (Cooney et al., 1998). Lastly, this explor-atory study did not have a control group, so extraneous variablesthat were not controlled in this study might influence the changeof MBT. It is necessary to compare video-based reflection in wikiswith other treatments in terms of reflection activities and thechange of MBT after controlling for extraneous variables like videotypes, individual differences, and the amount of study time.

The current study implies that teacher educators need toencourage pre-service teachers to conduct video-based reflectionfor the change of their naive beliefs about knowledge, students,and pedagogy. For effective video-based reflection, instructorsneed to help pre-service teachers to focus on topics closely re-lated to the change of beliefs (e.g., mathematics, mathematicalpedagogy). Before or after watching a video, for instance, instruc-tors can involve pre-service teachers in discussion about suchissues as how a mathematics problem can be solved and whatwould be the best way to teach a specific topic. In addition,instructional supports like prompts, examples, and feedbackshould be timely provided so that pre-service teachers deeplyreflect on meaningful events noticed in a video by explainingthem, elaborating thoughts, and asking deep-reasoning questions.Instructional supports for in-depth reflection may be more neces-sary for pre-service teachers with less advanced epistemologicalbeliefs than those with more advanced ones because the formerare less likely to elaborate their reflection with examples, reasons,and suggestions.

This study also indicates that online learning environments likewikis are beneficial for video-based reflection. In a classroom,reflection activities have several limitations due to a short lessonperiod and traditional classroom practices that lead to passivelearning. By contrast, online learning environments allow pre-service teachers to spend enough time to view a video repeatedly,reflect on an event noticed, and search for relevant information inthe Internet before sharing their thoughts and questions withothers. Online learning environments also provide some autonomyin a way to reflect on a video. Individuals can decide what videothey view, how many times they view it, what representation toolsthey use, when they publish their thoughts, how often theyinteract with peers, and so on. Previous studies found that theaffordances of online learning environments help students to jus-tify their thoughts, connect multiple ideas, and think critically(Guiller, Durndell, & Ross, 2008; Newman, Webb, & Cochrane,1995). Particularly, wikis enable pre-service teachers to easily cre-ate, modify, and share their reflection with others in a distance,which can enhance collaborative reflection and knowledge build-ing. However, online learning environments have some limitationslike delayed responses from peers and lack of social presence. Thus,teacher educators should carefully design and implement video-based reflection in online learning environments. More attentionshould be paid to improve the design of video-based reflectionfor pre-service teachers in a variety of contexts.

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Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53 51

Appendix A. Coding scheme for questions

Dimension Category Description Example

Topic Mathematics Mathematical concepts andproblem solving strategies

Is using manipulatives similar to counting on your fingers?

Studentmathematicalthinking

Students’ knowledge and problemsolving process

If students think they got the right answer at the first time, arethey less likely to change their answer even if the secondconclusion they came to also makes sense to them?

Mathematicalpedagogy

Mathematics tasks, tools, andteaching strategies

Had the first little girl been introduced to borrowing yet? Or wasthat the way they planned to introduce her to borrowing?

Generalpedagogy

General teaching strategies andclassroom management

How should teachers use their prompts to correct students’ waysof thinking?

Function Comprehension Asking to seek for a definition,example, feature, or meaning of anevent

Did the child know numbers have place value?

Deep-reasoning

Reason Asking about why an action iscarried out or what causally leadsto a result

Why did she insist that 53 was correct, even after she had seenthe correct answer represented in two other ways?

Consequence Asking about what would happenas a result of an action

What would happen if working in partners distracts childrenfrom learning rather than helps them?

Method Asking about how to achieve a goalor how to solve a problem

What would I do if I had a student who was making the mistakesthat the first student did? How do I help the child?

Judgment Asking to judge the value of an idea Do you think it is necessary in all classes, no matter the lesson, tohave the students go through multiple methods for finding theanswer to see which one works best for them?

Appendix B. Quality of answers

Score Description Example

4 An answer is supported by well-elaborated examples/reasons, and multiple perspectives are considered.

I think that it depends on the group of 1st graders. Some students arefar more advanced at math than others and have much higher orderthinking than their peers. Typically, however, it is not appropriate tointroduce ‘‘stacking’’ to 1st graders based on the sole reason that theyare just starting to learn how to add numbers, what the numberplaces mean, and how to apply them in situations. A better strategywould be to teach them how to add larger numbers by the ‘‘places’’method. (i.e. 28 + 31. . . you would take out the 8 and 1 and add themtogether to get ‘‘9’’. . . you then would take out the 20 and 30remaining and get 50. . . You now have to add the 50 + 9. . . Theanswer is 59!)

3 An answer is supported by well-elaborated examples/reasons, but multiple perspectives are not considered

Children preconceived notions about the way math works, often getsin the way of what they find is correct. Children often only basemathematics on formulas as the only way to correctly solve theproblem, when in fact these should only be things to fall back on. Toknow a formula does not necessarily mean that the child knows theinformation well, it just means that they can memorize how to solvethe problem, but when the student used other methods to figure outthis problem she received the correct answer. As future teachers weneed to keep this information in mind when thinking about the waysin which we teach our students, and how it is important to first teachthe methods the children can understand ‘‘why’’ and then once theinformation is comprehended, then show them a formula

2 An answer is supported by examples/reasons that aremoderately elaborated and explained

I would be sure to sit down with the student and re-explain thecorrect way to solve the problem. The student might just be confusingcertain aspects of the problem. By re-explaining the problem and

(continued on next page)

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Appendix B (continued)

Score Description Example

giving new representations the student might be able to make newconnections and understand how to solve it

1 An answer is supported by no or low-qualityexamples/reasons

Allow the student to stop and think for a while, and be encouraging. Itis important to stay positive and help the student learn

0 No answer or an irrelevant answer is given I am still working to answer this question, but I am sure that there areways that I have not even yet realized

52 Y.H. Cho, Y. Huang / Computers in Human Behavior 35 (2014) 39–53

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