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Mathematics and Science Teacher Educators' Use of Representations of Practice: A Mixed Methods Study

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Title: Mathematics and Science Teacher Educators' Use of Representations of Practice: A Mixed Methods Study
Language: English
Authors: Austin, Christine K., Kosko, Karl W., Heisler, Jennifer L.
Source: School Science and Mathematics. Jan 2023 123(1):14-25.
Availability: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
Peer Reviewed: Y
Page Count: 12
Publication Date: 2023
Sponsoring Agency: National Science Foundation (NSF)
Contract Number: 1908159
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: Mathematics Teachers, Science Teachers, Teacher Educators, Multimedia Materials, Multimedia Instruction, Methods Courses, Familiarity, Video Technology
DOI: 10.1111/ssm.12563
ISSN: 0036-6803
1949-8594
Abstract: This study sought to explore math and science teacher educators' use of various media to represent practice within methods courses. There is little understanding of why certain media is used over other representations and the rationale for these choices. Specifically, the study focused on the prevalence and familiarity of teacher educators with comics and animations, standard videos, and 360 videos. This mixed methods study utilized a survey and interviews to ascertain math and science teacher educators' level of familiarity and perceived usefulness of representations of practice. Results indicate that standard video is by far the most used representation of practice in methods classes with three themes explaining this finding: access to representations of practice, dimensions of representation, and pertinacity of using representations. Familiarity with representations of practice relates to teacher educators' perceptions of access thereby indicating a need for teacher educators to have better access to representations. Implications of this study include supporting current literature about the relationship between the level of familiarity and perceived usefulness in media along with the potential need for a central platform that houses these representations of practice resources for teacher educators.
Abstractor: As Provided
Entry Date: 2023
Accession Number: EJ1369245
Database: ERIC
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  Value: <anid>AN0162400342;ssm01jan.23;2023Mar15.08:54;v2.2.500</anid> <title id="AN0162400342-1">Mathematics and science teacher educators' use of representations of practice: A mixed methods study </title> <p>This study sought to explore math and science teacher educators' use of various media to represent practice within methods courses. There is little understanding of why certain media is used over other representations and the rationale for these choices. Specifically, the study focused on the prevalence and familiarity of teacher educators with comics and animations, standard videos, and 360 videos. This mixed methods study utilized a survey and interviews to ascertain math and science teacher educators' level of familiarity and perceived usefulness of representations of practice. Results indicate that standard video is by far the most used representation of practice in methods classes with three themes explaining this finding: access to representations of practice, dimensions of representation, and pertinacity of using representations. Familiarity with representations of practice relates to teacher educators' perceptions of access thereby indicating a need for teacher educators to have better access to representations. Implications of this study include supporting current literature about the relationship between the level of familiarity and perceived usefulness in media along with the potential need for a central platform that houses these representations of practice resources for teacher educators.</p> <p>Keywords: math education; science education; teacher education; technology</p> <hd id="AN0162400342-2">INTRODUCTION</hd> <p>Representations of practice are a vital tool for professional growth within teacher education methods courses (Grossman et al., [<reflink idref="bib13" id="ref1">13</reflink>]). Videos (standard) are highly beneficial for educating future teachers (Gaudin & Chaliès, [<reflink idref="bib12" id="ref2">12</reflink>]; Grossman et al., [<reflink idref="bib13" id="ref3">13</reflink>]), can help foster learning of classroom practices (Grossman et al., [<reflink idref="bib13" id="ref4">13</reflink>]), and increase a preservice teacher's (PST's) level of "pedagogical understanding" (Christ et al., [<reflink idref="bib7" id="ref5">7</reflink>], p. 32). Standard videos are commonplace as they are incorporated into methods courses across varying content areas about three to six times within an academic semester (Arya et al., [<reflink idref="bib2" id="ref6">2</reflink>]; Christ et al., [<reflink idref="bib7" id="ref7">7</reflink>]). Standard videos are defined at the videos that record and can only be viewed in a particular direction oriented by the point of view in which it was filmed. However, representations of practice are not limited to standard videos (Grossman et al., [<reflink idref="bib13" id="ref8">13</reflink>]), other forms used by teacher educators include, but are not limited to, comics and animations (Herbst et al., [<reflink idref="bib18" id="ref9">18</reflink>]), 360 videos (Roche & Gal‐Petitfaux, [<reflink idref="bib26" id="ref10">26</reflink>]), written vignettes (Seguin & Ambrosio, [<reflink idref="bib27" id="ref11">27</reflink>]), and lesson plans (Ho, [<reflink idref="bib21" id="ref12">21</reflink>]). We acknowledge that there are multiple other forms of representations, however video (standard) has been the main avenue of discussion within teacher education research. For this research, we also include variations of such videos which we believe include animations and 360 videos.</p> <p>Despite research advocating for the inclusion of these additional mediums, there are few studies reporting how prevalently teacher educators use various representations of practice. There is little understanding of the degree to which purported affordances associated with various representations are utilized in mathematics and science methods courses. Beyond our own initial pilot studying the prevalence of standard video, 360 video, and animations (Austin & Kosko, [<reflink idref="bib3" id="ref13">3</reflink>]), we have been unable to identify another study exploring how frequently teacher educators use various media to represent practice, nor scholarship on the rationales for use or non‐use of such media. This pilot revealed that MTEs were familiar with standard videos but were only slightly aware of 360 videos and animations/comics (Austin & Kosko, [<reflink idref="bib3" id="ref14">3</reflink>]). Despite this, teacher educators viewed both mediums as useful. Although past research has shown that the use of representations encourages professional noticing (Barnhart & van Es, [<reflink idref="bib4" id="ref15">4</reflink>]) and reflection (Arya & Christ, [<reflink idref="bib1" id="ref16">1</reflink>]; Gaudin & Chaliès, [<reflink idref="bib12" id="ref17">12</reflink>]; Sherin et al., [<reflink idref="bib28" id="ref18">28</reflink>]), scholars have not explored why some mediums are not utilized. Since technology is rapidly advancing and continuing to be implemented in teacher education, it is vital to understand which type of videos (standard, 360, and animations/comics) are being used in mathematics and science method courses and potential hindrances that may deter their use. The purpose of this study is to better understand the relationship between teacher educators' familiarity and perceived usefulness of videos (standard, 360, and animations/comics) and how this corresponds to their reported use.</p> <hd id="AN0162400342-3">THEORETICAL FRAMEWORK</hd> <p></p> <hd id="AN0162400342-4">Dimensions of representations</hd> <p>The incorporation of videos into mathematics and science methods courses are essential tools to allow for PSTs to engage in topics that are being discussed (Barnhart & van Es, [<reflink idref="bib4" id="ref19">4</reflink>]), to observe varying classroom practices (Weston & Amador, [<reflink idref="bib32" id="ref20">32</reflink>]), and to explore differing teaching methods (Grossman et al., [<reflink idref="bib13" id="ref21">13</reflink>]). These various media are referred to as <emph>representations of practice</emph> which Grossman et al. ([<reflink idref="bib13" id="ref22">13</reflink>]) defined as "the different ways that practice is represented in professional education and these various representations make visible to novices" (p. 2058). In the present article, we focus on three forms of multi‐media that have served as representations of practice: standard videos, 360 videos, and comics and animations. Standard videos record in a particular direction oriented by the person setting up the camera. By contrast, 360 video records omnidirectionally such that the viewer, not videographer, chooses where in the recorded "sphere" they look (Kosko, Ferdig, & Roche, [<reflink idref="bib22" id="ref23">22</reflink>]). Animations and comics use cartoon‐based characters and environments to portray classroom‐based events in either a motion (animation) or still‐frame (comic) format (Herbst et al., [<reflink idref="bib18" id="ref24">18</reflink>]).</p> <p>Given apparent distinctions in format, it is unsurprising that different representations provide certain affordances than others. To categorize these differences, three <emph>dimensions of representations of practice</emph> were proposed by various scholars: Herbst et al. ([<reflink idref="bib18" id="ref25">18</reflink>]) proposed the first two dimensions (<emph>temporality</emph> and <emph>individuality</emph>) and Kosko, Ferdig, and Roche ([<reflink idref="bib22" id="ref26">22</reflink>]) introduced a third dimension (<emph>perceptual capacity</emph>). Temporality "alludes to the sense to which representation of teaching ... immerse the user in the timeline and cadence of actions" (Herbst et al., [<reflink idref="bib18" id="ref27">18</reflink>], p. 94). For example, videos have a higher degree of temporality than a written vignette given it better represents the temporal nature of events. Comparatively, written vignettes slow the timeline of events in a descriptive manor of the environment and students that video would visually show. The second dimension, <emph>Individuality</emph>, is the "uniqueness of settings and participants and hence a sense of the differences among settings and participants" (Herbst et al., [<reflink idref="bib19" id="ref28">19</reflink>], p. 82). Clark et al. ([<reflink idref="bib8" id="ref29">8</reflink>]) suggest that comic‐based representations can provide a higher level of individuality of visual elements due to the freedom of being able to create differences between students (size, gender, race etc.). Rather, certain demographic differences may be less readily available in recorded scenarios of actual classrooms, and the comics provide a means of representing elements within the individuality dimension not able to be recorded (Clark et al., [<reflink idref="bib8" id="ref30">8</reflink>]).</p> <p>Recently, Kosko, Ferdig, and Roche ([<reflink idref="bib22" id="ref31">22</reflink>]); Kosko, Ferdig, and Zolfaghari ([<reflink idref="bib23" id="ref32">23</reflink>]) proposed the third‐dimension <emph>perceptual capacity</emph>, which refers to a representation's ability to convey aspects perceivable through human experience. Rather, human experiences are embodied and include references to <emph>senses</emph> such as sight, sound, touch, and spatial awareness (Kosko, Ferdig, & Zolfaghari, [<reflink idref="bib23" id="ref33">23</reflink>]). Thus, a 360 video has a higher degree of perceptual capacity than a standard video because it can represent the spatial sense of being in a classroom, such as the ability to turn to the left or right when wanting to look at one set of students or another (Kosko, Ferdig, & Roche, [<reflink idref="bib22" id="ref34">22</reflink>]; Kosko, Ferdig, & Zolfaghari, [<reflink idref="bib23" id="ref35">23</reflink>]). Thus, perceptual capacity is distinct from the previously defined dimensions. Whereas temporality focuses on the cadence of events and individuality on the uniqueness of its features, perceptual capacity describes the medium's ability to relay temporality and individuality through a sensory experience.</p> <p>The dimensions for representations are useful in considering general benefits of each medium. Such differences suggest that one representation is not "better" than the other, but that each representation has affordances and constraints. 360 video has a heightened degree of perceptual capacity for spatial sense than standard videos, however the levels of temporality and individuality are similar. On the other hand, certain comics can express the uniqueness (i.e., individuality) among the students that aren't available in accessible videos (360 or standard).</p> <hd id="AN0162400342-5">Use of representation in teacher education</hd> <p>Videos (standard, 360, and animations/comics) have all been researched regarding their benefits in facilitating teacher education. While standard videos are the primary medium researched, there are still few studies exploring the implications of use in teacher education. A common finding across all mediums is that they can facilitate professional noticing in the classroom (Barnhart & van Es, [<reflink idref="bib4" id="ref36">4</reflink>]; Thompson et al., [<reflink idref="bib30" id="ref37">30</reflink>]). Videos can depict scenarios that may not be widely enacted in real‐life classrooms (Hatch & Grossman, [<reflink idref="bib17" id="ref38">17</reflink>]), thus allowing both the educator and the user to create and witness a magnitude of classroom scenarios. In comparison to standard videos, 360 videos allow the user to view the classroom environment omnidirectionality. This gives the user freedom to choose where in the classroom they want to attend their attention to when being immersed in a classroom scenario (Roche & Gal‐Petitfaux, [<reflink idref="bib26" id="ref39">26</reflink>]). This freedom gives PSTs the opportunity to have individualized viewing experiences and provides a chance for PSTs to fully engage in what is of importance to notice in the scenario (Roche & Gal‐Petitfaux, [<reflink idref="bib26" id="ref40">26</reflink>]). On the other hand, animations/comics give teacher educators the chance to create hypothetical scenarios that may not be easily captured or may not occur as often in the classroom (Herbst et al., [<reflink idref="bib18" id="ref41">18</reflink>]). These creations can help facilitate PSTs' professional noticing (Casey & Amidon, [<reflink idref="bib6" id="ref42">6</reflink>]).</p> <p>The three mediums all can be used as a way for PSTs to reflect on their own teaching or reflect on the teaching of their peers. PSTs' reflections of their own teaching from standard videos allow to improve on their pedagogy (Arya & Christ, [<reflink idref="bib1" id="ref43">1</reflink>]; Gaudin & Chaliès, [<reflink idref="bib12" id="ref44">12</reflink>]; Sherin et al., [<reflink idref="bib28" id="ref45">28</reflink>]). For standard video to be effective for teacher reflection it needs to be supported by both an experienced educator (mentor or teacher educator) and the PST (Cunningham & Benedetto, [<reflink idref="bib10" id="ref46">10</reflink>]). Hamel and Viau‐Guay ([<reflink idref="bib15" id="ref47">15</reflink>]) reviewed 89 articles related to the use of [standard] video used for teacher reflection. They found that videos do help PSTs improve their teaching methods, noticings, and allowed for them to change their teaching practices. Other research suggests similar benefits through teachers' reflection of 360 videos (Buchbinder et al., [<reflink idref="bib5" id="ref48">5</reflink>]; Weston & Amador, [<reflink idref="bib32" id="ref49">32</reflink>]) and comic‐based representations (Herbst & Milewski, [<reflink idref="bib20" id="ref50">20</reflink>]) of their own teaching.</p> <hd id="AN0162400342-6">Familiarity and usefulness</hd> <p>An overview of prior research suggests that there is limited literature specifically addressing a teacher educators' level of familiarity and perceived usefulness of different media for teacher education (i.e., standard video, 360 video, animations/comics). However, there is scholarship on factors contributing to teacher educators' use of technology in their courses. For example, Uzan ([<reflink idref="bib31" id="ref51">31</reflink>]) observed that MTEs see the value (i.e., usefulness) in incorporating technology, however, "their practices and course designs change based on their skills, background, and comfort level in using technology" (p. 2313). Specifically, the four MTEs participating revealed that they would be more inclined to integrate other technologies into their courses if they were comfortable with them (Uzan, [<reflink idref="bib31" id="ref52">31</reflink>]). This suggests that familiarity of a representation plays a role in whether a teacher educator will imbed them into courses.</p> <p>Research from Austin and Kosko ([<reflink idref="bib3" id="ref53">3</reflink>]) found that teacher educators lack familiarity with 360 video and animations/comics. In addition to familiarity (including technological proficiency), adopting novel technologies is associated with an educator's instructional policies, institutional support, and time (Christ et al., [<reflink idref="bib7" id="ref54">7</reflink>]). Thus, educators who see the potential of a medium may still be uncertain in how to use the technology, how to embed it into their lessons, or have the time to explore and find these new representations (Christ et al., [<reflink idref="bib7" id="ref55">7</reflink>]). Similarly, Lampropoulos et al. ([<reflink idref="bib24" id="ref56">24</reflink>]) reported that the use of 360 video in education is viewed positively, but teachers may not be familiar with this medium nor have "the necessary technical skills or equipment to develop educational material using it or incorporating it into their teaching activities" (p. 20). Lack of skills/proficiency may also be affected by the needed time to develop and learn how to use a new medium and the need for institutional support.</p> <p>Past research has shown the benefits of using a video representation of practice for teacher education. With these benefits and in conjunction with our piloted work and past research on the use of technology in teacher education, we sought to better understand the relationship between level of familiarity and perceived usefulness of three specific mediums. Prior scholarship either does not address such factors explicitly or focuses only on one type of media used for representing practice. Types of videos have evolved, thus it is important to study how these mediums are perceived and establish how familiar teacher educators are with these advancements. Therefore, the goal of this study is to understand a teacher educators' decisions of embedding standard videos, 360 videos, and animations/comics within their methods courses and how they correspond to the reported use. Thus, we asked the following research questions:</p> <p></p> <ulist> <item> Does familiarity influence a teacher educators' average number of use and their perception of usefulness for each representation?</item> <p></p> <item> What is the relationship between a teacher educators' familiarity of a representation and their reasonings behind which to use in their methods course?</item> </ulist> <hd id="AN0162400342-7">METHODOLOGY</hd> <p></p> <hd id="AN0162400342-8">Participants</hd> <p>Participants included 71 MTEs, 2 science teacher educators (STEs), and 6 mathematics and science educators across the United Stated. Participants were recruited with the intent of identifying how many of each representation they employ in their method courses and their level of familiarity. Participants were recruited via email and social media through various mathematics and science professional organizations including: Association of Mathematics Teacher Educators (AMTE); Service, Teaching and Research (STaR) program members; and Association for Science Teacher Education (ASTE). Participants were asked to complete a survey reporting their use and perceptions of three mediums representing practice: standard video, 360 video, and animations/comics. Overall, our sample of 79 teacher educators focusing on either mathematics (<emph>n</emph> = 71), science (<emph>n</emph> = 2), or both (<emph>n</emph> = 6). Participants identified primarily as female (<emph>n</emph> = 64), with an additional 20% of participants identifying as male (<emph>n</emph> = 16), with an average 10.3 years of experience (<emph>SD</emph> = 5.43). Nearly half our sample teach at a R2 Doctoral University (47.5%, <emph>n</emph> = 38), followed by an R1 Doctoral University (<emph>n</emph> = 18), a Masters' college or university (<emph>n</emph> = 17), and lastly teach at baccalaureate college (<emph>n</emph> = 7). Following completion of the survey, eight participants engaged in voluntary interviews with the three authors (MTEs = 6; STEs = 2). The list of interviewed participants can be found in Table 1.</p> <p>1 TABLE Breakdown of interview participants</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Participant</th><th align="left">Focus</th><th align="left">Experience</th><th align="left">Type of institution</th></tr></thead><tbody valign="top"><tr><td>Blythe</td><td>Science</td><td>29</td><td>Baccalaureate college</td></tr><tr><td>Candace</td><td>Science/Math</td><td>11</td><td>Baccalaureate college</td></tr><tr><td>Nicky</td><td>Mathematics</td><td>10</td><td>Doctoral university (R1)</td></tr><tr><td>Will</td><td>Mathematics</td><td>4</td><td>Doctoral university (R1)</td></tr><tr><td>Karen</td><td>Mathematics</td><td>10</td><td>Doctoral university (R2)</td></tr><tr><td>Ben</td><td>Mathematics</td><td>10</td><td>Master's college and universities</td></tr><tr><td>Ethan</td><td>Mathematics</td><td>12</td><td>Doctoral university (R2)</td></tr><tr><td>Beck</td><td>Mathematics</td><td>5</td><td>Doctoral university (R2)</td></tr></tbody></table> </ephtml> </p> <hd id="AN0162400342-9">Procedure and survey</hd> <p>The participants were given a brief survey via Qualtrics. The survey was anonymous unless they indicated that they would be willing to be participate in a follow‐up interview. The survey consisted of demographic questions and their years of experience. The measure gave the participants a brief synopsis of each video representation (i.e., standard, 360, and animations/comics) which included both a written and visual explanation. The participants were asked to identify their area of focus (mathematics and/or science pedagogy) where they taught their methods courses between Fall of 2018 and 2020. Within the survey, participants were asked to state how many, on average, of each representation that they use within their methods courses. Participants were asked to report their familiarity of each medium using a 5‐point Likert (0 = <emph>not at all familiar</emph> to 4 = <emph>extremely familiar</emph>). Lastly, participants were asked to rank different types of representations of each medium—representation of one's own teaching, representation of an interview with a student or a small group, and depiction of a whole class—on a scale from 1 to 9 in usefulness. Video types that were <emph>not</emph> ranked are assigned a 10 (i.e., not useful). The survey data gave rise to the nine participants that were selected to be interviews.</p> <hd id="AN0162400342-10">Analysis</hd> <p>This primary research design for this study is an explanatory mixed method (Creswell & Plano Clark, [<reflink idref="bib9" id="ref57">9</reflink>]). The purpose of this method is for the qualitative data to explain the quantitative results (Creswell & Plano Clark, [<reflink idref="bib9" id="ref58">9</reflink>]). An inclusion of interviews was added due to wanting to understand both a MTEs and STEs rationale of why they reported using a particular medium over another and to better understand their ranking. The first phase consisted of teacher educators participating in the brief survey instrument and the second phase consisted of interviews based on how they responded to the inventory and if they were willing to engage in discourse. The interviews were structured around how they responded on the instrument, for example, if a teacher educator reported NOT using a 360 video, they were asked a specific question as to why and if they reported using the medium, they were asked how they used 360 videos in their courses.</p> <hd id="AN0162400342-11">Quantitative</hd> <p>Descriptive statistics was utilized to determine the average number of uses and the mean level of familiarity for each representation. To measure the degree of association between familiarity and frequency of use, Spearman rank was our tool for analysis. Spearman Rho coefficient was chosen over Pearson due to this analysis being more appropriate for examining ordinal and continuous data, particularly with smaller sample sizes (Siegel & Castellan, [<reflink idref="bib29" id="ref59">29</reflink>]). Further, Spearman Rho considers, and requires, the variables to be ordinal in order for the objects to be ranked (Siegel & Castellan, [<reflink idref="bib29" id="ref60">29</reflink>]).</p> <hd id="AN0162400342-12">Qualitative</hd> <p>Eight (<emph>n</emph> = 8) semi‐structured interviews were conducted with the goal of better understanding participants' responses more thoroughly (Hatch, [<reflink idref="bib16" id="ref61">16</reflink>]). Interviews were conducted online, recorded, and then transcribed by the research team. Interview questions were based on participants' survey responses and included opportunities for elaboration. For example, one initial prompt began "In your survey responses, you said you used ___ number of standard videos in an average methods course. Can you tell me more about what that number means?" Other prompts focused on participants' impressions of the representation or resources needed. This protocol was applied for each medium to make the dimensions of representation visible and elucidate the different forms of practice in professional education. Transcribed interviews were analyzed using Systemic Functional Linguistics (SFL); a form of discourse analysis that examines how grammar conveys meaning (Halliday & Matthiessen, [<reflink idref="bib14" id="ref62">14</reflink>]). SFL was chosen as the form of discourse analysis because it provides a means to examine how language conveys meaning. Units of analysis were reference chains, which represent how particular referents are conveyed in text either through repetition or contextualization. We examined the patterns in how references to particular mediums (i.e., standard video) were conveyed and examined these for emergent themes. In examining reference chains and how they conveyed particular meanings, we also incorporated Martin and White's ([<reflink idref="bib25" id="ref63">25</reflink>]) Appraisal model, which examines how attitude, judgment, and evaluation are conveyed in text. The below excerpt serves as an example of this analysis. Specifically, the participant is describing their use of standard video, which they continue to reference in the excerpt [high school level concepts; more examples; those]. Yet this reference chain has meaning tied to it that expresses a position. Namely, the modals "would like" enhance the reference to "more examples" to convey a negative appraisal regarding the lack of high school level videos. By examining for trends in the referents and reference chains appraised, themes emerged from the data.</p> <p>I always get the push back: where are the high school level concepts? .... I would like to have more examples that I can show routinely, but I've struggled with finding with where to find those ...</p> <hd id="AN0162400342-13">RESULTS</hd> <p></p> <hd id="AN0162400342-14">Quantitative</hd> <p>Teacher Educators within this sample reported to have a high familiarity with standard videos ( <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:00366803:media:ssm12563:ssm12563-math-0001" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>M</mi><mo>=</mo><mn>3.52</mn><mo>,</mo><mi mathvariant="italic">SD</mi><mo>=</mo><mn>0.79</mn></mrow></math> </ephtml> ). Recall, the Likert scale for each representation ranged between 0 (not at all familiar) to 4 (extremely familiar). This suggests that, on average, STEs and MTEs are moderately to extremely familiar with standard videos. Conversely, participants reported to be somewhat familiar ( <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:00366803:media:ssm12563:ssm12563-math-0002" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>M</mi><mo>=</mo><mn>1.69</mn><mo>,</mo><mi mathvariant="italic">SD</mi><mo>=</mo><mn>1.008</mn><mo>)</mo></mrow></math> </ephtml> with animations/comics and even less familiar ( <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:00366803:media:ssm12563:ssm12563-math-0003" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>M</mi><mo>=</mo><mn>0.80</mn><mo>,</mo><mi mathvariant="italic">SD</mi><mo>=</mo><mn>1.005</mn></mrow></math> </ephtml> ) with 360 videos. Figure 1 depicts how familiar teacher educators are with standard videos, how unfamiliar they are with 360 videos, and how they are somewhat familiar with animations/comics.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/SSM/01jan23/ssm12563-fig-0001.jpg?ephost1=dGJyMNHX8kSepq84v%2bvlOLCmsE6epq5Srqa4SK6WxWXS" alt="ssm12563-fig-0001.jpg" title="1 Familiarity of each representation" /> </p> <p></p> <p>Evidence suggests that familiarity does not necessarily influence a teacher educators perceived usefulness. Teacher educators were asked to rank on a hierarchy the types (of one's own teaching, interview with a student, and video of the whole class) of representation they indicated to be useful on a scale of 1 (the most useful) to a 9 (not as useful). If the teacher educators did not rank the representation type to be useful then the medium was assigned a 10 in our coding. Thus, a rank score of 10 suggests that the representation was perceived to not be useful by the teacher educator. Our results showed that, on average, teacher educators ranked all types of standard videos within the top three for usefulness (Table 2). Interestingly, the three types of 360 videos were in the middle of the rank while all animations/comics were ranked at the bottom. From Table 2, a 360 video of an interview with ones' own student was narrowly considered to be more useful than animations/comics. The mode has been included in Table 2 to note the most frequent ranking for each representation.</p> <p>2 TABLE Ranking of videos</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Rank</th><th align="left">Video type</th><th align="left">Mean</th><th align="left">Std. dev.</th><th align="left">Mode</th></tr></thead><tbody valign="top"><tr><td>Top 3</td><td>Std. video of one's own teaching</td><td>3.07</td><td>2.14</td><td>1.00</td></tr><tr><td>Std. video of an Interview with a student</td><td>3.49</td><td>1.83</td><td>2.00</td></tr><tr><td>Standard video of whole class</td><td>3.53</td><td>1.72</td><td>3.00</td></tr><tr><td>Middle 3</td><td>360 video of ones' own teaching</td><td>4.71</td><td>3.25</td><td>1.00</td></tr><tr><td>360 video of while class</td><td>4.92</td><td>2.94</td><td>4.00</td></tr><tr><td>360 video of an interview with a Student</td><td>6.03</td><td>3.28</td><td>10.00</td></tr><tr><td>Bottom 3</td><td>Animation/comic of an interview with a student</td><td>6.07</td><td>2.38</td><td>10.00</td></tr><tr><td>Animation of whole class</td><td>6.29</td><td>1.82</td><td>10.00</td></tr><tr><td>Animations of one's own teaching</td><td>6.48</td><td>2.36</td><td>10.00</td></tr></tbody></table> </ephtml> </p> <p>Despite the reported perceived level of usefulness for a representation this does not necessarily translate into a teacher educators use of a medium in their methods courses (Table 3). Table 3 reports the mean number per each representation used by both STEs and MTEs in a single methods course. Within our sample, standard videos are the primary video representation incorporated into a MTEs and STEs methods courses more than animations/comics and 360 videos. Our findings suggest that 360 videos are rarely shown in methods courses.</p> <p>3 TABLE Average number of uses of each representation in a methods course</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left" /><th align="left">Standard video</th><th align="left">360 video</th><th align="left">Animations/comics</th></tr></thead><tbody valign="top"><tr><td>Mathematics education (n = 77)</td><td>M = 10.17, SD = 7.140</td><td>M = 0.17, SD = 0.616</td><td>M = 0.90, SD = 2.010</td></tr><tr><td>Science education (n = 8)</td><td>M = 7.88, SD = 6.556</td><td>M = 0.13, SD = 0.354</td><td>M = 0.63, SD = 0.916</td></tr></tbody></table> </ephtml> </p> <p>Comparing a teacher educators' level of familiarity to their reported use of these mediums suggests that familiarity plays a role in their decisions to include a representation in their courses (Figure 2). Figure 2 combines findings from Figure 1 and Table 3 to illustrate the relations of the level of familiarity and their reported number of uses.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/SSM/01jan23/ssm12563-fig-0002.jpg?ephost1=dGJyMNHX8kSepq84v%2bvlOLCmsE6epq5Srqa4SK6WxWXS" alt="ssm12563-fig-0002.jpg" title="2 Familiarity versus average number of reported times used in a methods course" /> </p> <p></p> <p>To further elaborate on the findings in Figure 2, a Spearman Rho coefficient was used to measure the relationship between familiarity and frequency of use. STEs were removed from this analysis due to our small sample size. For standard videos, a MTEs frequency of use and level of familiarity was found to be statistically significant ( <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:00366803:media:ssm12563:ssm12563-math-0004" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ρ</mi></mrow></math> </ephtml> = 0.242, <emph>p</emph> = 0.034) along with the familiarity and perceived usefulness ( <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:00366803:media:ssm12563:ssm12563-math-0005" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ρ</mi></mrow></math> </ephtml> = 0.272, <emph>p</emph> = 0.018). For 360 videos, the frequency of use and level of familiarity has been found to be statistically significant ( <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:00366803:media:ssm12563:ssm12563-math-0006" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ρ</mi></mrow></math> </ephtml> = 0.473, <emph>p</emph> < 0.001) however familiarity and perceived level of usefulness was not found to be significant ( <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:00366803:media:ssm12563:ssm12563-math-0007" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ρ</mi></mrow></math> </ephtml> = −0.032, <emph>p</emph> = 0.79). Similarly with animations/comic, the relationship between frequency of use and the level of familiarity was found to be statistically significant ( <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:00366803:media:ssm12563:ssm12563-math-0008" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ρ</mi></mrow></math> </ephtml> = 0.399, <emph>p</emph> < 0.001) while familiarity and perceived level of usefulness was not found to be significant ( <ephtml> <math display="inline" overflow="scroll" altimg="urn:x-wiley:00366803:media:ssm12563:ssm12563-math-0009" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ρ</mi></mrow></math> </ephtml> = 0.20, <emph>p</emph> = 0.09). This suggests that familiarity of each mediums impacts a teacher educators' decision to use each medium, which offers support to Figure 2. However, a teacher educators' level of familiarity does not necessarily influence their level of perceived usefulness.</p> <hd id="AN0162400342-17">Qualitative</hd> <p>From the interviews of STEs and MTEs, three themes emerged from the discussion of their representations of practice. The Appraisal model contributed to the determination of themes in identifying the meaning making "registers" that were contextually situated throughout the participants linguistic choices (Martin & White, [<reflink idref="bib25" id="ref64">25</reflink>]). The themes directly or indirectly corroborate the quantitative findings while also providing additional insights. The key themes identified were access to, dimensions of, and pertinacity with representations of practice.</p> <hd id="AN0162400342-18">Access</hd> <p>The first theme focuses on teacher educators' perceptions of <emph>access</emph> to representations. Discussing standard videos, six participants explicitly identified the prevalent availability of elementary grades mathematics representations, with some noting the lack of such representations at the middle and high school level, as well as comparatively less access to videos of science lessons generally. For example, one MTE, Beck, commented.</p> <p>I feel like in elementary ed, there's a whole lot of videos that capture cognitively guided instruction (CGI) work and you know, like different things and there might be things with middle school focus, but I have not seen as broad a variety of things in the secondary content.</p> <p>Beck also negatively appraised the availability of secondary and middle grades content videos. Similar to Beck's appraisals, both STEs interviewed noted a perceived prevalence of elementary mathematics videos. Candace explicitly stated that "it seems to be the case" there is more access to representations of practice in mathematics education than science education.</p> <p>Negative appraisals of access were common across nearly all participants, albeit with positive appraisals often accompanying negative ones. For example, Karen noted how her experience with standard videos and animations "is generally positive" and noted that 360 videos have "been really helpful here. I've gotten positive feedback from my students with it." Despite generally positive appraisals of multiple mediums, Karen still conveyed a need for more access (negative appraisal) to specific topics. This mixed stance of positive and negative appraisal toward access was noted by others. For example, Will noted:</p> <p>I would like to see more diversity in videos. While I think CGI are great ... I really want more bilingual classrooms or multilingual classrooms.</p> <p>Intermixed with positive and negative appraisals of access are explicit references to specific videos or collections of representations. For standard video, such prevalence included explicitly referencing cognitive guided instruction videos, Boaler and Humphrie, videos from the National Council of Teachers of Mathematics, and various other well‐known representations (Deborah Ball's lessons, College Preparatory Mathematics, TIMMS, Austin's Butterfly, etc.). For animations/comics, explicit references to collections included Lesson<emph>Sketch</emph>, GoAnimate, and PowTown. For 360 videos, there was only one collection referenced (XRi) and this was by one participant interviewed. Referencing these various collections appeared to influence conveyed access. Rather, the more prevalent and numerous references to media collections, the higher participants' self‐reported use of such mediums appeared to be.</p> <hd id="AN0162400342-19">Dimensions of representations</hd> <p>The next theme that emerged across participants' responses were appraisals of representations of practice through the lens of their dimensions. Most prevalently referenced were facets corresponding to the dimensions of individuality and perceptual capacity. Although participants' descriptions of standard and 360 video typically positioned a higher degree of individuality as positive, participants descriptions of animations/comics was more complex. For example, Candace noted that comics could allow her to simplify characteristics of both the students and setting to allow for "boiling down" to essential pedagogical features. By contrast, Will described comics having a lower degree of individuality, stating "I feel like it's easier for people to separate themselves from it [events in the classroom]." Notably, both Candace and Will referenced Lesson<emph>Sketch</emph> comics in their descriptions, but neither had used such representations. This lack of familiarity may have led to the perception that individuality in comic‐based representations was static. By contrast, Ben, a prevalent user of the same platform, noted the ability to adjust the individuality dimension:</p> <p>[animations] allow me to determine the amount of complexity I want my students to see. So, for instance, I can put as much or as little detail in the background as I want. I can make all the students look different or I can make them look like the little blue egg men. I can have 10 people talk at once. I can have one person talk at once.</p> <p>In examining appraisals of Candace, Will, and Ben, we do not evaluate who is "correct" in their assessment of how comics convey individuality. Rather, findings here expose how participants' valuing of individuality in a representation informs their appraisal of it.</p> <p>In addition to individuality, participants appraised representations on their degree of perceptual capacity. In general, this dimension was implicitly referenced when participants discussed an inability to hear or see events in the classroom. Discussing standard video, Beck noted "you can't zoom in and hear individual conversations or the audio is so crappy ..." This notion of being able to hear and see what groups of students are doing was common among participants. For example, Karen observed affordances of 360 video used in her courses:</p> <p>It's just a way for them to see a classroom that they otherwise would not be able to see. And I guess give them a nice perspective to be able to manipulate what they look at, if they are looking at the teacher or looking at the students ...</p> <hd id="AN0162400342-20">Pertinacity</hd> <p> <emph>Pertinacity</emph> is the act of being persistent or stubborn in the adoption of different mediums in teaching teachers. Pertinacity was observable when participants used negative appraisals of a medium, supported by rationales for such appraisals. These rationales were predominately justified, such as the lack of access in certain media. However, our focus here is on rationales outside of access to illuminate the nuance of this theme. For example, Blythe noted that finding (or creating) videos of sufficient quality took time, "I think they [standard videos] are pretty effective. It takes time to find the right ones." Will struggled with the "cartoony environment" of comics and animations and argued that they did not want to "fight the medium" in order to have challenging conversations about issues such as race. Will elaborated on his perspective of comics stating, "I mean that might be my particular bias for now, but I mean I can see the value in those things [comics and animations] and I am sure others have highlighted that value." Thus, Will is displaying justifiable stubbornness (i.e., pertinacity) in his hesitancy in adopting a representation he is concerned may deter conversations about injustice in mathematics classrooms.</p> <p>The previous two examples incorporated rationales related to needs and resources of teacher educators, pertinacity is also evident in their experiences. Nicky displayed pertinacity when focusing on the need for seeing modeling of the representation of practice and being able to model the use of said practices. They stated "I was able to model what I saw. The [teacher educators] that I watched teach these things—I was modeling their use of video. And they did not use comics and they did not use animations. so therefore, I didn't try to do that." This level of systemic vertical pertinacity wherein mentees use only what mentors have modeled suggests a distinction between when teacher educators desire mediums to meet a need (Blythe & Will) and a lack of exposure (Nicky). Notably, Nicky's noted lack of exposure was different than the rationale as it was coupled with a negative evaluation of certain media. For example, Will positively appraised 360 video, while noting his lack of use was a matter of exposure. Will conveyed an openness toward 360 video whereas Nicky did not for comics/animations.</p> <hd id="AN0162400342-21">Summary of results and findings</hd> <p>Participants reported generally high usage of standard video in methods courses for both mathematics (<emph>M</emph> = 10.17, <emph>SD</emph> = 7.14) and science education (<emph>M</emph> = 7.88, <emph>SD</emph> = 6.56). However, use of animations/comics and 360 video was infrequent, with few teacher educators reporting their use or familiarity. Indeed, correlation coefficients indicated a positive relationship between familiarity and frequency of use. Findings from interviews revealed that participants with lower reported use of different media tended to describe a lack of access to appropriate representations of practice. Perceived affordances of 360 video and animations/comics varied by familiarity with each medium, which also corresponded with teacher educators' usage. Additionally, when teacher educators lacked exposure or experience with a medium, they were less likely to use it or describe relevant features of it. As such, findings corroborate the quantitative results but present a more nuanced understanding of the correlation coefficients.</p> <hd id="AN0162400342-22">DISCUSSION</hd> <p>This study investigated the relationship between the level of familiarity and perceived usefulness of videos (standard, 360, and animations/comics) and how these impact a mathematics and science teacher educators' decision to use them in their methods courses. Results from 71 MTEs, 2 STEs, and 6 mathematics and science educators across the United Stated suggests the level of familiarity does not necessarily coincide with the level of perceived usefulness. Our findings suggest that a teacher educators' level of familiarity may deter an educator to adopt a new medium. These findings coincide with Uzan ([<reflink idref="bib31" id="ref65">31</reflink>]) in which educators could see value in a resource but, often do not incorporate them in due to lack of comfort (i.e., familiarity). Our research is consistent with other studies regarding standard video being the most familiar and widely used medium within teacher education (Arya et al., [<reflink idref="bib2" id="ref66">2</reflink>]; Austin & Kosko, [<reflink idref="bib3" id="ref67">3</reflink>]; Christ et al., [<reflink idref="bib7" id="ref68">7</reflink>]). Although animation/comics have been deemed a valid representation (Herbst et al., [<reflink idref="bib18" id="ref69">18</reflink>]), many teacher educators did not perceive the value that has been outlined in prior research (Clark et al., [<reflink idref="bib8" id="ref70">8</reflink>]). Interestingly, participants were less familiar with 360 videos than animations/comics but still perceived 360 videos to be generally useful and animations/comics to not be as seen in their rankings.</p> <p>Despite many articles supporting the use of animations/comics (e.g., Casey & Amidon, [<reflink idref="bib6" id="ref71">6</reflink>]; Herbst et al., [<reflink idref="bib18" id="ref72">18</reflink>]) and 360 video (Ferdig & Kosko, [<reflink idref="bib11" id="ref73">11</reflink>]; Roche & Gal‐Petitfaux, [<reflink idref="bib26" id="ref74">26</reflink>]) our results show that MTEs and STEs are unfamiliar with these mediums. Our results indicate that familiarity may coincide with what representation tools teacher educators are using but not their perceived level of usefulness. Rather, the dimensions of representations (temporality, individuality, perceptual capacity) described by Herbst et al. ([<reflink idref="bib18" id="ref75">18</reflink>]) and Kosko, Ferdig, and Roche ([<reflink idref="bib22" id="ref76">22</reflink>]); Kosko, Ferdig, and Zolfaghari ([<reflink idref="bib23" id="ref77">23</reflink>]) seem to influence an educator's level of pertinacity to use a particular medium. Our participants largely viewed standard and 360 videos as having a higher level of individuality than animations/comics and one participant noted that he cannot see past the "cartoony" look of the "blue" figures. Additionally, participants noted the perceptual capacity of mediums, such that 360 videos allow a PST to see perspectives that a standard video could not.</p> <p>Our findings align with our piloted work which studied a representative sample of MTEs in a single state (Austin & Kosko, [<reflink idref="bib3" id="ref78">3</reflink>]). Namely, standard videos were the most common representation of practice and neither 360 videos nor comics/animations were used frequently (Austin & Kosko, [<reflink idref="bib3" id="ref79">3</reflink>]). However, this current study explored the potential reasons for using a medium more than another. Our interviews further elaborated on how a teacher educator uses a medium or reasoning as to why they did not use another. The interviews established that those who were not familiar with a particular medium were hesitant to learn and explore the new representation. Thus, findings from this research suggest that time for adoption and learning the technology were significant factors in their willingness to use such a representation. Several participants noted that creating content takes time, and they would prefer to have ready‐made content available. Furthermore, we found that the more "collections" of representations referenced by teacher educators, the more likely they were to use various media at a higher frequency. Such "collections" need to expand beyond elementary videos and need to include higher grade bands such as middle and high school levels. Additionally, knowledge of collections appears to be gathered by word of mouth, with no common index referenced for various representations of practice. Given this finding, an important implication for practice is for such an index to be developed and, preferably, made accessible through organizations such as Association of Mathematics Teacher Educators (AMTE), Association for Science Teacher Education (ASTE), and the Society for Information Technology and Teacher Education (SITE).</p> <hd id="AN0162400342-23">Limitations</hd> <p>Despite an overall sample size of 79 teacher educators, our sample is not representative. First, we had a relatively small sample of participants who identified as STEs (<emph>n</emph> = 8). This limited the claims we could make and the analyses we could conduct (Spearman rho excluding STEs). Although we include 72 MTEs, we believe this sample was not representative. Second, the sample largely consisted of former participants in the STaR program. The program engages early career mathematics education faculty with the first cohort beginning in summer 2010. Although STaR purposefully engages faculty at varying types of institutions of higher education, the current sample excludes MTEs who began their careers as teacher educators before the 2009–2010 academic year and who did not participate in this selective program. Despite this limitation, results from the present study mirror those of Austin and Kosko ([<reflink idref="bib3" id="ref80">3</reflink>]), who did collect data from a representative sample from a single state. A final limitation in the present study is that it relies entirely on self‐report data. It is likely that more nuances would be gleaned from observational data of teacher educators in their use of different representations of practice.</p> <hd id="AN0162400342-24">CONCLUSION</hd> <p>Our findings suggest that standard videos are the primary representation used in mathematics and science methods courses. This medium appears to be preferred due to educators being familiar; particularly compared to animations/comics and 360 video. Additionally, teacher educators' familiarly with representations is intimately connected with their perceptions of access, which includes knowledge of various collections of representations of practice and various other factors. The goal of this study was to better understand the relationship between familiarity and perceived usefulness of standard videos, 360 videos, and animations/comics and how it influences their use of each medium in their methods courses. This study highlights the need for teacher educators to have better access these representations. This access could encompass the need of platform to house these resources or an institution offering support/funding for the materials needed to learn these representations.</p> <hd id="AN0162400342-25">ACKNOWLEDGMENTS</hd> <p>Research reported here received support from the National Science Foundation through DRK‐12 Grant #1908159. 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(2021). Investigating student teachers' noticing using 360 video of their own teaching. Journal of Technology and Teacher Education, 29 (3), 309 – 338.</bibtext> </blist> </ref> <aug> <p>By Christine K. Austin; Karl W. Kosko and Jennifer L. 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  Data: Mathematics and Science Teacher Educators' Use of Representations of Practice: A Mixed Methods Study
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– Name: Author
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  Data: <searchLink fieldCode="AR" term="%22Austin%2C+Christine+K%2E%22">Austin, Christine K.</searchLink><br /><searchLink fieldCode="AR" term="%22Kosko%2C+Karl+W%2E%22">Kosko, Karl W.</searchLink><br /><searchLink fieldCode="AR" term="%22Heisler%2C+Jennifer+L%2E%22">Heisler, Jennifer L.</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22School+Science+and+Mathematics%22"><i>School Science and Mathematics</i></searchLink>. Jan 2023 123(1):14-25.
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  Data: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
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– Name: Pages
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  Data: 12
– Name: DatePubCY
  Label: Publication Date
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  Data: 2023
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  Data: National Science Foundation (NSF)
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  Data: 1908159
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  Data: Journal Articles<br />Reports - Research
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  Data: <searchLink fieldCode="EL" term="%22Higher+Education%22">Higher Education</searchLink><br /><searchLink fieldCode="EL" term="%22Postsecondary+Education%22">Postsecondary Education</searchLink>
– Name: Subject
  Label: Descriptors
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  Data: <searchLink fieldCode="DE" term="%22Mathematics+Teachers%22">Mathematics Teachers</searchLink><br /><searchLink fieldCode="DE" term="%22Science+Teachers%22">Science Teachers</searchLink><br /><searchLink fieldCode="DE" term="%22Teacher+Educators%22">Teacher Educators</searchLink><br /><searchLink fieldCode="DE" term="%22Multimedia+Materials%22">Multimedia Materials</searchLink><br /><searchLink fieldCode="DE" term="%22Multimedia+Instruction%22">Multimedia Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Methods+Courses%22">Methods Courses</searchLink><br /><searchLink fieldCode="DE" term="%22Familiarity%22">Familiarity</searchLink><br /><searchLink fieldCode="DE" term="%22Video+Technology%22">Video Technology</searchLink>
– Name: DOI
  Label: DOI
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  Data: 10.1111/ssm.12563
– Name: ISSN
  Label: ISSN
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  Data: 0036-6803<br />1949-8594
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study sought to explore math and science teacher educators' use of various media to represent practice within methods courses. There is little understanding of why certain media is used over other representations and the rationale for these choices. Specifically, the study focused on the prevalence and familiarity of teacher educators with comics and animations, standard videos, and 360 videos. This mixed methods study utilized a survey and interviews to ascertain math and science teacher educators' level of familiarity and perceived usefulness of representations of practice. Results indicate that standard video is by far the most used representation of practice in methods classes with three themes explaining this finding: access to representations of practice, dimensions of representation, and pertinacity of using representations. Familiarity with representations of practice relates to teacher educators' perceptions of access thereby indicating a need for teacher educators to have better access to representations. Implications of this study include supporting current literature about the relationship between the level of familiarity and perceived usefulness in media along with the potential need for a central platform that houses these representations of practice resources for teacher educators.
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  Data: 2023
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  Data: EJ1369245
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        Value: 10.1111/ssm.12563
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      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 12
        StartPage: 14
    Subjects:
      – SubjectFull: Mathematics Teachers
        Type: general
      – SubjectFull: Science Teachers
        Type: general
      – SubjectFull: Teacher Educators
        Type: general
      – SubjectFull: Multimedia Materials
        Type: general
      – SubjectFull: Multimedia Instruction
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      – SubjectFull: Methods Courses
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      – SubjectFull: Familiarity
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      – SubjectFull: Video Technology
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      – TitleFull: Mathematics and Science Teacher Educators' Use of Representations of Practice: A Mixed Methods Study
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