Developing and Validating a Reliable TPACK Instrument for Secondary Mathematics Preservice Teachers

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Developing and Validating aReliable TPACK Instrumentfor Secondary MathematicsPreservice TeachersJeremy Zelkowskia, Jim Gleasona, Dana C. Coxb &Stephen Bismarckc

a University of Alabamab Miami Universityc University of South Carolina—UpstatePublished online: 21 Feb 2014.

To cite this article: Jeremy Zelkowski, Jim Gleason, Dana C. Cox & StephenBismarck (2013) Developing and Validating a Reliable TPACK Instrument for SecondaryMathematics Preservice Teachers, Journal of Research on Technology in Education,46:2, 173-206, DOI: 10.1080/15391523.2013.10782618

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Volume 46 Number 2 | Journal of Research on Technology in Education | 173

Copyright © 2013, ISTE (International Society for Technology in Education), 800.336.5191(U.S. & Canada) or 541.302.3777 (Int’l), [email protected], iste.org. All rights reserved.

Developing and Validating a Reliable TPACK Instrument for Secondary Mathematics Preservice Teachers

JRTE | Vol. 46, No. 2, pp. 173–206 | ©2013 ISTE | iste.org/jrte

Developing and Validating a Reliable TPACK Instrument for Secondary Mathematics Preservice Teachers

Jeremy ZelkowskiJim Gleason

University of Alabama

Dana C. CoxMiami University

Stephen BismarckUniversity of South Carolina—Upstate

Abstract

Within the realm of teaching middle and high school mathematics, the abil-ity to teach mathematics effectively using various forms of technology is now more important than ever, as expressed by the recent development of the Common Core State Standards for Mathematical Practice. This article pres-ents the development process and the results from 15 institutions and more than 300 surveys completed by secondary mathematics preservice teach-ers. The results suggest that technological, pedagogical, and content knowl-edge; technology knowledge; content knowledge; and pedagogical knowledge constructs are valid and reliable, whereas pedagogical content knowledge, technological content knowledge, and technological pedagogical knowledge domains remain difficult for preservice teachers to separate and self-report. (Keywords: TPACK, survey, secondary, mathematics education, teacher edu-cation, preservice)

With the recent development and adoption of the Common Core State Standards for Mathematics (CCSSM) (NGA & CCSSO, 2010) come new standards for mathematical practice that re-emphasize

the importance of technological tools in mathematics classrooms. This renewed commitment to helping students model their world and strategi-cally select tools for mathematical pursuits essentially requires teachers of mathematics to be knowledgeable and effective at teaching mathematics with technology and assessing the learning of mathematics by students who use technology when doing mathematics (Stein, Smith, Henningsen, & Silver 2010). The CCSSM are not the first set of standards that attend to the importance of integrating technology into the teaching and learning of mathematics. The National Council of Teachers of Mathematics (NCTM)

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174 | Journal of Research on Technology in Education | Volume 46 Number 2

Zelkowski, Gleason, Cox, & Bismarck


and the Association of Mathematics Teacher Educators (AMTE) have also made specific recommendations regarding the role of technology in the mathematics classroom and for the development of mathematics teachers. NCTM’s Technology Principle provides a vision of mathematics teaching where technology is essential, driving curricular changes in the mathematics that can and should be learned in the classroom. The technology principle states, “Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning” (NCTM, 2000, p. 24). To enact this vision, AMTE (2006) recommends that “mathematics teacher preparation programs must ensure that all math-ematics teachers and teacher candidates have opportunities to acquire the knowledge and experiences needed to incorporate technology in the context of teaching and learning mathematics” (p.1). The specialized knowledge that teachers require to effectively integrate technology into teaching practices is currently referred to as technological, pedagogical, and content knowledge (TPACK) (Mishra & Koehler, 2006).

Given that some mathematics teachers utilize technology effectively and consistently in their classrooms, while others seem to avoid technology, we must ask whether teachers’ values and beliefs are at the heart of this paradox. Further, because of the growing national perspective that K–12 students should have access to technological tools and the hope that this access will greatly influence the way mathematics is taught and learned, it behooves current teacher preparation programs to examine their current programs and ensure that they are producing technologically effective mathematics teachers. The purpose of this study was to develop, establish the reliability of, and validate constructs for, an instrument that would enable preservice sec-ondary mathematics teacher educators to examine their preservice teachers’ (PSTs’) self-perceptions of TPACK and evaluate their program’s effectiveness at developing PSTs’ TPACK.

Theoretical Background

Defining Mathematical TPACK TPACK emerged in the literature as a theoretical framework for teachers’ knowledge of effective technology use in the classroom for teaching and learning (Mishra & Koehler, 2006). The TPACK framework was developed by expanding the construct of pedagogical content knowledge (PCK) to in-clude the integration of technology knowledge (TK) for teaching (see Figure 1). Shulman’s (1986) construct of PCK referred to the teaching knowledge that specifically blends both content knowledge (CK) and pedagogical knowledge (PK). Specific to mathematics, CK and PK, as well as PCK, frameworks have been proposed and studied relatively extensively during the past two decades (Ball, 1990; Ball, Hill, & Bass, 2002; Brown & Borko, 1992; Hill, 2011; Lampert & Ball, 1998; Ma, 1999; Silverman & Thompson,

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Developing and Validating a Reliable TPACK Instrument


2008; Strawhecker, 2005; Van Voorst, 2004), though more so at the primary grade levels than secondary grade levels.

Because of this work, teacher education programs have placed much greater attention on the development of these teacher knowledge do-mains (Ball, Lubienski, & Mewborn, 2001; Dede & Soybas, 2011; Fryk-holm & Glasson, 2005; Kahan, Cooper, and Bethea, 2003; Wilson, Floden, Ferrini-Mundy, 2001). With the inclusion of TK as an additional teacher knowledge domain and the advanced technology developments for teaching mathematics, teacher education programs for teachers of mathematics, now must examine their program effectiveness at develop-ing seven domains of knowledge in PSTs. These seven domains include, TK, PK, CK, PCK, technological pedagogical knowledge (TPK), techno-logical content knowledge (TCK), and TPACK (see Figure 1).

For a more general treatment and description of each of these domains, we refer the reader to Schmidt, Baran, Thompson, Mishra, Koehler, and Shin (2009) and the literature above. Here, we elaborate on TK, TCK, and TPACK in the context of secondary mathematics. To begin crafting these working definitions, we acknowledge the considerable amount of accomplished work in the field (see “TPACK in secondary mathematics” below).

TK in secondary mathematics. TK in secondary mathematics refers to knowledge of technologies that are relevant to secondary mathematics

Figure 1. Seven knowledge domains central to the TPACK framework (http://tpack.org).

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teaching and learning. The list of technologies specific to secondary math-ematics classrooms is ever growing and includes technologies developed specifically for the mathematics classroom as well as mainstream tech-nologies that serve computational and/or instructional needs. In the first category, the list surely includes computer algebra systems (CAS), dynamic mathematical software (e.g., Fathom, Geogebra, Geometer’s Sketchpad, TI-Nspire Teacher’s Edition Software), online Java applets, and graphing handhelds. In the second category, the list minimally includes calculat-ing devices, spreadsheets, data collection devices such as calculator-based laboratories (CBLs), interactive whiteboards, personal response systems, and many others.

TCK in secondary mathematics. TCK in secondary mathematics refers to the knowledge that incorporating technology fundamentally changes the mathematics that students can learn. Three examples will highlight the impact of technology on mathematical content in the classroom. First, dynamic mathematical software transforms the classroom into a mathemati-cal laboratory, giving students the opportunity to engage with mathematical concepts and relationships in an empirical environment. This, in turn, opens up new perspectives and problem-solving techniques that would otherwise not be possible. Second, graphing handheld devices give students immedi-ate access to multiple representations of mathematical relationships. These representations and the connections between them are not only reasoning tools, but also communication tools that assist students as they learn to negotiate shared meanings. Third, spreadsheets and data collection devices give students access to larger, more complex data sets with which to model real-world phenomena. These data sets would be incomprehensible to stu-dents working exclusively with pencil and paper.

TPACK in secondary mathematics. Beyond the questions of what technolo-gies are relevant to the teaching of mathematics and what mathematics can be taught with the inclusion of technology is the question of how best to leverage the power of technology in the classroom. Knowledge about how technologies can influence the teaching and learning of mathematics is referred to as TPACK. Teachers of mathematics must possess enough spe-cialized knowledge to make critical classroom decisions of pedagogy with respect to mathematical content and appropriate technologies. Internation-ally, research has shown students learn more mathematics and learn it more deeply by using technology effectively and appropriately during the teaching and learning of mathematics—including some studies showing the closing of achievement gaps in underrepresented students (Barkatsas, Kasimatic, & Gialamas, 2009; Bos, 2007; Doerr & Zangor, 2000; Duda, 2011; Dugdale & Kibbey, 1990; Dunham & Dick, 1994; Guckin & Morrison, 1991; Hol-lebrands, 2003; Kaput, 1995; Li & Ma, 2010; López, 2010; Mitchell, Bailey, & Monroe, 2007; Page, 2002; Schmidt, Kohler, & Moldenhauer, 2009; Weng-linsky & Educational Testing Service, 1998; Zbiek, 1998). However, some

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studies have shown little to no achievement effects specific to the integration of technology into the mathematics classroom (Kelly, Carnine, Gersten, & Grossen, 1986; Shapley, Sheehan, Maloney, & Caranikas-Walker, 2011; Torff & Tirotta, 2010). The distinguishing factor between the research findings appears to be fundamentally grounded in how the technology is used peda-gogically by the teacher, their beliefs about technology, and whether students are using the device to make mathematical connections and check for un-derstanding rather than simply for computation, also referred to as answer-getting. Teachers’ effective technology implementation in the mathematics classroom has been slow, according to the literature, for various reasons, including but not limited to: (a) resistance to change, (b) lack of confidence, (c) access, (d) usefulness, (e) fears (i.e., technical failures, students know-ing more about technology than the teacher), and (f) inhibitors (Beaudin & Bowers, 1997; Keating & Evans, 2001; Leatham, 2007; Li, 2003; McKinney & Frazier, 2008; Norton, McRobbie, & Cooper 2000; Pierce & Ball, 2009; Quinn, 1998; Stallings, 1995; Thomas, 2006; Thompson, 1992; Ursini, San-tos, & Juarez Lopez, 2005).

There are many examples in the field of studies that purport to document, define or teach the appropriate use of technology in the mathematics class-room (i.e., Demana & Waits 1990, 1998; Drier, 2001; Kutzler, 2000; Niess, 2001; 2005; Salinger, 1994; Shoaf, 2000). With this existing knowledge of research, the AMTE (2009) adopted the Mathematics TPACK framework for teacher educators. Specifically, the Mathematics TPACK framework consists of four essential components: (1) Design and develop technology-enhanced mathematics learning environments and experiences, (2) Facilitate math-ematics instruction with technology as an integrated tool, (3) Assess and evaluate technology-enriched mathematics teaching and learning, and (4) Engage in ongoing professional development to enhance TPACK. Further, Niess and her colleagues (2009) produced the TPACK development model for teachers. They indicate that:

… many mathematics teachers’ PCK lacks a solid and consistent inte-gration of modern digital technologies in mathematics curriculum and instruction. Technologies, such as dynamic geometry tools or advanced graphing calculators with computer algebra systems (CAS), are primarily used for modeling and providing examples, where students imitate the actions and use the technologies for verification, demonstration, and drill and practice. In essence then, while digital technologies have evolved, strategies for their effective integration into the learning of mathematics have not evolved as rapidly (p. 6).

With the recent development and adoption of the CCSSM, along with the advancement of educational technologies specific to mathematics, the expectation to teach and learn mathematics with the appropriate use of technology has increased dramatically, as can be seen in the standards for

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mathematical practices (NGA & CCSSO, 2010). It has become increasingly important for researchers to develop instruments for monitoring the profes-sional growth of preservice mathematics teachers’ ability and self-efficacy to use technology effectively and appropriately (or not) for teaching mathemat-ics (i.e., TPACK). As mathematics teachers increase their self-awareness and confidence in the use of technology in the classroom, many increase their pedagogical toolbox that utilizes technology to enhance the teaching and learning of mathematics (Lawless & Pellegrino, 2007). Since its incep-tion in 2005, TPACK has been of great interest among those concerned with preservice preparation programs, yet much of the large-scale studies have been along the lines of Schmidt et al. (2009) and involve preservice elemen-tary generalists, where preservice populations are large, rather than second-ary specialists in mathematics with preservice populations that are generally small at universities across the United States. What was not clear in the literature is a systematic way to longitudinally study TPACK development on a grand scale. The purpose of our study was to create an instrument for such research.

Developing an Instrument to Measure TPACK for Preservice Secondary Mathematics TeachersIn their recent review of the TPACK literature, Young, Young, and Shaker (2012) studied the instruments and methods of studying TPACK in pre-service teachers. Their conclusion revealed no specialized instrument for secondary mathematics TPACK. The TPACK development model (Neiss et al., 2009) has been a framework for TPACK development in preservice teachers, yet the research community lacks the instruments to measure and monitor TPACK development. Some performance assessments exist for use with preservice elementary (i.e., Angeli & Valandies, 2009) or inservice (i.e., Bos, 2011; Harris, Grandgenett, & Hofer, 2010) teachers, and these generally take the form of surveys.

One benefit of using a survey format is that it measures self-efficacy. The self-efficacy of preservice and inservice teachers influences whether or not they can and will implement technology supported classroom lessons (Bowers & Stephens, 2011; Dunham & Henessey, 2008; Kastberg & Leatham, 2005; Kendal & Stacey, 2001; Harris & Hofer, 2011; Niess, 2013; Tharp, Fitzsimmons, & Ayers, 1997; Zbiek & Hollebrands, 2008). Özgün-Koca, Meagher, and Edwards (2010) used the mathematics technology attitudes survey (MTAS) as part of their secondary mathematics preservice prepara-tion program. Hofer and Grandgenett (2012) conducted a one-year longi-tudinal study on a cohort of alternative certification preservice teachers but limited the study to a small sample size (<10) and less than one year of data collection. Surveys have been designed and tested in large-scale studies on a number of different populations, including K–12 online educators (Archam-bault & Crippen, 2009; Archambault & Barnett, 2010) as well as preservice

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teachers, including both primary and secondary in Singapore (Koh, Chai, & Tsai, 2010) and the United States (Sahin, 2011) and U.S. elementary PSTs (Lux, Bangert, & Whittier, 2011; Schmidt et al., 2009).

Although we can assume that Koh, Chai, and Tsai (2010) and Sahin (2011) included secondary preservice mathematics teachers in their samples, neither distinguished this group within the whole. There is an absence in the literature with respect to a valid and reliable survey to monitor and assess TPACK development in secondary mathematics PSTs. In a recent review of the literature on measuring TPACK among PSTs, Abbitt (2011) conjectures that the survey developed by Schmidt et al. (2009) “may also provide a solid foundation for similar surveys that would be applicable to PSTs who will be teaching other content areas and grade levels,” (p. 292), a conjecture that is echoed by Niess (2011), who adds that more work is needed to validate such an instrument, including more large-scale studies.

Our current large-scale study aimed to establish a valid and reliable instrument for monitoring and assessing TPACK development in secondary mathematics PSTs, including the seven interrelated knowledge domains that TPACK encompasses. In theory, a valid and reliable TPACK instrument for this population would permit secondary mathematics teacher preparation programs to longitudinally study program effectiveness at TPACK develop-ment, fine-tune program components, conduct large-scale multi-institution-al research studies, and make changes to maximize TPACK development in next generation of teachers of mathematics.

MethodOur goal was to develop an instrument that answers the need to monitor the development of TPACK in preservice secondary mathematics teachers throughout preparation programs. Adapting the TPACK survey for elemen-tary PSTs (Schmidt et al., 2009), this project focused on developing and validating a reliable content-specific survey for the population of interest: preservice secondary mathematics teachers.

Instrument DevelopmentWe began by examining the reliable and nonreliable items from the Schmidt et al. (2009) survey by deleting items that did not specifically pertain to the teaching of secondary mathematics. Specifically, we deleted the items relat-ing to social studies, literacy, and science, as the instrument was established for generalists at the elementary level. Next, we wrote an additional 22 items to fill gaps in the seven knowledge domain constructs (TK, PK, CK, PCK, TPK, TCK, TPACK) by focusing on specific content areas in mathematics. We wrote these items to adhere to item development guidelines (Fink, 2003; Fink & Kosecoff, 1998; Fowler, 2008; Pattern, 2001). Six researchers, includ-ing two external to the project, with expertise in secondary mathematics education reviewed all of the items to be included in the survey for content

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validity (Lawshe, 1975), even though the Schmidt survey development team had previously vetted many of the survey items. We then revised seven items based on the feedback from the expert panel. Three items received minor editing, such as moving a word to a different location in the item or using a word with similar meaning that was more specific to mathematics. Six items received major editing, such as completely restructuring the item wording. After this revision, the final survey instrument contained 62 items consisting of 8 TK items, 8 CK items, 8 PK items, 7 PCK items, 7 TPK items, 12 TCK items, and 12 TPACK items. Each item used a 5-point Likert scale response (SD = “strongly disagree,” D = “disagree,” N = “neither agree nor disagree,” A = “agree,” SA = “strongly agree”).

For the purposes of this study, we designed a cover sheet to collect addi-tional demographic data, including participants’ age, level in college, practi-cum experience, gender, and ethnicity. We also designed an additional cover sheet to gather information about the context in which data was collected, including the name of the course for which the survey was administered, date of survey, whether students completed a technology course, if technol-ogy is used in mathematics content courses, and the grade-band of teacher certification for secondary mathematics at each respective institution.

ParticipantsThe research team sought to collect data from a variety of secondary math-ematics teacher preparation programs across the United States in an effort to maximize the diversity in our national sample. For this project, diversity included size of institution, type of institution, size of secondary mathemat-ics education program, demographics of student population, experience of faculty teaching program courses, and geographic location. We contacted 24 secondary mathematics education faculty around the country to inquire whether they would be willing to administer the survey to their PSTs. Half (12) agreed to organize administering the survey in addition to the three institutions of the co-authors. The sample was a mix of convenience and strategically chosen institutions to produce a diverse sample. To maximize authentic responses and completion rates, paper surveys were administered in classes rather than online out-of-class surveys (Adams & Gale, 1982; Lefever, Dal, & Matthiasdottir, 2007; Norris & Conn, 2005). Faculty were encouraged to arrange administering the survey at the start of class but were permitted to administer the survey at their convenience. Faculty had gradu-ate students or teaching assistants administer the survey in accordance with IRB requirements. Due to these efforts, our survey completion return rate was over 90% and as we will mention later, the surveys returned seemed to contain predominantly legitimate responses.

We collected 315 surveys completed by PSTs prior to student teaching from 15 institutions across the United States (see Table 1) with class sizes ranging from 4 to 26 students during the 2010–11 academic year. Survey

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administrators at different sites reported that the survey took an average of 15–20 minutes for participants to complete after the instructions were read and any questions were addressed. Upon receiving the completed surveys from each institution, the project’s principal investigator worked with his graduate assistant to begin coding the paper survey responses into spread-sheet format. We created a simple spreadsheet for all 315 returned surveys, which included the demographic responses in Table 1 as well as the re-sponses to the 62-item survey. To guarantee accurate coding, an additional graduate student randomly selected 25% of the surveys and rechecked the original spreadsheet entries. Four entry cells were miscoded (<0.001% error rate), so the graduate student rechecked the remaining 75% of the surveys,

Table 1. Demographic Data of Total Responses

% by region % by institution type

Variable % MW NE SE W RI RT

Age

< 19 0.3 1.5 0.0 0.0 0.0 0.7 0.0

19–22 68.3 89.7 66.7 62.8 40.6 67.1 68.2

23–26 19.0 5.9 15.8 22.6 43.8 19.9 20.3

27–30 2.9 0.0 3.5 3.6 6.3 2.1 4.1

> 30 9.5 2.9 12.3 11.7 9.4 11.0 8.8

Class

Sophomore 8.6 36.8 3.5 0.0 0.0 6.8 12.2

Junior 17.8 16.2 26.3 16.8 0.0 17.1 16.2

Senior 50.8 41.2 40.4 61.3 50.0 43.8 58.8

Graduate 20.6 2.9 26.3 21.2 50.0 30.8 12.2

Gender

Male 32.4 39.7 24.6 32.1 43.8 32.2 25.0

Female 67.3 60.3 75.4 67.9 53.1 67.8 75.0

Practicum

Yes 58.4 46.0 44.0 70.0 59.0 69.9 47.3

No 41.6 54.0 56.0 30.0 41.0 30.1 52.7

Ethnicity

African Am 4.1 36.8 1.8 5.8 3.1 6.2 2.0

Am Indian 0.3 0.0 0.0 0.7 0.0 0.0 0.7

Asian 1.3 0.0 3.5 0.7 3.1 2.1 0.7

Hisp/Latino 3.5 1.5 1.8 0.7 25.0 0.7 6.1

Pac Islander 1.0 0.0 1.8 0.7 3.1 0.7 0.7

White 85.7 94.1 84.2 88.3 56.3 87.0 83.1

Other 2.2 1.5 5.3 0.7 3.1 0.7 6.1

Notes:. Regional classifications (Midwest, Northeast, Southeast, West) based on higher education consortia’s of states (e.g. West-ern Interstate Commission on Higher Education). Institutional classification based on Carnegie classification and labeled as either RI=Research Intensive, RT=Some research and/or Teaching only. Some percentages may not sum to 100 due to non-responses and/or rounding.

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found an additional eight cell-entry errors, and corrected them. The project PI then randomly selected 10% of the surveys and found no entry errors. This verification method of checking, correcting, and rechecking authenti-cates that the 19,530 cells in the spreadsheet had virtually a zero error rate for entry before the analyses.

The final sample reported in Table 1 reflects 49.6% of responses from sec-ondary mathematics PSTs at eight research-intensive, institutions with the remaining amount coming from seven institutions with some research activ-ity and/or teaching only. The national sample consisted of responses from institutions in the Midwest (23.1%), Northeast (19.4%), Southeast (46.6%), and West (10.9%) regions of the United States. Our sample oversampled approximately 10% higher in the Southeast and 10% lower in the West when examining the 2010 U.S. census populations. The Midwest and Northeast are within 2% of census populations to the region.

Determining the Final Sample for AnalysisAs the participants were asked to complete the survey in class, they may have felt compelled or obligated to complete the survey but lacked the motivation to engage in the survey. To account for this possible lack of engagement, we used four criteria for removing cases from the sample that demonstrated lack of engagement. First, the research team determined that students who gave nearly the same response for all items on the survey dem-onstrated a lack of engagement, so we examined all 315 completed surveys for less than 10% variance in the responses. Four surveys met the first filter criteria with respective total survey variances of responses with 1.6%, 3.2%, 4.9%, and 6.4% (the next closest variation was 10.8%). We deleted these four surveys. Similarly, if we found zero variance on any one of three pages of survey items (approximately 20 items), we removed those surveys. We removed 14 remaining surveys that met this criterion, 4 of which had more than one page with zero variance, indicating nonengagement in reading the items and distinguishing any variation on roughly 20 items. Third, we per-formed a manual inspection of surveys to look for patterning to determine if students appeared to fill in their responses in unlikely ways. We determined patterning on two surveys not already deleted. One survey had responses that were 1, 2, 3, 4, 5, 4, 3, 2, 1, etc., item to item, and the other alternated between two responses for every item. Fourth, we applied the criterion of completeness (all 62 items answered) and removed one incomplete survey from the sample. In all, we removed 21 surveys (6.67% of the sample) from the 315 surveys completed, resulting in a sample of 294 surveys for the main analysis on 62 items (18,228 cells).

Data AnalysisTo determine the structure of the TPACK instrument, we randomly split the data into two equal groups based on the overall TPACK summation score of

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Likert scale items so that the distribution between the two groups was the same. We used an exploratory factor analysis (EFA) with the first group of 147 student surveys to determine which items should be retained for the fi-nal instrument. We used a confirmatory factor analysis on the second group of 147 student surveys to verify the structure obtained through the explor-atory factor analysis. This method gives more strength and validity to the research method and results (Fink, 2003; Litwin, 1995; Thompson, 2004). To determine the internal reliability of each of the subscales, we used a graded response model (Samejima, 1996) with the full sample of 294 surveys to analyze the instrument in addition to the traditional Cronbach alpha for reliability measures.

Results

Exploratory Factor Analysis (EFA)Based on the theoretical construct that TPACK includes TK, CK, PK, PCK, TCK, and TPK, our initial analysis explored the possibility of seven fac-tors, one for each trait. However, the initial EFA on the data showed distinct factors only for TK (Factor 2), CK (Factor 5), PK (Factor 3), and TPACK (Factor 1) (see Table 2, p. 184). The items written to measure PCK, TCK, and TPK loaded on various factors with no obvious pattern or more than three items loading on a single factor. Therefore, we decided to remove the PCK, TCK, and TPK items from the remainder of the analysis and to leave the measurement of the two-knowledge latent traits for future studies with a new item development process.

After the removal of the PCK, TCK, and TPK items from the analysis, we completed an exploratory factor analysis on the remaining items with four factors. The four-factor analysis matches the data well, with TK loading on Factor 2, CK loading on Factor 3, PK loading on Factor 4, and TPACK load-ing on Factor 1 (see Table 3, p. 186).

Confirmatory Factor Analysis (CFA) and Internal Reliability MeasuresTo finalize the instrument, we performed a CFA using a four-factor structure and included all items with a factor loading greater than or equal to 0.500. During the analysis, we monitored particularly a number of fit indices and sta-tistics. Thompson (2004) indicates the CFA fit indices measures and statistics of particular interest for our particular instrument type are the chi-squared statistical significance test, non-normed fit index (NNFI), comparative fit in-dex (CFI), and root-mean-square error of approximation (RMSEA). Further, Thompson indicates that all four should be carefully examined and considered to determine a final model. The non-normed and comparative fit statistics should be close to 0.95 or greater to indicate an excellent model fit (0.90–0.95 is acceptable to good). The RMSEA estimates how well the model parameters will perform at reproducing the population covariances. The RMSEA should

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Table 2. Factor Loadings for EFA with Varimax Rotation of Seven Factors

Item Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7

TK01 -0.175 0.738 -0.226

TK02 -0.274 0.837

TK03 0.860 -0.187 0.141

TK04 0.845 -0.121

TK05 0.695

TK06 0.739 -0.134 0.169 0.103

TK07 0.228 0.513 -0.102 0.157

TK08 0.120 -0.421 0.203 -0.113

CK09 -0.196 -0.102 0.732

CK10 0.103 0.899 -0.276

CK11 0.778 -0.265

CK12 0.503 0.170

CK13 -0.159 0.564 0.199

CK14 0.128 0.491 0.345

CK15 -0.183 -0.127 0.257 0.640

CK16 -0.154 0.119 0.451 0.203

PK17 0.627 0.130 -0.101

PK18 -0.120 0.828

PK19 -0.168 0.147 0.907 -0.179

PK20 -0.149 0.766

PK21 0.252 0.613 -0.165 -0.125

PK22 0.443 0.262

PK23 0.436 -0.144 0.191

PK24 0.630 0.132 0.110

PCK25 0.386 0.146 0.233

PCK26 0.168 0.659

PCK27 -0.180 0.110 0.751

PCK28 0.342 0.235 0.209 -0.167

PCK29 0.193 0.129 0.189 0.151 0.109

PCK30 -0.151 0.180 0.591

PCK31 -0.161 -0.173 0.130 0.501 0.144 0.291 0.152

TCK32 0.318 -0.100 0.219 -0.162 0.441

TCK33 -0.145 0.536 -0.194

TCK34 0.494 -0.107 0.375 -0.123 -0.323

TCK35 0.608 0.124 -0.259 0.102 -0.390

TCK36 0.872 -0.116 -0.128

TCK37 -0.111 0.754

TCK38 0.349 0.148 -0.171 -0.213

TPK39 0.733 -0.111 -0.121 -0.206

TPK40 0.713 -0.127 0.146 0.150 -0.128 -0.172

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be zero if we can produce the exact population covariance. Values approxi-mately 0.06 or less are considered very reasonable for a model fit. Once we determined the finalized instrument through a CFA, we checked internal reliability for measuring the internal consistency on each unidimensional construct. The statistics for internal reliability are the Cronbach’s alpha, stan-dard error of measurement, and number of respondents within one and two standard deviations (Cronbach & Shavelson, 2004; Green, Lissitz, & Mulaik, 1977; Schmitt, 1996). Cronbach’s alpha is used to indicate the degree to which set of items measures the unidimensional construct and is acceptable when greater than 0.70, good when greater than 0.80, and excellent when greater than 0.90. Reporting the standard errors and respondents within one and two standard deviations demonstrates a normalized set of responses from the population and determines if there is a strong skew in the respons-es for each construct.

Confirmatory factor analysis (CFA). Using the second group of 147 students, the CFA was conducted. The initial analysis had some minor questions with fit to explore and refine. Using an iterative process of removing items with

Table 2 continued

Item Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7

TPK41 0.488 0.131 0.192 -0.195

TPK42 0.485 0.198 0.106 0.109 -0.303

TPK43 0.583 0.156 -0.236

TPK44 -0.134 0.256

TPK45 0.207 0.542 0.113

TPK46 0.143 0.188 -0.112 0.120 0.322

TPK47 0.457 0.146 0.129 0.159 -0.172

TPK48 0.124 -0.187

TPK49 0.254 -0.118 0.262 -0.105

TPK50 0.147 0.159 -0.112 -0.254

TPACK51 0.759 -0.115 0.149 0.122

TPACK52 0.987 -0.150 -0.197 -0.156

TPACK53 1.009 -0.141 -0.120 -0.147 -0.101

TPACK54 0.495 0.255 -0.119

TPACK55 0.717 0.149 0.219

TPACK56 0.505 0.204 0.354

TPACK57 0.321 0.157 0.184 -0.193 0.534 0.335

TPACK58 0.210 -0.131 0.748 0.269

TPACK59 0.758 0.249

TPACK60 0.623 -0.185 0.119 0.219 0.259

TPACK61 0.119 0.913 0.491

TPACK62 -0.121 0.802 0.390

Notes. Factor loadings ≥ 0.500 are in boldface. Test of the hypothesis is that seven factors are sufficient. Chi-square statistic is 2375.54 on 1,478 degrees of freedom, p<0.001.

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Table 3. Factor Loadings for EFA with Varimax Rotation of Four Factors.

Item Factor 1 Factor 2 Factor 3 Factor 4

TK01 -0.163 0.706

TK02 -0.248 0.848 0.102

TK03 0.843 -0.174

TK04 0.828 -0.114

TK05 0.115 0.669

TK06 0.713

TK07 0.212 0.462

TK08 0.120 -0.405 0.161

CK09 -0.197 0.755

CK10 0.725

CK11 -0.113 0.655

CK12 0.536 0.108

CK13 0.636

CK14 0.118 0.662

CK15 -0.113 -0.118 0.794

CK16 -0.166 0.632

PK17 0.667

PK18 0.801

PK19 -0.118 0.158 0.822

PK20 -0.123 0.758

PK21 0.195 -0.176 0.656

PK22 0.172 0.166 0.479

PK23 0.479

PK24 0.104 0.571

TPACK51 0.864 -0.103 -0.120

TPACK52 0.857 -0.151

TPACK53 0.923 -0.143

TPACK54 0.516 0.233 -0.154

TPACK55 0.798

TPACK56 0.239 0.490

TPACK57 0.570 0.154

TPACK58 0.386 0.236

TPACK59 0.829

TPACK60 0.750 0.133 -0.147

TPACK61 0.507 0.216 -0.141

TPACK62 0.281 0.100 0.305

Notes. Factor loadings ≥ 0.500 are in boldface. Test of the hypothesis is that four factors are sufficient. Chi-square statistic is 861.66 on 492 degrees of freedom, p<0.001.

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small loadings onto the desired factor and/or loadings onto undesired fac-tors, we established a final instrument with 22 items (6 TK, 5 CK, 5 PK, 6 TPACK). The iterative process included determining items that loaded onto multiple factors. For example, we deleted TPACK62 due to cross-loading almost equally on two constructs. Items with less than a 0.5 factor loading were considered for deletion. Remaining items with a factor loading over 0.5 were examined for high correlations with other items. The remaining items deleted were due to high correlations with other times. For example, TPACK54 had a high correlation (>0.8) with TPACK51. We determined that TPACK51 was a much stronger and more meaningful item than TPACK54. Further, some of the indices indicated that the fit would be greatly improved by removing CK10 and allowing TPACK59 and TPACK60 to interact. This is natural, as the geometry and algebra items for TPACK should have some correlation for secondary mathematics PSTs because much of the content is interconnected (NCTM, 2000). The CFA for four factors is presented in Table 4 (p. 188).

Further, as the analysis of the instrument includes using a graded re-sponse model to estimate the standard error curve, each of the subscales must be confirmed to be unidimensional. To verify the unidimensionality, we analyzed each subscale (TK, CK, PK, TPACK) using all 294 students.

Internal reliability. The Technology Knowledge (TK) subscale had a Cronbach’s alpha of 0.8899 with the graded response model (see Figure 2, p. 189) giving a standard error of measurement below 0.35 for most of the respondents. For the TK subscale, 74% of the respondents were within one standard deviation of the mean, and 96% were within two standard devia-tions of the mean.

The Content Knowledge (CK) subscale had a Cronbach’s alpha of 0.8554 with the graded response model (see Figure 3, p. 189) giving a standard error of mea-surement below 0.53 for participants within one standard deviation of the mean. For the CK subscale, 73% of the respondents were within one standard deviation of the mean, and 99% were within two standard deviations of the mean.

The Pedagogical Knowledge (PK) subscale had a Cronbach’s alpha of 0.8768 with a graded response model (see Figure 4, p. 190), giving a stan-dard error of measurement below 0.5 for all of the participants. For the PK sub-scale, 72% of the respondents were within one standard deviation of the mean and 93% were within two standard deviations of the mean.

The TPACK subscale had a Cronbach’s alpha of 0.8966 with a graded re-sponse model (see Figure 5, p. 190) giving a standard error of measurement below 0.5 for almost all of the participants. For the TPACK subscale, 71% of the respondents were within one standard deviation of the mean, and 94% were within two standard deviations of the mean.

As Cronbach’s alpha for each of the four subscales is above a 0.85 for each construct, the internal reliability is very good to excellent in measure for differences at the group level, and therefore the subscales meet the desired

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requirements for survey research instruments (DeVellis, 2011). The iterative item removal process resulted in a model with good to excellent fit indices. The model fit index statistics are presented in Table 5 (p. 191), and the over-all model is presented as a diagram (see Figure 6, p. 192).

The chi-square statistic for the PK subscale is worth further discussion. Thompson (2004) indicates this statistic is important but not the end-all statistic. However, all the fit indices need serious consideration as well. Our

Table 4. Factor Loadings for CFA with Varimax Rotation of Four Factors after Iterative Process for Item Removal

Item TPACK TK CK PK

TK01 0.663

TK02 -0.179 0.801

TK03 0.853 -0.161

TK04 0.831 -0.132

TK05 0.133 0.665

TK06 0.667

CK09 -0.228 0.774

CK10 0.826

CK11 0.754

CK12 0.579 0.102

CK13 0.593

CK14 0.108 0.555

PK17 0.142 0.625

PK18 0.821

PK19 -0.109 0.133 0.827

PK20 -0.121 0.730

PK21 0.208 0.608

TPACK51 0.801 -0.122

TPACK52 0.880 -0.103

TPACK53 0.929

TPACK55 0.710 0.111

TPACK59 0.750

TPACK60 0.678 0.139 0.147 -0.152

Factor 1 Factor 2 Factor 3 Factor 4

SS loadings 3.949 3.541 2.963 2.738

Proportion Variance 0.172 0.154 0.129 0.119

Cumulative Variance 0.172 0.326 0.454 0.573

Factor Correlations

Factor 1 -0.333 0.438 0.347

Factor 2 -0.187 -0.348

Factor 3 0.348

Notes. Factor loadings ≥ 0.500 are in boldface. Test of the hypothesis is that four factors are sufficient. Chi-square statistic is 272.38 on 167 degrees of freedom, p<0.001.

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Figure 2. TK subscale standard error and participant distribution.

Figure 3. CK subscale standard error and participant distribution.

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Figure 4. PK subscale standard error and participant distribution.

Figure 5. TPACK subscale standard error and participant distribution.

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analysis leads us to conclude that the PK subscale is likely valid because all three fit indices are the strongest compared to the TK, CK, and TPACK subscales. The NFI, CFI, and RMSEA are all beyond excellent with respect to acceptable ranges for these fit indices for the PK subscale. Table 6 (p. 193) presents the final model with parameter estimates for the finalized items on the TPACK instrument for the TK, CK, PK, and TPACK constructs. The data presented includes the parameter estimates, standard errors, z-values, and model error term (e#) on each item.

Discussion

Key Findings and Extending the TPACK LiteratureThe methodology and data analysis provide a consistent protocol for de-veloping and testing an instrument that can be used for examining TPACK knowledge in secondary PSTs. In doing so, we report three major findings. First and foremost, the results from this research indicate a proficient instru-ment for monitoring and measuring secondary mathematics PSTs’ self-assessment of TK, PK, CK, and TPACK. This is the first survey instrument designed specifically for secondary mathematics PSTs. Unlike prior studies (e.g. Archambault & Crippen, 2009; Schmidt et al., 2009) that focused on teachers of multiple disciplines, our study was unique because it focused specifically on the next generation of teachers of mathematics.

Second, our findings revealed that PCK, TPK, and TPK items did not produce a measurable factor for each knowledge domain. This finding brings up an issue with trying to develop an instrument that can identify knowledge domains that overlap between two categories for secondary mathematics teachers. This result adds a finding to the literature that differs from the instrument of Schmidt et al. (2009), in which elementary PSTs reported a reliable seven-factor instrument. TPK, PCK, and TCK remain elusive to quantify and measure well through the survey items we tested. In fact, TPK, PCK, and TCK self-reporting may be more difficult for preservice mathematics teachers to grasp during preservice preparation. TPK, PCK, and TCK require PSTs to mentally remove one knowledge construct, which is abstract and likely difficult for PSTs to do when responding to these items. This could stem from the compartmentalized nature of many programs that

Table 5. Confirmatory Factor Analysis Statistical Fit Indices for Final Model and Subscales

Description Chi-square df p NNFI CFI RMSEA

Four-factor model 374.40 202 0.00000 0.940 0.947 0.052

TK subscale 37.67 9 0.00002 0.947 0.968 0.104

CK subscale 18.82 5 0.00207 0.945 0.972 0.097

PK subscale 8.60 5 0.12607 0.990 0.995 0.049

TPACK subscale 44.55 8 0.00000 0.932 0.964 0.125

Notes. Four-factor model statistics and each subscale unidimensionality statistics.

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Figu

re 6

. Con

firm

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ana

lysi

s m

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-fac

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divide pedagogy, technology, and content knowledge into separate courses. However, this may be supported by the reliability of the TK, PK, and CK items. Additional reasons may include the fact that specialized secondary education content areas are so content focused that PSTs may have difficulty removing one of the three knowledge domains in their own minds.

Lastly, the correlation (see Figure 6) between the four factors revealed that TK and PK have a very low correlation (0.020), whereas the others all have moderate correlations (≥0.348). So we examined these factor correlations further. We interpret these correlational findings to imply that TPACK is cor-related moderately with TK, PK, and CK. The relationship is nearly the same for each factor. This indicates that TPACK development may be influenced by each factor about the same. CK’s correlation to PK and TK is about the same, implying that CK may be influenced by both PK and TK about the same. However, the low TK–PK relationship may indicate that preservice secondary mathematics teachers (PSMTs) who have made up their minds about pedago-gy strategies (PK) may not be strong candidates for believing they do not need

Table 6. Final Survey Instrument Model Statistics for Four-Factor Model

ItemParameterCoefficient

StandardError (SE)

Error Terme#

Error Term SE

TK01 0.629 0.049 0.472 0.042

TK02 0.638 0.040 0.251 0.026

TK03 0.744 0.046 0.316 0.033

TK04 0.765 0.049 0.395 0.039

TK05 0.679 0.049 0.442 0.041

TK06 0.575 0.039 0.273 0.026

CK09 0.312 0.029 0.174 0.016

CK11 0.411 0.030 0.145 0.016

CK12 0.451 0.032 0.161 0.018

CK13 0.360 0.031 0.184 0.018

CK14 0.524 0.044 0.364 0.035

PK17 0.488 0.034 0.205 0.020

PK18 0.500 0.032 0.156 0.017

PK19 0.499 0.034 0.195 0.019

PK20 0.505 0.032 0.163 0.017

PK21 0.461 0.034 0.220 0.021

TPACK51 0.465 0.034 0.230 0.021

TPACK52 0.568 0.032 0.126 0.015

TPACK53 0.557 0.033 0.156 0.017

TPACK55 0.553 0.036 0.214 0.022

TPACK59 0.531 0.038 0.260 0.024

TPACK60 0.515 0.041 0.342 0.031

Notes. Z-values for all 22 items >8.97 with p<0.0001. The error term (SE) values for the interaction between TPACK59 and TPACK60 is 0.113 (0.021).

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TK. On the other hand, if PSMTs have strong TK, it does not imply that they see they have strong pedagogy beliefs. The key finding of all this sense-making is that the fact that CK is correlated well with PK and TK may simply imply that higher CK is likely when PSMTs have higher TK and PK, instead of that a PSMT with lower TK or PK will have lower content knowledge. It could be possible that PSMTs with more education methods courses may have stronger CK, as K–12 content is focused on more in those courses, as opposed to math-ematics department upper-division content courses (e.g., analysis, abstract algebra). PSMTs who have completed upper-division mathematics courses may perceive themselves as having lower CK because their strong self-efficacy in mathematics may be challenged in theoretical-based courses.

With these results, our goal of developing a valid and reliable instrument to monitor and assess preservice mathematics teachers’ TPACK develop-ment within teacher education programs was lucrative for a four-factor in-strument. Although no instrument is perfect, our instrument provides a ro-bust survey aimed at one specific population that traditionally is very small at respective institutions of higher education, making it nearly impossible to largely quantify TPACK components through research at one or even a few institutions. This adds to the TPACK literature with a large-scale quantita-tive study of a historically low population, institution to institution, in the United States. Our instrument builds on the work of Mishra and Koehler (2005a, 2005b, 2006) through the adapting of the Schmidt et al. work (2009). We extend the TPACK literature domain with this instrument as compared to previous study findings for different populations.

The main goal of this research project was to develop a valid and reliable instrument for the population of secondary mathematics PSTs to help math-ematics teacher educators (MTEs) monitor and assess their own programs’ ability to develop TPACK in their PSTs. The data from this research resulted in survey items to reliably monitor and assess the constructs of TK, PK, CK, and TPACK so historically low populations of students at institutions can use a valid and reliable instrument to examine their program effectiveness. This instrument can be used to better inform a single program course and can provide overall information for an entire program. If the instrument is applied as a pre–post survey for a program, the information does not provide detailed information regarding course specific material. A limitation arises with programs where secondary mathematics PSMTs’ content knowl-edge is targeted by a mathematics department and their pedagogical knowl-edge is targeted by an education department, and there is a lack of commu-nication between both departments. This is not uncommon in secondary mathematics teacher preparation programs across the United States.

This study was not specifically about what students know, but rather an objective assessment of what they think they know. PSMTs’ personal beliefs change positively and negatively over time during preservice prepara-tion. This instrument gives researchers and educators the ability to reliably

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measure these beliefs regarding TPACK and the contributing factors of PK, TK, and CK during preservice preparation programs. PSMTs can easily be overconfident or lack confidence. Our experiences provide us with knowl-edge that PSMTs can be exposed to new ways of thinking during coursework and improve or diminish their sense of self-efficacy. Learning can go in both directions, so our study provides an opportunity for programs and educators to understand their learning environment to improve TPACK development in PSMTs.

LimitationsA limitation worth noting is the potential of variation in the administration of surveys. Specific instructions were given to each site, and we rely on the professionals following those guidelines, and we must rely on an assumption that the surveys were administered in a similar fashion at each institution. More significant, we were unable to isolate PCK, TCK, and TPK knowledge domains specifically in the population of secondary mathematics PSTs. We acknowledge that this is limiting in terms of the use of our survey, yet we see unearthing such a limitation as a key finding in expanding the TPACK literature domain.

Implications for Practice, Directions for Future ResearchIt is imperative that we develop TPACK in our preservice mathematics teachers in order to fully enact the vision for teaching set forth by AMTE, CCSSM, and NCTM. The finalized instrument presented in Table 6 (p. 193) represents a valid, reliable, and manageable 22-item survey (or 16 items without TPACK items) with which secondary mathematics teacher educa-tion programs can monitor and assess PSMTs’ perceptions of their devel-opment of TPACK. Further, for the successful integration of technology into the teaching of secondary mathematics, preservice teachers need to be comfortable with their own perceived abilities to do so during their prepara-tion programs. Our instrument will give researchers and MTEs the ability to conduct TPACK research in preservice courses and programs using a variety of methods.

First, using the instrument in a pre–post format can allow for and detect changes over a semester course or during the student teaching internship. We see the instrument, for example, aiding in discovering which cooperat-ing teachers are effective at helping grow TPACK in PSMTs during their student teaching. This instrument can also be used longitudinally over two years. This will provide insights into when and what aspects of preparation programs improve PSMTs’ perceptions of TPACK knowledge growth. We also see this instrument as useful in the development of TPACK practices in the classroom accompanied by an observational instrument (e.g., Hofer et al., 2011). This research needs to be done in the future. Additionally, there may be potential in using the instrument to help PSTs recognize their own

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professional growth and development. Helping PSTs overcome their precon-ceived beliefs is difficult, yet this instrument can aid in the development and assessment early in a preparation program.

In the future, mixed-methods research designs would be strong for exam-ining TPACK in PSTs using this survey along with classroom observational techniques, including interviews and video analyses. Moreover, combining our instrument with observations during student teaching may provide a rich data set of both quantitative and qualitative data. Such a rich set of data will allow for strong, valid, and more generalizable research findings. Fur-ther, it would be useful to begin to index specific curricular events (e.g., in-structional strategies, assignments, goals) or clinical experiences for growth in TPACK and improvement in the technological self-efficacy of PSTs. This can be accomplished by using this instrument as an element of large-scale comparative studies.

There is a great deal of work to be done with respect to TPACK develop-ment in the next generation of secondary mathematics preservice teachers. We hope our instrument will aid in some of that work.

AcknowledgmentsThe authors wish to thank individuals who helped us by administering or arranging the admin-istration of our survey to the secondary mathematics preservice teachers at their respective insti-tutions. Thank you, Ginny Bohme, Daniel Brahier, Anna Marie Conner, Kelly Edenfield, Carla Gerberry, Shannon Guerrero, Gary Martin, Ginger Rhodes, Wendy Sanchez, Tommy Smith, Toni Smith, Jami Stone, Anthony Thompson, and Jan Yow. We also wish to express our gratitude to the preservice secondary mathematics teachers who engaged and diligently completed surveys at each of the respective institutions of higher education. Finally, we wish to thank Barbara and Robert Reys for their visionary mission to link early career mathematics teacher educators through the STaR program to advance the future of the mathematics education field. Without their hard work and the mentoring professionals of the STaR program, the data collection for this project may have taken years and the professional relationships might never have been established.

Author Notes

Jeremy Zelkowski, PhD, is an assistant professor of secondary mathematics education in the Department of Curriculum and Instructions in the College of Education at the University of Alabama, Tuscaloosa. His research interests focus on TPACK development in preservice teachers, appropriate use of technology in teaching mathematics, mathematical college readiness, and pro-fessional development learning communities. Please address correspondence regarding this article to Dr. Jeremy Zelkowski, Department of Curriculum and Instruction, University of Alabama, 902 University Blvd, Tuscaloosa, AL 35487-0232. Email: [email protected]

Jim Gleason, PhD, is an associate professor in the Department of Mathematics in the College of Arts & Sciences at the University of Alabama, Tuscaloosa. His research interests focus on teacher content knowledge, assessment, and psychometrics pertaining to mathematics teaching and learning.

Dana C. Cox, PhD, is an assistant professor in the Department of Mathematics in the College of Arts & Sciences at Miami University, Oxford, Ohio. Her research interests focus on curriculum design, TPACK development in preservice teachers, and studying the emergent professional vision of teaching with technology held by preservice teachers.

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Stephen Bismarck, PhD, is an assistant professor of middle/secondary mathematics education in the School of Education at the University of South Carolina—Upstate in Spartanburg. His research interests focus on appropriate use of technology, developing mathematical knowledge for teaching with preservice teachers, and exploring best practices for building conceptual knowledge.

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Manuscript received April 3, 2013 | Initial decision April 26, 2013 | Revised manuscript accepted May 20, 2013

Appendix A

Administered SurveyThank you for taking time to complete this survey. Please answer each question to the best of your knowledge. You should answer demographic information first, then read each item and choose your first belief. You need not spend any lengthy time on any one item. You should be finished in about 15 minutes.

Your thoughtfulness and candid responses will be greatly appreciated. Your confi-dentiality will not be compromised and your name will not, at any time, be associated with your responses.

Your responses will be kept completely confidential and will not influence your course grade.

Demographic Information

Age range:

a. Under 19b. 19–22c 23–26d. 27–30e. 30+

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Year in college:

a. Freshmanb Sophomorec. Juniord. Seniore. Graduate student

Have you completed a practicum or clinical placement in a middle grades or high school math classroom?

a. Yesb. No

Gender:

a. Maleb. Femalec. I prefer not to say

Ethnicity:

a. African American or blackb. Alaskan Nativec. American Indiand. Asiane. Hispanic or Latinof. Pacific Islanderg. White or Caucasianh. Other: _____________i. I prefer not to say

Technology is a broad concept that can mean a lot of different things. For the purpose of this questionnaire, technology is referring to digital technology/technologies—that is, the digital tools we use, such as computers, laptops, iPods, handhelds, interactive whiteboards, computer software programs, graphing calculators, etc. Please answer all of the questions, and if you are uncertain of or neutral about your response, you may always select “Neither agree nor disagree.”

All items appeared as a SD, D, N, A, SA response set up.

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TK1 I know how to solve my own technical problems.

TK2 I can learn technology easily.

TK3 I keep up with important new technologies.

TK4 I frequently play around with the technology.

TK5 I know about a lot of different technologies.

TK6 I have the technical skills I need to use technology.

TK7 I have had sufficient opportunities to work with different technologies.

TK8 When I encounter a problem using technology, I seek outside help.

CK9 I have sufficient knowledge about mathematics.

CK10 I can use mathematical ways of thinking.

CK11 I have various strategies for developing my understanding of mathematics.

CK12 I know about various examples of how mathematics applies in the real world.

CK13 I have a deep and wide understanding of algebra.

CK14 I have a deep and wide understanding of geometry.

CK15 I have a deep and wide understanding of calculus.

CK16 I have a deep and wide understanding of advanced undergraduate mathematics.

PK17 I know how to assess student performance in a classroom.

PK18 I can adapt my teaching based upon what students currently understand or do not understand.

PK19 I can adapt my teaching style to different learners.

PK20 I can assess student learning in multiple ways.

PK21 I can use a wide range of teaching approaches in a classroom setting.

PK22 I am familiar with common student understandings and misconceptions.

PK23 I know how to organize and maintain classroom management.

PK24 I know when it is appropriate to use a variety of teaching approaches (e.g., problem/proj-ect-based learning, inquiry learning, collaborative learning, direct instruction) in a classroom setting.

PCK25 I know how to select effective teaching approaches to guide student thinking and learning in mathematics.

PCK26 I know different teaching approaches to teach ratio and proportion concepts.

PCK27 I know different strategies/approaches for teaching probability and statistics concepts.

PCK28 I know different strategies/approaches for teaching algebra concepts.

PCK29 I know different strategies/approaches for teaching geometry concepts.

PCK30 I know different strategies/approaches for teaching trigonometry concepts.

PCK31 I know different strategies/approaches for teaching calculus concepts.

TCK32 I know about technologies that I can use for understanding and doing ratio and proportion.

TCK33 I know about technologies that I can use for understanding and doing probability and statistics.

TCK34 I know about technologies that I can use for understanding and doing algebra.

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TCK35 I know about technologies that I can use for understanding and doing geometry.

TCK36 I know about technologies that I can use for understanding and doing trigonometry.

TCK37 I know about technologies that I can use for understanding and doing calculus.

TCK38 I know that using appropriate technology can improve one’s understanding of mathematics concepts.

TPK39 I can choose technologies that enhance the teaching of a lesson.

TPK40 I can choose technologies that enhance students’ learning for a lesson.

TPK41 My teacher education program has caused me to think more deeply about how technology could influence the teaching approaches I use in my classroom.

TPK42 I am thinking critically about how to use technology in my classroom.

TPK43 I can adapt the use of the technologies that I am learning about to different teaching activities.

TPK44 Different teaching approaches require different technologies.

TPK45 I have the technical skills I need to use technology appropriately in teaching.

TPK46 I have the classroom management skills I need to use technology appropriately in teaching.

TPK47 I know how to use technology in different instructional approaches.

TPK48 My teaching approaches change when I use technologies in a classroom.

TPK49 Knowing how to use a certain technology means that I can use it for teaching.

TPK50 Different technologies require different teaching approaches.

TPACK51 I can use strategies that combine mathematics, technologies, and teaching approaches that I learned about in my coursework in my classroom.

TPACK52 I can choose technologies that enhance the mathematics for a lesson.

TPACK53 I can select technologies to use in my classroom that enhance what I teach, how I teach, and what students learn.

TPACK54 I can provide leadership in helping others to coordinate the use of mathematics, technologies, and teaching approaches at my school and/or district.

TPACK55 I can teach lessons that appropriately combine mathematics, technologies, and teaching approaches.

TPACK56 Integrating technology in teaching mathematics will be easy and straightforward for me.

TPACK57 I can teach lessons that appropriately combine ratio and proportion, technologies, and teaching approaches.

TPACK58 I can teach lessons that appropriately combine probability and statistics, technologies, and teaching approaches.

TPACK59 I can teach lessons that appropriately combine algebra, technologies, and teaching approaches.

TPACK60 I can teach lessons that appropriately combine geometry, technologies, and teaching approaches.

TPACK61 I can teach lessons that appropriately combine trigonometry, technologies, and teaching approaches.

TPACK62 I can teach lessons that appropriately combine calculus, technologies, and teaching approaches.

This survey was spread out in a four page format so items did not appear to run together.

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Appendix B

Finalized Survey ItemsTK1 I know how to solve my own technical problems.

TK2 I can learn technology easily.

TK3 I keep up with important new technologies.

TK4 I frequently play around with the technology.

TK5 I know about a lot of different technologies.

TK6 I have the technical skills I need to use technology.

CK9 I have sufficient knowledge about mathematics.

CK11 I have various strategies for developing my understanding of mathematics.

CK12 I know about various examples of how mathematics applies in the real world.

CK13 I have a deep and wide understanding of algebra.

CK14 I have a deep and wide understanding of geometry.

PK17 I know how to assess student performance in a classroom.

PK18 I can adapt my teaching based upon what students currently understand or do not understand.

PK19 I can adapt my teaching style to different learners.

PK20 I can assess student learning in multiple ways.

PK21 I can use a wide range of teaching approaches in a classroom setting.

TPACK51 I can use strategies that combine mathematics, technologies, and teaching approaches that I learned about in my coursework in my classroom.

TPACK52 I can choose technologies that enhance the mathematics for a lesson.

TPACK53 I can select technologies to use in my classroom that enhance what I teach, how I teach, and what students learn.

TPACK55 I can teach lessons that appropriately combine mathematics, technologies, and teaching approaches.

TPACK59 I can teach lessons that appropriately combine algebra, technologies, and teaching approaches.

TPACK60 I can teach lessons that appropriately combine geometry, technologies, and teaching approaches.

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Documents

Developing and Validating a Reliable TPACK Instrument for Secondary Mathematics Preservice Teachers