EDEL 3250 #9

Gabcast! EDEL 3250 #9

EDEL 3250 #8

Gabcast! EDEL 3250 #8

Chapter 4: Results

Technical Use Analysis

The first important step in clarifying the concepts of technological content knowledge, technological pedagogical knowledge, and technological pedagogical content knowledge was to determine how each of the terms were previously used in the literature. The primary resources for this technical use analysis were the recently published Handbook of Technological Pedagogical Content Knowledge (TPCK) for Educators as well as the Proceedings of the International Conference of the Society for Information Technology and Teacher Education for 2007 and 2008. Additional articles from the researcher’s literature review on TPCK were also utilized.

To complete the technical use analysis, the researcher read through each resource making note of definitions of each of the constructs. For this analysis, only phrases that were explicitly used to define or describe the constructs were chosen. After compiling these definitions, the researcher analyzed each definition for its essential features. She then compared the definitions to look for common attributes as well as differences.

Technological Content Knowledge (TCK)

The researcher noted 13 definitions of TCK in the selected resources (See Table 4.1). As defined by Koehler and Mishra, TCK is an “understanding of the impact of technology on the practices and knowledge of a given discipline (2008, p. 16, italics added). Indeed, all but one of the definitions cited here include the concepts of technology and content and some form of relationship between them. This interaction is expressed in a number of ways including impact (Koehler & Mishra, 2008, p. 16), influence and constrain (Koehler & Mishra, 2008, p. 16), dictates or changes (Koehler & MIshra, 2008, p. 16), representation (Koehler & Mishra, 2008, p. 21), reconceptualization (Hughes & Scharber, 2008, p. 102), interconnected (van Olphen, 2008, p. 113), reciprocally related (Mishra & Koehler, 2006, p. 1028), changed (Mishra & Koehler, 2006, p. 1028), transformed (Koehler & Mishra, 2005a, p. 134), affords and constrains (Mishra & Koehler, 2007, p. 2220), limit (Mishra & Koehler, 2007, p. 2220), electronic format (Archambault, 2008, p. 5192), and interaction (Robertson, 2008, p. 2219).

Table 4.1. Definitions of TCK found in the literature.

Definitions of TCK found in the literature

“Understanding the impact of technology on the practices and knowledge of a given discipline.” (Koehler & Mishra, 2008, p. 16) “an understanding of the manner in which technology and content influence and constrain one another.” (Koehler & Mishra, 2008, p. 16) “Teachers need to understand which specific technologies are best suited for addressing subject-matter learning in their domains and how the content dictates or perhaps even changes the technology – or vice versa.” (Koehler & Mishra, 2008, p. 16) “the relationships between technology and content representations” (Koehler & Mishra, 2008, p. 21) “how technological changes in our society affect these reconceptualizations of literacy” (102) “what teachers know about how technology and subject matter knowledge are interconnected (Koehler & Mishra, 2005). Specifically, TCK for foreign language teachers is defined as the body of knowledge that teachers have about their target language and its culture and how technology is used to represent this knowledge.” (113, emphasis added) “knowledge about the manner in which technology and content are reciprocally related.” (2006,1028) “Teachers need to know not just the subject matter they teach but also the manner in which the subject matter can be changed by the application of technology.” (2006, 1028) “useful for describing teachers knowledge of how a subject matter is transformed by the application of technology (e.g., the use of simulations in physics).” (2005a, 134) “The choice of technologies affords and constrains the types of content ideas that can be taught. Likewise, certain content decisions can limit the types of technologies that can be used. Technology constrains the types of possible representations but conversely affords the construction of newer and more varied representations. Furthermore, technological tools can provide a greater degree of flexibility in navigating across these representations. Thus, we can define TCK as an understanding of the manner in which technology and content influence and constrain one another. Teachers need to master more than the subject matter they teach, they must also have a deep understanding of the manner in which the subject matter (or the kinds of representations that can be constructed) can be changed by the application of technology. Teachers need to understand which specific technologies are best suited for addressing subject-matter learning in their domains and how the content dictates or perhaps even changes the technology—or vice versa.” (Mishra & Koehler, 2007, p. 2220) “An essential part of the role of the online instructor is to not only have a strong command of their subject matter (content knowledge), but also be able to design and deliver materials and activities in an electronic format for students (technological content knowledge).” (Archambault, 2008, 5192) “that is technologies that could be considered new content in their disciplines.” (Hughes, 2008, 5229) “One short aside: the astute will notice that this modified model purports there is no such thing as an educationally-important “TC:” one cannot have meaningful expressions of technological content in education without first having a specific set of students, goals, and environment in mind (pedagogy). From page 1028 of the Mishra & Koehler (2006) paper: “Teachers need to know not just the subject matter they teach but also the manner in which the subject matter can be changed by the application of technology. For example, consider Geometer’s Sketchpad as a tool for teaching geometry. It allows students to play with shapes and form, making it easier to construct standard geometry proofs.” While I do not disagree that outside of education there may be room for a study of the pure interaction of content and technology, I believe that within education there is no such thing: to whit, even the example given by the authors assumes a certain age group, student skill-set, defined learning goals, and level of environmental support.” (Robertson, 2008, 2219)

Thus, it appears that TCK can be conceptualized as an understanding of the relationship between technology and content. In particular, that relationship seems to manifest itself in the representation of content through technology. However, Koehler and Mishra as well as Archambault add another dimension to TCK which may be the source of some of the confusion surrounding this construct. In two of their definitions, Koehler and Mishra mention teaching or learning and Archambault mentions students. These definitions seem to imply that, though pedagogy is theoretically not present in this construct, the classroom context is. Meanwhile, Robertson (2008) argues that TCK cannot exist in a classroom context as that context necessarily injects pedagogical considerations. This is one of the major questions that must be answered by TPCK experts. At this point in the conceptual analysis, pedagogical context will not be listed as an essential feature of the TCK construct.

Finally, one definition of TCK takes a very different stance on this construct. Hughes (2008, p. 5229) states that TCK is an understanding of “technologies that could be considered new content in their disciplines.” This statement seems to imply that TCK is, or at least involves, the acceptance of technology as a new area of study in a given content area – the teaching of appropriate technologies to students. There are few references in the TPCK literature to the teaching of technology to students. Most focus on the use of technology to teach content. However, this is a very important concept to consider in the attempt to clarify and define the constructs as students must learn how to use the technology, particularly those that are specific to a given content, in order to successfully implement them.

With the inclusion of this facet of TCK, a precising definition of this construct based on the technical use analysis may be: An understanding of the technologies that may be utilized in a given discipline and how the use of those technologies interacts with the content of that discipline. Examples of the construct from the same literature may help to further define the construct. These examples were specifically labeled as representing TCK in the literature.

Table 4.2 Examples of TCK found in the literature.

Examples of TCK found in the literature

“Inspiration, StorySpace, HyperStudio, ClarisWorks, a web-based asynchronous communication tool, and the Internet were used during the project.” (92) “thinking about the web’s applicability in education” (96) “learned about…web authoring to construct hypertext narratives.” (97) “determine if she could actually use the technology with her students in the ways she imagined.” (97-98)

“Understanding the contributions that CALL can make to the field of foreign language education” (114) “It is fundamental for teachers to understand how CALL shapes their teaching practices. The contributions of CALL to the field of foreign language education are crucial to the understanding of TCK.” (114) “synchronous networked discussions” (114) “the World Wide Web offers an ample spectrum of authentic materials for teachers and students.” (114) “the implementation of hypertext and hypermedia applications has proven to be of great benefit for the acquisition and retention of new vocabulary.” (115) “multimedia packages, hypermedia technologies, CALL software, and other media.” (115) “Researchers have found the use of Microsoft Word (and its editing tools) to be beneficial for both student-teacher and peer-review activities. Another example is the use of concordancing and other packages in teaching both English as a second language and modern languages.” (115) “asynchronous networks” or “telecommunication networks” (115) “One of the best assets that teachers can have for teaching culture is access to authentic materials and environments that, in most cases, are physically far away.” (115) “TCK is involved as teachers use chat tools to present content. Thus, the use of chat tools modifies the way teachers present content to the students.” (120)

“For example, consider Geometer’s Sketchpad as a tool for teaching geometry. It allows students to play with shapes and form, making it easier to construct standard geometry proofs. In this regard, the software program merely emulates what was done earlier when learning geometry. However, the computer program does more than that. By allowing students to ‘play’ with geometrical constructions, it also changes the nature of learning geometry itself; proofs by construction are a form of representation in mathematics that was not available prior to this technology. Similar arguments can be made for a range of other software products.” (1028)

“Juliet’s team also grappled with questions about how to represent some of the content. For example, in her face-to-face classes, she had students physically rearrange furniture to facilitate discussions about how physical space and furniture configurations influence people’s activity and interactions with one another. In order to accomplish that online, a technology expert created a module that allowed Juliet’s students to view and rearrange a virtual classroom floor plan. Subsequently, Juliet planned to use it in her face-to-face classes instead of having students physically move furniture around the room. Jim noted that his challenge with the content was that the online context required extensive preplanning and frontloading of content into the web site. This was counter to his face-to-face classes where he usually had a general structure in mind for the course but he liked the freedom to make small changes from week to week based on students’ needs and interests, and on his own continuing investigations into relevant literature. Mikala’s challenge was figuring out how to weave software applications into the content because all of the activities required students to use a variety of computer programs to do things like literature reviews, search for web-based resources, participate in synchronous and asynchronous conversations, and create power point presentations and spreadsheets.” (2211)

“For example, a response categorized as technological content knowledge would provide evidence of an understanding of how technology influenced mathematical knowledge including, but not limited to, the varied representations of a concept or procedure through technology.” (5266) “I enjoyed working with a partner and discussing different ideas and techniques of representing the math problem. I was challenging but very helpful to see two different representations of a math idea using the tutorial and sandbox.” (5267)

Technology Content Knowledge (TCK) Using technology can fundamentally change the way people understand math concepts. “aesthetic and practical decisions about how to lay out and “chunk” the content across the number of weeks the course would run, and looking into and experimenting with technological solutions for representing the content” (Peruski, Mishra, & Koehler, 2007, 2209-2210).

The confusion surrounding the TCK construct is more evident in the examples provided here. These examples vary from lists of technologies that might be used with a given content to detailed examples of how a teacher might use a given technology in the classroom. The only unifying idea throughout the examples is that of representation – more specifically, how technology can help teachers represent content in new ways.

Throughout this conceptual analysis, the researcher must focus on clarifying this construct through discussion with TPCK experts and classifying examples based on the essential features of the construct. Thus far, the essential features of TCK are: (1) the use of technology (2) in a particular content area (3) to change the representation of that content. Issues of concern with regard to TCK are: (1) whether a pedagogical context is appropriate when considering TCK and, if so, where the “line” between TCK and TPCK is; (2) whether listing technologies used in a particular content area constitutes a level of TCK; and (3) whether or not TCK can, in fact, exist in an educational context.

Technological Pedagogical Knowledge (TPK)

The researcher located 10 definitions of TPK in the selected resources (See Table 4.3). Koehler and Mishra (2008, p. 16) defined this construct as “an understanding of how teaching and learning changes when particular technologies are used.” After a review of the TPK definitions, components of the construct were revealed in more detail. First, TPK requires an understanding of the technological tools available for teaching and the affordances and constraints of each. Second, TPK includes knowing how to use those tools in an educational context, often by repurposing a tool not originally intended for instruction. Third, one with TPK could also recognize how the use of that technology interacts with pedagogy by either changing or supporting the strategies that are used and, conversely, how the choice of a particular pedagogical strategy will influence the choice of technology.

Table 4.3. Definitions of TPK found in the literature.

Definitions of TPK found in the literature

“an understanding of how teaching and learning changes when particular technologies are used. This includes knowing the pedagogical affordances and constraints of a range of technological tools as they relate to disciplinarily and developmentally appropriate pedagogical designs and strategies. This requires getting a deeper understanding of the constraints and affordances of technologies and the disciplinary contexts within which they function.” (Koehler & Mishra, 2008, p. 16-17) “an important part of TPK is developing creative flexibility with available tools in order to repurpose them for specific pedagogical purposes.” (Koehler & Mishra, 2008, p. 17) “TPK requires a forward-looking, creative, and open-minded seeking of technology, not for its own sake, but for the sake of advancing student learning and understanding.” (Koehler & Mishra, 2008, p. 17) “how to use digital tools to teach more effectively” (Koehler & Mishra, 2008, p. 21) “knowledge of the existence, components, and capabilities of various technologies as they are used in teaching and learning settings, and conversely, knowing how teaching might change as the result of using particular technologies.” (2006, 1028) “knowledge of how technology can support pedagogical goals (e.g., fostering collaboration).” (2005a, 134) “The pedagogy of how to use and apply the technology is technological pedagogical knowledge.” (McCormick & Thomann, 2007, 2204) “Technological pedagogical knowledge is an understanding of how teaching and learning changes when particular technologies are used. This includes knowing the pedagogical affordances and constraints of a range of technological tools as they relate to disciplinarily and developmentally appropriate pedagogical designs and strategies. This requires getting a deeper understanding of the constraints and affordances of technologies and the disciplinary contexts within which they function.” (Mishra & Koehler, 2007, 2220) “Thus an important part of TPK is developing creative flexibility with available tools in order to repurpose them for specific pedagogical purposes. TPK becomes particularly important because most popular software progra ms are not designed for educational purposes. Software programs such as the Microsoft Office Suite (Word, PowerPoint, Excel, Entourage, and MSN Messenger) are usually designed for a businesses environment. Furthermore, web-based technologies such as blogs or podcasts are designed for purposes of entertainment/communication/social networking. Teachers need to reject functional fixedness, and develop skills to look beyond the immediate technology and “reconfigure it” for their own pedagogical purposes. Thus TPK requires a forward-looking, creative and open-minded seeking of technology, not for its own sake, but for the sake of advancing student learning and understanding.” (2220) “ideas of how to use technology as a general pedagogical tool.” (Hughes, 2008, 5229)

Hughes (2008) emphasizes that TPK refers to the use of technology “as a general pedagogical tool” (p. 5229, italics added). However, Koehler and Mishra repeatedly refer to the role of “disciplinary contexts” in TPK (Koehler & Mishra, 2008, p. 17; Mishra & Koehler, 2007, p. 2220). This reference to content highlights what is perhaps the greatest debate surrounding the TPCK framework – namely, is it possible for teachers to possess and/or demonstrate knowledge of the interaction of technology and pedagogy without considering content? This is another major issue that must be addressed with the TPCK experts.

For the purpose of creating a precising definition of this construct which will facilitate classification of examples, this research will posit that reference to a particular content is not an essential feature of the TPK construct. Thus, the definition presented here is that TPK is an understanding of the technologies that may be used in a given pedagogical context, including the affordances and constraints of those technologies, and how those technologies influence or are influenced by the teacher’s pedagogical strategies. Again, examples from the literature should illuminate the features of this construct.

Table 4.4 Examples of TPK found in the literature

Examples of TPK found in the literature

“communicated as needed via email and discussion boards” (92) “thinking about the web’s applicability in education” (96) “she searched for ‘catacombs’ on the web and found the Vatican offered an electronic field trip through catacombs and shared that with her students.” (96) “using the web to access information, sometimes instantaneously, offered her students the supplementary information required to understand concepts and stories they read about in class but that were not available in the school library.” (96)

“This might include an understanding that a range of tools exists for a particular task, the ability to choose a tool based on its fitness, strategies for using the tool’s affordances, and knowledge of pedagogical strategies and the ability to apply those strategies for use of technologies. This includes knowledge of tools for maintaining class records, attendance, and grading, and knowledge of generic technology-based ideas such as WebQuests, discussion boards, and chat rooms.” (1028)

“For TPK, integrating spreadsheets into teaching mathematics was new to all but Ms. S. The highest level observed during this summer was that of adapting where the teachers were adapting the ideas they experienced in the summer for teaching and learning mathematics with spreadsheets. Ms. S, Ms. K, Ms. J and Mr. C actively demonstrated their adaptation abilities as they designed lessons and units that they planned for teaching in the coming year. As time progressed, Ms. A grew increasingly resistant to creating lessons that integrated spreadsheets even though she initially voiced her approval for spreadsheets as useful tools for problem solving. She was labeled at the recognizing level rather than the accepting level because she was unable to complete any lessons that integrated spreadsheets. Her reluctance was based in her firm belief that students needed to initially learn the mathematics in more traditional ways and then only use spreadsheets for applications of the mathematical ideas.” (2242)

“Realizing their pedagogical goals online initially proved challenging and troublesome. All three faculty had preconceived notions about what the online context would be like. In face-to-face, you have much more feedback. The students are there and generally speaking because they’re compliant. They’ll do what you ask but those are the very things, which are going to happen online. They can choose not to do that or enter it only partially. They can do that in class too but it’s much more difficult to hold back in class because you can do things as a teacher which invites people if they’re reticent to participate (Jim, May 7, 2001). I tried to think about things that would be interesting and how to engage them and how to coerce them to do that. In a classroom, you coerce them by your social persuasion skills. In an online format, your grades are tied to this because they won’t do it unless you provide some sort of incentive to do it because there is more anonymity so I’ve tried to think that through (Juliet, May 2, 2001). Alternatively, Mikala believed that transporting her pedagogical practices to the online context was fairly simple because she relied more heavily on others to deal with the technology. I have this zone of comfort around technology that I need to know only what I need to know…. I don’t want to be accountable and responsible for it. So, integrating the use of different programs as well as the important questions that (students) had to deal with was explicitly woven into every activity. I often said, ‘I’d like this or this to happen. Can you make it happen’ (Mikala, August 21, 2001)? Navigation through the course web site also became an important issue for all three faculty as they considered ways to engage students with the course content. Their conversations indicated that the teams were engaging more deeply with the issue of how teaching in an online environment requires finding technological solutions to pedagogical concerns. We wanted people to be able to move easily and with minimal number of clicks so that if they’re deep into the problem and they wanted to go back and read the original problem again, they’re one click away from that. We wanted the navigation to be sensible and intuitive (Jim, May 7, 2001). Jim and Juliet engaged directly with the technology to solve these issues, while Mikala relied mainly on her team and an external a technology expert employed by the university to assist faculty in putting their courses online. The technology expert determined how to divide the work on the pages of the web site based on Mikala’s syllabus. However, Mikala still gained understanding about technological solutions to pedagogical problems by virtue of her interaction with the technology expert. The navigation part was only concrete after we saw what the (technology expert) constructed so we had no idea but the needs were stressed by (me). It was a continuous construction. We had pages available and ideas would pop up and so we went back to (the technology expert) and he constructed something else and we were adding and sharing ideas and discussing those ideas. It was a real iterative process (Mikala, August 21, 2001).” (2210-2211)

“in order to help ensure effective student learning outcomes, online pedagogy needs to address a variety of factors. These include the following: reducing students’ reliance on text, exploring and valuing students’ backgrounds, developing knowledge beyond the level of transmission, promoting reflective practices, establishing an inclusive learning environment, fostering communication among classmates as well as instructors, helping students become more self-regulated and engaged, and developing a group identity that connects students with their learning as well as with their social environment.” (citing Brennam, 5193)”

“This project benefited me in a great way. I never had the opportunity to work with a PowerPoint in high school so have this experience was helpful. I feel that as teacher some day, knowing how to work with such technology will enhance my students’ learning and educational experiences” (5267)

Technology Pedagogical Knowledge (TPK) I know how to use technology in collaborative learning. “experimentation and decisions about what technologies would support their pedagogical goals” (Peruski, Mishra, & Koehler, 2007, 2209-2210)

Again, the confusion surrounding this construct is evident in the examples provided. With this construct, the questions lie in whether or not content can play a role in TPK. Additionally, it is extremely difficult to draw the line between TPK and TPCK in that both are used in an educational context and it seems to be a matter of how much detail is provided regarding that context to classify the example as belonging to one or the other. Another question that has arisen between the researcher and her committee chair (Cox & Graham, 2008) pertains to which instructional strategies are being implemented. Does TPK refer to the use of general pedagogical strategies (e.g., collaborative learning, problem-based learning, etc.) with technology rather than content-specific pedagogical strategies (e.g., primary source research (social science), inquiry-based learning (science), etc.) that use technology? Or is the distinction not that clear?

Based on the definitions and examples provided in the resources investigated here, the researcher proposes that the essential features of TPK are (1) the use of technology (2) as part of a pedagogical strategy (3) and how the technology and pedagogy interact. The questions to be posed to the TPCK experts include (1) whether content can/should play a role in TPK; (2) how one can distinguish between TPK and TPCK, particularly because teachers do not often separate teaching from content; and (3) whether the nature of the instructional strategy plays a role in TPK/TPCK classification.

Technological Pedagogical Content Knowledge (TPCK)

The most succinct definition of TPCK this researcher has found to date is this: “how to use technology to help students learn a particular topic” (Koehler & Mishra, 2008, p. 21). But as further examination of 89 definitions from the selected resources (See Table 4.5) demonstrated, that definition is, perhaps, too simplistic to represent the complexity of this construct. This oversimplification of the construct in the literature has, in Leatham’s words, “hamper[ed] the usefulness of the TPCK framework” (2008, p. 5281). The true outcome of TPCK, according to researchers, is the ability to “develop meaningful learning experiences for students that integrate technology use effectively” (AACTE, 2008, p. 293) or “good teaching with technology” (Koehler & Mishra, 2008, p. 11) or “effective teaching with technology” (Koehler & Mishra, 2008, p. 12). These statements suggest a much richer definition of the construct than the one above, implying a level of quality in the technology use. Thus it is important to consider the essential features of TPCK to determine how that quality is produced.

Table 4.5 Definitions of TPCK found in the literature.

Definitions of TPCK found in the literature

not just in each of these key domains (T, P, and C) but also in the manner in which these domains interrelate, so that they can effect solutions that are sensitive to specific contexts.” (18) “Teachers constantly negotiate a balance between technology, pedagogy, and content in ways that are appropriate to the specific parameters of an ever-changing educational context.” (21) “how to use technology to help students learn a particular topic” (21) “a true understanding of the intersection of knowledge about technology, content (content areas or subjects such as mathematics, science, or English), and pedagogy (specific instructional practices that are effective for teaching the subject. Teachers with high levels of TPCK possess not only general technology skills, but also knowledge about the types and specific uses of technology that are most likely to facilitate teaching and learning in each subject.” (51) “always applied in the context of a specific, idiosyncratic teaching-learning situation, and its effectiveness is highly dependent on the extent to which teachers are able to pedagogically accommodate that context.” (51) “While the teacher may be able to select from a menu of prefabricated or ‘canned’ strategies, at a minimum these have to be tweaked on the spot to fit the current context.” (56) “how technology might be used to teach literacy more effectively or how technology might change the way students actually learn to read and write” (61) “the connections and interactions between the knowledge of content, pedagogy, and technology with respect to teaching literacy” (62) “For K-6 literacy, good teaching with technology will look very different for individual teachers who teach students with diverse instructional needs.” (71) “thoughtfully consider how to best connect literacy content and technology with research-based practices in their classrooms.” (72) “Teachers must be prepared to plan for and then facilitate learning environments where elementary students are engaged with learning literacy using proven pedagogical and technological approaches.” (77) “E-TPCK and TPCK in general are temporary concepts that draw attention to the interconnections between technological tools, concepts, activities, and perspectives and the well-developed teacher knowledge, content knowledge, pedagogical knowledge, and pedagogical content knowledge.” (88) “adaptive to conditions and context.” (90) “understand, consider, and choose to use technologies when they uniquely enhance the curriculum, instruction, and/or students’ learning in a subject matter area.” (103) “a framework that incorporates the indispensable trait of an educator’s knowledge as he/she integrates technology into his/her teaching practice at the same time as attending to the complexities of this particular kind of knowledge. TPCK is an emergent form of knowledge as a response to the growing need for a scaffold that supports the sound integration of technology. TPCK is not an extension or appendix of content, pedagogy, and technology but rather a complex form of knowledge that blends all three components and the dynamic relationships that exist among them.” (117) “it is a matter of thinking imaginatively about ‘how’ technology may support teaching and learning more than focusing too much on ‘what’ technologies may be used.” (118) “separately conceitve of technology, pedagogy, and content and then consider their interplay.” (129) “teachers might also enhance, transform, or otherwise reorganize social studies subject matter given technological pedagogical contexts.” (131) “a teacher decides and plans for appropriate use in their classroom given knowledge of learners, knowledge of curriculum, the needs of the school community, and the goals or purposes of the course and subject.” (132) “an emergent form of knowledge that goes beyond all three components (content, pedagogy, and technology). This knowledge is different from knowledge of a disciplinary or technology expert and also from the general pedagogical knowledge shared by teachers across disciplines. TPCK is the basis of good teaching with technology and requires an understanding of the representation of concepts using technologies; pedagogical techniques that use technologies in constructive ways to teach content; knowledge of what makes concepts difficult or easy to learn and how technology can help redress some of the problems that students face; knowledge of students’ prior knowledge and theories of epistemology; and knowledge of how technologies can be used to build on existing knowledge and to develop new epistemologies or strengthen old ones.” (2006, 1028-1029) “’TPCK represents a class of knowledge that is central to teachers’ work with technology. This knowledge would not typically be held by technologically proficient subject matter experts, or by technologists who know little of the subject or of pedagogy, or by teachers who know little of that subject or about technology.’” (2006, 1029) “The core of our argument is that there is no single technological solution that applies for every teacher, every course, or every view of teaching. Quality teaching requires developing a nuanced understanding of the complex relationships between technology, content, and pedagogy, and using this understanding to develop appropriate, context-specific strategies and representations.” (2006, 1029) “if we jointly consider all three elements (T, P, and C), we get Technological Pedagogical Content Knowledge (TPCK). True technology integration, we argue, is understanding and negotiating the relationships between these three components of knowledge. Good teaching is not simply adding technology to the existing teaching and content domain. Rather, the introduction of technology causes the representation of new concepts and requires developing a sensitivity to the dynamic, transactional relationship between all three components suggested by the TPCK framework.” (2005a, 134) “We argue that intelligent pedagogical uses of technology require the development of a complex, situated form of knowledge we call Technological Pedagogical Content Knowledge (TPCK).” (2005b, 95) “At the heart of TPCK is the dynamic, transactional relationship between content, pedagogy, and technology. Good teaching with technology requires understanding the mutually reinforcing relationships between all three elements taken together to develop appropriate, context specific strategies and representations.” (2005b, 95) “TPCK helps teachers define the best uses of technology to effectively teach mathematics or social studies or reading, and emphasizes the fact that the technology used and the approach will be quite different for each content area. Thus, the way a skilled teacher effectively uses technology for teaching science will look quite different than the way a skilled teacher effectively uses technology to teach history. Differences include both the type of technology used and the pedagogy involved.” (Thompson, 2005, 46) “for technology to become an integral component or tool for learning, science and mathematics preservice teachers must also develop an overarching conception of their subject matter with respect to technology and what it means to teach with technology – a technology PCK (TPCK).” (Niess, 2005, 510) “the integration of the development of knowledge of subject matter with the development of technology and of knowledge of teaching and learning.” (Niess, 2005, 510) “TPCK for teaching with technology means that as teachers think about particular mathematics concepts, they are concurrently considering how they might teach the important ideas embodied in the mathematical concepts in such a way that the technology places the concept in a form understandable by their students.” (Niess, 2006, 196) “social studies students are using disciplinary content knowledge that is culled from the real world and pedagogically repackaged to enable democratic experiences.” (141) “As Mishra and Koehler argued, realizing the potential of the technology requires skills and knowledge not just of technology, pedagogy, and content in isolation but rather of all three taken together. Teaching successfully with technology requires continually creating, maintaining, and re-establishing a dynamic equilibrium among all three components. Teachers constantly negotiate a balance between technology, pedagogy, and content in ways appropriate to the specific parameters of an ever-changing educational context. Teachers construct curricula through an organic process of iterative design and refinement, negotiating among existing constraints to create contingent conditions for learning.” (Bull, et al, 2007, p. 130) “that technology should be introduced in the context of content instruction and that teachers should take advantage of the unique features of technology to teach content in ways they otherwise could not (Garofalo et al., 2000). If the pedagogical content knowledge required for each discipline differs, it follows that the ways in which technology might best be used for each discipline may also differ.” (131) “Our point here is that the full range of possibilities should be employed, matching the tool to the pedagogical goal and need” (135) “TPCK involves an awareness of the strategies that incorporate the use of technology to create a student-centered learning environment, and is focused in the overlapping areas of content knowledge, pedagogical knowledge, and technology (Mishra & Koehler 2006). It is the link between the use of technology as a performance tool and the use of technology within a teaching strategy as a pedagogical tool.” (Cavin & Fernandez, 2007, 2180) “To effectively make such decisions requires an understanding of the interaction of the three components of TPCK: the technology, the pedagogy related to teaching a specific content, and the content itself.” (2180) “TPCK refers to a true understanding of the intersection of three kinds of knowledge: knowledge about technology, content knowledge (knowledge about subjects such as mathematics, science or English), and pedagogical knowledge (specific instructional practices that are effective for teaching each subject) (Koehler and Mishra, 2007). Teachers with high levels of TPCK possess not only general technology skills, but also knowledge about the types and specific uses of technology that are most likely to facilitate the teaching and learning of each subject. TPCK is always applied in the context of a specific, idiosyncratic teaching-learning situation, and its effectiveness is highly dependent on the extent to which teachers are able to pedagogically accommodate that context.” (Kelly, 2007, p. 2199) “it is important that teachers’ TPCK includes knowledge and skills in identifying and appropriately responding to differential levels of access to technology among students. In this regard, an entry level TPCK skill teachers should possess, across content areas, is the ability to obtain, at the start of a class, information about the technology access of students.” (2200) “The integration of choosing the appropriate pedagogy for teaching content and technology and the appropriate technology for the content is TPCK.” (McCormick & Thomann, 2007, 2204) “TPCK is an emergent form of knowledge that goes beyond all three components (content, pedagogy, and technology). Technological pedagogical content knowledge is an understanding that emerges from an interaction of content, pedagogy, and technology knowledge. Underlying truly meaningful and deeply skilled teaching with technology, TPCK is different from knowledge of all three concepts individually. We argue that TPCK is the basis of effective teaching with technology and requires an understanding of the representation of concepts using technologies; pedagogical techniques that use technologies in constructive ways to teach content; knowledge of what makes concepts difficult or easy to learn and how technology can help redress some of the problems that students face; knowledge of students’ prior knowledge and theories of epistemology; and knowledge of how technologies can be used to build on existing knowledge and to develop new epistemologies or strengthen old ones. By simultaneously integrating knowledge of technology, pedagogy and content, TPCK is a form of knowledge that expert teachers bring into play any time they teach. Each “wicked problem” or situation presented to teachers is a unique combination or weaving together of these three factors, and accordingly, there is no single technological solution that applies for every teacher, every course, or every view of teaching. Rather, solutions lie in the ability of a teacher to flexibly navigate the space defined by the three elements of content, pedagogy, and technology and the complex interactions among these elements in specific contexts. Ignoring the complexity inherent in each knowledge component, or the complexity of the relationships among these components can lead to oversimplified solutions or failure. Thus, teachers need to develop fluency and cognitive flexibility not just in each of these key domains (T, P, and C) but also in the manner in which these domains interrelate, so that they can effect solutions that are sensitive to specific contexts. This is the kind of deep, flexible, pragmatic and nuanced understanding of teaching with technology that we advocate.” (2220-2221) “TPCK, interconnection and intersection of content (mathematics), pedagogy (teaching and student learning), and technology (spreadsheets) (Margerum-Leys & Marx, 2002; Mishra, & Koehler, 2006; Niess, 2005; Pierson, 2001; Zhao, 2003), is that mode of thinking that integrates these multiple domains of knowledge in ways that rely on planning, organizing, critiquing and abstracting ways to integrate technologies such as spreadsheets with specific mathematical content and specific student needs.” (Niess, 2007, “TPCK emphasizes teachers’ knowledge of the connections, interactions, affordances, and constraints between and among technology, pedagogy, and content. The theory also specifies the importance of how and in what context teachers learn to integrate technological with pedagogical and content knowledge. A key component of TPCK is the “Learning Technology by Design” approach where teachers participate in “design teams” comprised of individuals with varying expertise in content, pedagogy, and technology, to develop technological solutions to authentic problems of practice.” (Peruski, Mishra, & Koehler, 2007, 2208) “pedagogy, and technology are no longer independent of each other, and members can develop contextualized, domain-specific strategies and representations.” (Sun & Deng, 2007, 2270) “We believe that technology can inform pedagogical practices appropriate to the epistemological considerations of the content in part by opening up opportunities previously unavailable.” (Wellman & Snow, 2007, 2280) “use technology as an instructional tool within their content areas” (Hardy, 2008) “involves an understanding of the complexity of relationships among students, teachers, content, technologies, practices, and tools.” (Archambault, 2008, 5190) “These include technical considerations (technological aspects that impact the extent to which technology facilitates student learning), differences in online pedagogy (the differences in teaching strategies that have to be implemented when adapting curriculum to a distance environment, involving issues such as student interaction, evolving teacher roles, student access, and evaluations of student outcomes), and principles of instructional design (sufficiently knowing a particular content to be able to use adopted technology to develop and offer quality online instruction).” (5191) “Simply using technology in the classroom does not represent TPCK. Using technology in a manner that enhances student learning by employing specific technological tools and using specific technology-related teaching strategies in presenting a content lesson does.” (Cavin, 2008, 5214) “TPACK refers to the idea that learning occurs best when teachers engage in equal parts of knowledge of technology, knowledge of content, and knowledge of pedagogy in their instruction” (Fath & Genalo, 2008, 4690) “the special form of knowledge helping teachers know how to use particular technologies to teach content-specific concepts” (Hughes, 2008, 5229) “While the intersection of content, pedagogical and technological knowledge is a necessary condition for effective integration of technology into instruction, it is not a sufficient condition. Teaching with technology, like all other teaching, does not occur in a vacuum. It occurs in a teaching-learning context that is rich in characteristics—physical, social, psychological, cultural. These characteristics can interact with content, pedagogy and technology in unique ways to affect the achievement of learning outcomes. Therefore, in addition to content, pedagogy and technology, the teaching-learning context, hereafter referred to as the context, is a fourth area of knowledge teachers must incorporate into their TPACK-based instructional designs if these are to be effective with all children.” (Kelly, 2008, 5257) “Instructional design based on the TPACK framework should be concerned about incorporating, responding to, and influencing the context and through it, the psycho-social functioning and achievement of all students.” (Kelly, 2008, 5258) “teachers need a knowledge that exists in the intersection of Technology, Pedagogy and Content” (Leatham, 2008, 5277) “TPCK is different from the technological knowledge. It is a kind of integrated knowledge system supported by PCK and the knowledge about technology simultaneously” (Lin et al, 2008, 4730). “Although the definition and extent of TPCK are still in controversy, the researchers of this project attempt to sum up the rationale into 5 categories as described below. 1. Belief: The value and opinion about technology embedded teaching hold by a teacher. 2. Evaluation: Whether a teacher know how to evaluate students’ learning achievement through technological tools. 3. Content: How a teacher gets information about the content knowledge s/he will teach by utilizing technology tools. 4. Design: How a teacher transfer content knowledge to curriculum or teaching activities through technology. 5. Representation: How a teacher uses proper technological tools to represent knowledge or concepts in her/his course.” (4731) “Thus, to implement TPCK correctly, it is important to first understand what content to target, and then develop appropriate pedagogy and technology to facilitate meaningful learning” (McGuire, et al, 2008, 2119) “Technological, pedagogical, and content knowledge (TPACK) describes that body of knowledge that teachers need for teaching with and about technology in their assigned subject areas (such as mathematics) and grade levels. TPACK (previously called technological pedagogical content knowledge or TPCK) is depicted as knowledge that relies on the interconnection and intersection of content, pedagogy (teaching and student learning), and technology. TPACK must be viewed as more than a set of multiple domains of knowledge and skills that teachers need for teaching their students particular subjects at specific grade levels. TPACK is a way of thinking that integrates these multiple domains of knowledge of mathematics, pedagogy and technology, but it is more than simply knowledge of these three domains of knowledge.” (Niess, 2008, 5297) “Considering the goal of engaging students in mathematical problem solving, a mathematics teacher’s TPACK must focus thinking strategically in planning, organizing, implementing, critiquing results and abstracting plans for specific mathematics content and diverse student needs.” (5297) “Niess further clarified these central components of TPACK as the knowledge and beliefs that a mathematics teacher demonstrates that is consistent with: 1. An overarching conception about the purposes for incorporating technology in teaching mathematics. This conception is what the teacher knows and believes about the nature of mathematics, what is important for students to learn, and how technology supports learning mathematics. These foundations of the teacher’s knowledge and beliefs about teaching mathematics with technology serve as a basis for their decisions about classroom instruction (objective, strategies, assignments, curriculum and text, and evaluation of student learning). 2. Knowledge of students’ understandings, thinking, and learning in mathematics with technology. In this area, the teacher relies on and operates from knowledge about how students learn mathematics with technologies and believes that technologies are useful in learning appropriate mathematics. 3. Knowledge of curriculum and curricular materials that integrate technology in learning and teaching mathematics. With respect to the curriculum, the teacher discusses and implements various technologies available for teaching particular topics and how the topics and ideas in a technology-enhanced environment with concern for how the activities are organized, scaffolded, structured, and assessed throughout the curriculum. 4. Knowledge of instructional strategies and representations for teaching and learning mathematics with technologies. With respect to teaching and learning, the teacher adapts mathematical representations with technologies in multiple ways to meet specific instructional goals and the needs of the breadth of learners in the class.” (5298) “Teachers do not demonstrate that they either have or do not have TPACK for teaching mathematics with appropriate technologies. They differ in their actions with respect to each of the components as they are confronted with whether to accept or reject the use of various technologies in teaching mathematics. Their differences are a function of their knowledge of mathematics, their knowledge of the technologies, and their knowledge of teaching and learning (pedagogy).” (5298) “From this perspective, teachers’ development of TPACK for teaching mathematics with appropriate technologies such as spreadsheets is a developmental process.” (5269) “Early studies (Niess et al., 2006) on continuing in-service education directed at developing teachers’ TPACK preparing them for teaching mathematics with spreadsheets described these five levels of teachers’ TPACK for teaching mathematics with spreadsheets using ideas from Rogers’ (1995) five levels: 1. Recognizing (knowledge) where teachers are able to use the technologies and recognize alignment of the capabilities of the technologies with mathematics content. 2. Accepting (persuasion) where teachers form a favorable or unfavorable attitude toward teaching and learning mathematics with appropriate technologies. 3. Adapting (decision) where teachers engage in activities that lead to a choice to adopt or reject teaching and learning mathematics with appropriate technologies. 4. Exploring (implementation) where teachers actively integrate teaching and learning of mathematics with appropriate technologies. 5. Advancing (confirmation) where teachers evaluate the results of the decision to integrate teaching and learning mathematics with appropriate technologies.” (5299) “The concept of integrating technology with the more traditionally held notions of teacher work, pedagogy and content, ensures that a technology-integrating teacher capable of using any appropriate tools to supplement teaching of 21st century skills is indeed the goal of all teacher preparation.” (Pierson, 2008, 5305) “This short paper recommends the formal inclusion of “context” as an additional class of knowledge in the “Technological Pedagogical Content Knowledge” (TPCK) framework” (Reeve, 2008, 5310) “The TPCK framework indicates that teachers need to develop an integrated class of knowledge that will enable them to consider a multiple set of complex relationships that include such knowledge components as the affordances of the technology, pedagogical techniques that relate to the specific content area and the relationship of these technological affordances to these pedagogical approaches. It is suggested here that discussion about and knowledge of the actual school context, in these Design Study Group meetings, is a critical element in ensuring the successful implementation of technology-rich approaches.” (5311) “that context is a frame within which knowledge of technology, pedagogy and content can be understood.” (5312) “I believe the TPACK model is useful not just for explaining what teachers need to know, but also the order in which they decide to use that knowledge when teaching. I propose that the TPACK model, in its expression of what teachers actually do, can be better diagramed as per Figure 2. While Content, Pedagogy, and Technology are each important and sustainable educational fields, they are not dealt with by educators equally or simultaneously: 1) The educational process begins with Content: what we are going to teach takes priority. Until we have determined what will be taught, none of the other parts of the TPACK model make sense. 2) Once we have determined the subject, necessarily the particular students, goals, and environment must be considered. 3) Consistent with the arguments of Shulman (1986), Pedagogical Content – the determination of content appropriate to the given teaching situation – is next. Mishra & Koehler (2006) correctly state that Shulman’s neglect in mentioning technology was neither lack of its importance nor an intentional dismissal. When Mishra & Koehler cite Bruce & Hogan’s (1998) term “transparent,” they are explaining that technology in Shulman’s time was not rapidly changing, had little variety, and was “commonplace and not even regarded as technology” (page 1023). What I believe that Mishra & Koehler fail to take into account is that technology, while it has certainly “come to the forefront of educational discourse” (page 1023), is still the third consideration of a teacher when performing within the domain of the art. In other words, to continue the order of events, I propose that next: 4) Technology must be considered, for it is true that the instructor must understand how to use the technology, what support systems are required for its operation and maintenance, and even how to troubleshoot it when things do not go as planned. 5) Then the topic of Technological Pedagogy comes into play, for the instructor must understand how technology will related to the students, goals, and environment in place. This is true even outside of the particular content within which instructor is determined to teach. 6) Finally, the instructor must relate Technological Pedagogy with the particular content at hand. This is the TPC Knowledge, or TPACK, discussed by Koehler & Mishra (2005). This Modified TPACK 6-step model is the theoretical foundation I will use to substantiate a use-base typology for technology in Education. This typology occurs at Steps #5 and #6 above, where technology is evaluated in terms of the outcomes we are primarily seeking as it interacts with content and pedagogy.” (Robertson, 2008, 2218-2219 “the complex interplay between technology, pedagogy, and content knowledge (TPACK).” (Schmidt, et al, 2008, 5313) “TPACK is still defined as an emergent form of knowledge that goes beyond all three components (technology, pedagogy and content). At the intersection of these three types of knowledge, there is an intuitive understanding of teaching content with appropriate pedagogical methods and technologies. Thus, it is a framework for thinking about what knowledge teachers need to integrate technology into teaching and how they might develop this knowledge.” (5314) “The new name does much more than just buy a vowel for TPCK. We see TPACK as capturing two key aspects of our work with technology integration. First, it emphasizes, through the letters, the three kinds of knowledge (Technology, Pedagogy And Content) that we believe are essential building blocks for intelligent technology integration. Second, and as important, it captures the fact that these three knowledge domains should not be taken in isolation, but rather that they form an integrated whole, a “Total PACKage” as it were, for helping teachers take advantage of technology to improve student learning.” (Thomspon & Mishra, 2007-2008, 64) “Effective use of technology, we have learned, involves the ability to make informed decisions on how to take advantage of the affordances of technology (with a sensitivity to the concomitant constraints technologies bring to the table) to support specific pedagogies within a particular content area. Thus, teachers need the Total PACKage: the knowledge that lies at the intersection of knowledge of Content, Pedagogy And Technology i.e., TPACK. If all goes well, we will begin to see TPACK appear as our shared descriptor of the powerful ideas involved in creating a synergy among technology, content and pedagogy that honors the interdependence of these three important parts of teacher education and teaching. Emphasizing creating the total package for effective teaching and teacher education will help bring clarity and simplicity to developing knowledge of the most effective ways to help teachers take advantage of technology.” (64) “Teachers must be able to integrate technological skills and understandings with considerations about pedagogy and subject matter.” (Trautmann & MaKinster, 2008, 4792) “The size of this overlap indicates the extent to which a teacher has developed an integrated understanding of the complex relationships between subject matter understanding, pedagogical goals, and available technologies.” (4792) “Technological pedagogical content knowledge (TPCK) defines that body of knowledge that teachers now need for teaching with and about technology in their assigned subject areas and grade levels. TPCK is described as the interconnection and intersection of content, pedagogy (teaching and student learning), and technology. However, TPCK is more than a set of multiple domains of knowledge and skills that teachers need for teaching their students particular subjects at specific grade levels. TPCK is a way of thinking within these multiple domains of knowledge.” (Niess, 2008, 224) “TPCK is a way of thinking strategically while involved in planning, organizing, critiquing, and abstracting for specific content, specific student needs, and specific classroom situations while concurrently considering the multitude of twenty-first century technologies with the potential for supporting students’ learning.” (224) “TPCK is revealed as the knowledge, skills, and dispositions that teachers have for teaching with technology – or knowledge that includes: An overarching conception of what it means to teach the content with technology, Knowledge of instructional strategies and representation for teaching the content with technology, Knowledge of students’ understanding, thinking, and learning the content with technology, and Knowledge of curriculum and curriculum materials that integrate technology in their subject (Niess, 2005a).” (248) “It is important to note that technological pedagogical content knowledge (TPCK) is interdependent with content, pedagogical, and technological knowledge; and also pedagogical content, technological content, and technological pedagogical content knowledge…Moreover, each and all of these are influenced by contextual factors, such as culture, socioeconomic status, and organizational structures. Thus, TPCK as it is applied in practice must draw from each of these interwoven aspects, making it a complex and highly situated educational construct.” (Harris, 2008, 255) “Extension of the concept to ‘technological pedagogical content knowledge’ (TPCK) brings much-needed recognition of the central role of content and pedagogy in uses of educational technology – a role typically missing in discussions until recently.” (Bull, Bell, & Hammond, 2008, 273) “To refine and articulate TPCK, collaborative work across the disciplines must be conducted with full awareness of the differing goals, inquiry processes, and habits of mind of each content area.” (283) “TPCK can provide the conceptual frame for moving teachers toward effective and meaningful applications of technology that are directed at improving both learning and teaching.” (AACTE, 2008, 290) “Focusing on developing curriculum and pedagogy within content areas that are rooted in TPCK will allow teachers to build the knowledge and skill necessary for them to develop meaningful learning experiences for their students that integrate technology use effectively.” (293) “Using TPCK can shift the emphasis away from focusing upon technology itself and toward appropriate applications of technologies of all types within curriculum areas, based upon operational knowledge of the unique affordances and constraints of particular tools and resources used for learning in particular content areas.” (293)

Inherent in the TPCK acronym is the idea that this construct is composed of three distinct knowledge domains – technology, pedagogy, and content. The researcher discovered 89 definitions/descriptions of TPCK in the literature selected for this review (See Table 4.5) that illuminate further features of the construct. The first, and most often mentioned, of these is the complexity of TPCK.

Researchers have repeatedly emphasized that TPCK is not a simple construct and that the relationships between the knowledge types is equally intricate. The following list of terms is a sampling of how researchers have described that complex relationship: Interaction, relationship, interrelate, negotiate, intersection, connection, interconnections, blends, dynamic relationships, interplay, goes beyond, jointly, transactional, mutually reinforcing relationships, integration, all three taken together, dynamic equilibrium, balance, overlapping, simultaneously integrating, flexibly navigate, affordances and constraints, equal parts, synergy, interdependence, concurrently considering, interwoven. Thus it is apparent that, in order for one to possess TPCK, one must first possess each of the knowledge types and second understand the intricacy of the relationship between those domains. McCormick and Thomann illustrate this relationship by describing TPCK as “the integration of choosing the appropriate pedagogy for teaching content and technology and the appropriate technology for the content” (2007, p. 2204, italics added).

Also contributing to the complexity of the construct is the nature of the knowledge involved. Technological knowledge, pedagogical knowledge, and content knowledge are each very dense and multifaceted domains. New skills and understandings emerge when these domains are combined. Koehler and Mishra describe the understandings required for TPCK as: “(1) the representation of concepts using technologies; (2) pedagogical techniques that use technologies in constructive ways to teach content; (3) knowledge of what makes concepts difficult or easy to learn and (4) how technology can help redress some of the problems that students face; (5) knowledge of students’ prior knowledge and theories of epistemology; and (6) knowledge of how technologies can be used to build on existing knowledge and to develop new epistemologies or strengthen old ones” (Koehler & Mishra, 2008, p. 17-18; Mishra & Koehler, 2006, p. 1028-1029; Mishra & Koehler, 2007, p. 2221, numbering added).

Alternatively, Niess uses the framework for PCK provided by Grossman (1991) to describe the four central components of TPCK as (1) an overarching conception about the purposes for incorporating technology in teaching [a given content]; (2) Knowledge of students’ understandings, thinking, and learning in [a given content] with technology; (3) Knowledge of curriculum and curricular materials that integrate technology in learning and teaching [a given content]; and (4) knowledge of instructional strategies and representation for teaching and learning [a given content] with technologies (Niess, 2008, p. 5298; Niess, 2005, p. 511). Thus, it is apparent that, while researchers can agree that TPCK is complex, it is not yet clear what exactly that knowledge entails.

A second feature of TPCK, and one that is currently enjoying much attention in the research, is context. One reason why TPCK (and PCK before it) has proven so difficult measure is that it must take place in some context. Included in the idea of context are such things as the school environment, the physical features of the classroom, the availability of technology, the demographic characteristics of students and teachers including prior experience with technology, the particular topic being taught, the preferred instructional methods of the teacher, etc. (Kelly, 2008). The effect of context is that TPCK is unique, temporary, situated, idiosyncratic, adaptive, and specific and will be different for each teacher in each situation. As Koehler and Mishra described it, “there is no single technological solution that applies for every teacher, every course, or every view of teaching” (2006, p. 1029). Thus, any true example of TPCK must necessarily include the context of that example. Koehler and Mishra have acknowledged the importance of context in the TPCK framework by adapting the visual model to include context as a major feature as shown in Figure 4.1.

Figure 4.1. The revised model of TPCK as seen in Koehler & Mishra, 2008, p. 12.

Another aspect of the construct that makes it difficult to measure is that TPCK is, in reality, a “way of thinking” (Niess, 2008, p. 5297; Niess, 2008, p. 224), an “intuitive understanding” (Schmidt, Seymour, Sahin, & Thompson, 2008, p. 5314) or, as van Olphen describes it, “a matter of thinking imaginatively about ‘how’ technology may support teaching and learning” (2008, p. 118). Therefore, in order to measure TPCK one would have to measure what teachers are thinking as they plan, organize, critique, and abstract for the context (Niess, 2008, p. 224). Thus it would seem that an exemplar of TPCK must include a description of why the teacher created the learning environment described. However, most published examples of technology integration provide description of the actual implementation rather than the reasoning behind that implementation, making it difficult to find a model case that would include this feature.

Kelly argues that another feature of TPCK involves a teacher’s “knowledge and skills in identifying and appropriately responding to differential levels of access to technology among students” (2007, p. 2200). Perhaps the issue of access could be included with demographic issues under context, but it may be wise to further consider this issue as recent research demonstrates that access to technology may contribute to a widening of both educational and economic gaps between the poor and the wealthy (Lucas & Sylla, 2003; Williams, Carr, & Clifton, 2006). With the global perspective of the 21^st century, teachers with TPCK should consider issues concerning access to technology including determining levels of access among one’s students, being aware of local resources for access, and providing differentiation. However, for the purposes of this study, as this is a very new inclusion in the TPCK debate, access will not be an essential feature for a TPCK exemplar.

Some researchers have also acknowledged that teachers can possess different levels of TPCK and that TPCK development is a process (for example, Kelly, 2008; Kelly, 2007; Niess, 2008; Niess, 2006). Therefore, when examining TPCK, one must also consider that different teachers will demonstrate differing levels of TPCK, further complicating the measurement of the construct. Niess (2008) illuminated these levels as follows:

“1. Recognizing (knowledge) where teachers are able to use the technologies and recognize alignment of the capabilities of the technologies with content.

2. Accepting (persuasion) where teachers form a favorable or unfavorable attitude toward teaching and learning [content] with appropriate technologies.

3. Adapting (decision) where teachers engage in activities that lead to a choice to adopt or reject teaching and learning [content] with appropriate technologies.

4. Exploring (implementation) where teachers actively integrate teaching and learning of [content] with appropriate technologies.

5. Advancing (confirmation) where teachers evaluate the results of the decision to integrate teaching and learning [content] with appropriate technologies” (p. 5299).

Heretofore, what has generally been accepted as TPCK resembles the exploring phase as Niess describes it. The decision must be made as to whether or not the level of TPCK is a consideration when classifying examples as TPCK.

In addition to the idea of levels, Robertson argues that the implementation of TPCK actually occurs in a series of steps (2008). She posits that a teacher begins with the content, then considers the context. Next, pedagogical content knowledge is used to determine which content to teach in the particular context. Fourth, technology can be considered, followed by technological pedagogy as the teacher decides how the technology will fit into the pedagogy being used. Finally, “the instructor must relate Technological Pedagogy with the particular content at hand” (Robertson, 2008, p. 2219). Though this theoretical model has not yet been tested, it is an interesting illustration of the possible progression of TPCK on a daily basis in a classroom setting.

Bull et al (2007) illustrate another difficulty in measuring or exemplifying TPCK when they state that TPCK can be examined from at least three different perspectives. “For instance, one could focus on Pedagogy and see how it interacts with Technology and Content. Alternatively, one could focus on one content area, and see how Pedagogy and Technology can be best utilized to develop student understanding of core content ideas.” A third possibility is “considering the affordances (and constraints) imposed by one particular technology and its interaction with content areas and pedagogical goals” (p. 131). This statement implies that TPCK may look different depending on the perspective from which one is examining it. However, it also indicates the breadth of research possibilities that are suggested by this construct, demonstrating the value of the use of the framework.

The precising definition presented here is that technological pedagogical content knowledge is a way of thinking about the complex relationships between technology, pedagogy, and content in a specific context which is represented through the carefully considered implementation of technology in a classroom setting in order to help students better understand a particular topic.

As with the definitions, there are many more examples of TPCK than of the other constructs. Additionally, these examples are longer and more detailed because, as was stated earlier, an example of TPCK generally also contains an explanation of the context in which it took place. Some of these examples are real and other are invented by the authors, but an examination of all of the examples should provide a more solid foundation for defining the construct.

Table 4.6 Examples of TPCK found in the literature.

Examples of TPCK found in the literature

“Mr. Cole implements writer’s workshop using technology in his fourth-grade classroom. During their scheduled writing time each day, his fourth-grade students have one-on-one access to wireless laptops in the classroom. Each student begins a new story by choosing a topic of interest based upon his/her own background experiences and knowledge. At the prewriting stage students begin to brainstorm and generate their story ideas using Inspiration. Using this software students create concept maps to visually represent their thoughts and ideas before beginning to write their story. “Next, the students use the concept map to guide their thinking while composing the first draft of their stories using SubEthaEdit. SubEthaEdit is a text editor that allows collaborative editing so compositions can be shared online with others for the purpose of providing feedback and response. Once the first draft is complete, students participate in a recursive process that involves several exchanges back and forth between peers and/or teachers while revising, editing, and re-drafting the stories. Using SubEthaEdit, a student sends his/her draft to a peer in the classroom (or anyone in the world) who reads the piece and makes suggestions revising the document. Another unique feature of SubEthaEdit is that it is available in multiple langues like Chinese, Russian, Korean, Japanese, German, and French so communicating and collaborating with a diverse audience is possible. After students have re-drafted their writing using the suggestions offered during the revising stage, the collaborative editing process is later replicated by using SubEthaEdit during the editing stage focusing on correcting mechanics and spelling. “Finally, after revising and editing their stories the students publish their compositions. Although publishing in writer’s workshop can have multiple purposes and be done in a variety of ways, technology can still play a significant role in completing the writing process cycle. After completing edits and revisions, the students might print out their stories and then during author’s chair time the students share their stories with the entire class. At times, Mr. Cole provides the opportunity for his students to publish their work online as a means to motivate them to write.”(76-77)

“the preservice teachers engaged in web-based communication with each other about their experiences” (92) “Once comfortable with StorySpace software, Nell wanted to use it to support her teaching of hypertext concepts to her students.” (98) “Nell’s students participated in an interdisciplinary Slavery Project with a group of students from Ghana. The two groups of students shared in writing an African’s story from his/her life in Africa, capture and deportation to America, and sale as a slave to an owner. The Ghana students collaboratively wrote four versions of the first half of the story depicting the African’s life up until he/she boards a slave ship. Nell’s students chose one of the four versions and completed the story to the point when the African is sold as a slave at auction. Nell’s students imported the first half of the story into the Story Space software and constructed it as a hypertext narrative.” (98-99) “Though Nell believed the most effective way to communicate notions of text, writing, and reading to her students required the use of technology” (99) “Nell felt StorySpace allowed simpler and clearer illustrations of the concepts” (99) “Nell developed and used her TPCK to design a lesson in which her students used the technology to engage in writing nonlinear, hypertext narratives, co-authored with African students.” (100)

“For example, teaching chemistry (the content) would drive the kind sof representations to be used (symbolic representations such as equations, or visual representations such as molecular diagrams – that is, the pedagogy) and the technologies used to display and manipulate them. In this example, suitable technologies include special plug-ins, such as CHIME, that allow students to dynamically view and manipulate molecular representations. If, on the other hand, the technology currently available would not support the writing of equations or representations, it would force an online instructor to develop other ways to represent content and thus impact pedagogy. Similarly, if the course content is about learning simple facts about the properties of each of the periodic chemical elements, then some pedagogical representations (e.g., essyas) are not as attractive. Likewise, a course about film might require certain technological tools, like digital video. These interactions go both ways; deciding on a particular technological tool will offer constraints on the representations that can be developed and the course content that can be covered and delivered, which in turn affects the pedagogical process as well.” (2006, 1030)

“Adding a pressure sensor to the demonstration can allow students to replay a video of the experiment with a graph of the internal pressure superimposed beside the video. By providing synchronized multiple representations of the event, students can visualize the meaning of the graph and connect the graph to pertinent features of the phenomenon” (133) “In contrast, ready access to primary source documents offers social studies teachers the possibility of different kinds of instructional approaches. Digital history centers and institutions such as the Smithsonian and the Library of Congress are increasingly making digital copies of historical documents such as photographs, artwork, and maps available online. These digital resources afford students the opportunity to create digital documentaries – short digital movies that contain a montage of images, text, or video accompanied by a narration done in the student’s voice. Educators believe that students who effectively use primary source documents can develop enhanced historical thinking skills.” (134) “Evidence exists that struggling readers sometimes have difficulty forming accurate images associated with the words that they are reading. The ability to combine images with words to create digital movies offers an avenue for reinforcing visual imagery — contextualizing the text in ways not previously possible. When the words are narrated in the student’s own voice, the process may also offer opportunities for auditory reinforcement.” “Students typically experience difficulty in understanding the relationship between a triangle and the characteristic shape of a sine wave – one has three sharp corners while the other has rounded peaks and valleys. This relationship is difficult to see in a static image in a textbook. However, when a tool such as the Geometer’s Sketchpad is used to create a digital animation over time, the relationship is more easily understood. The potential is further enhanced when the possibility of interactivity is considered — that is, students manipulating the variables and seeing changes to the animation or video in realtime.” (135)

“Responses coded as TPC included reference to such issues as using technology to encourage “student discovery” and the ability to perform quick visual assessment by glancing at the computer screen which allowed for immediate feedback to the students as needed.” (2183) “When asked to identify a lesson that she liked and enjoyed working through as a student, Connie stated, “I really liked the slope lesson that we did. I really liked how it was student-centered, with the students discovering it for themselves and then tying it back to, I guess, the formal way of doing it; the y equals m x plus b.” The value she places on student-centered exploration ties directly to the TPCK concept related to an awareness of the strategies that incorporate the use of technology to create a student-centered learning environment.” (2183) In the slope lesson, Connie was also impressed with the fact that the visual image made it possible for both the students and the instructor to determine quickly which students were making progress and which students required assistive feedback. During the modeled lesson, the instructor circulated the room, providing feedback if the coded cells did not indicate correct responses had been entered. In her interview Connie stated that she "really liked how when you entered an answer it either said good job or try again. I really loved that because it gives the student right on if they did it correctly or not. I also liked how it was convenient to have it pull up on all the computers and for each individual student so one student could have gotten it wrong, and instead of you checking all of them, they got immediate results at the same time." She incorporated this same visual assessment and feedback into her group’s lesson. When asked in her interview, "Do you have any other things you might want to mention that might have been different about the teaching of your lesson without the technology?" Connie responded, "With technology I could visually assess whether or not they could do it.” This allowed her to provide immediate assistive feedback as needed. This is confirmed in the field notes from the observation of her lesson which make note that as Connie circulated around the class she assessed what the students were creating and provided immediate feedback, reminding them that a tessellation has no gaps and no overlaps. She also indicated that "Not all shapes tessellate – keep that in mind." Without the use of the technology the quick visual assessment followed by assistive feedback would not be possible. At the conclusion of the microteaching phase of the project, a second interview was conducted and the data folder for each participant was reviewed. Upon completion of this review, several additional themes related to the development of TPCK during the MLS process emerged. Throughout the semester an emphasis was placed on teaching student-centered lessons. Connie indicates an awareness of this in her MLS feedback form when she answers the question, "What did you learn about teaching strategies while developing the lesson?" She replied: "I learned about teaching strategies: having the room student centered and using technology to aid in the learning process. The students created their own tessellations on the computer." When asked about any changes made between the first and second teaching of the lesson, Connie makes note that, "We altered the lesson to incorporate a bit more hands-on activities with technology." This confirms her awareness of the merits of using technology to promote student-centered learning.” (2183-84) “The decision to use the technology to incorporate this visual imaging option reflects an awareness of the use of a technological tool within a teaching strategy; one important aspect of TPCK.” (2184) “Kelly indicated that when making the decision for the technology to be used in their MLS lesson, her group did consider the use of Excel, but decided against it because "we were a little nervous about using it…. We weren’t exactly comfortable teaching it." She expanded by adding, "Are you asking if my experiences as a student affected or influenced my decision? (Yes.) I would say so. I chose something that I knew wouldn't be too complicated for the students to do. . . I wasn't teaching about technology. I was teaching for, you know, percents proportions and circle graphs and I needed a technology resource that would help me do that. I feel like the one I chose served that purpose instead of something else." In this case, her group’s lesson could have been accomplished using a spreadsheet, but her group chose a tool that would accomplish the same mathematical goal without teaching about the technology. Since the goal of TPCK is to apply technology in the teaching of content rather than teaching about technology, Kelly's group decision demonstrated the development of TPCK and its use in making pedagogical decisions.” (2184-85) “Teaching and reflecting on the MLS lesson helped to perturb Kelly’s thinking about the use of calculators and her belief in mental mathematics in a way that helped her transition her thinking toward a more appropriate use of technology in a mathematical lesson, indicating development of TPCK.” (2185) “In Connie’s case, the emphasis placed on visual assessment and immediate feedback indicated an awareness of the important pedagogical aspects of a technology-enhanced learning environment. Decisions such as the one made by Kelly’s MLS group to move from a classroom setting to a lab setting reflected the value of the strategies that incorporate the use of technology to create a student-centered learning environment. Also, the awareness of the benefit the calculators may have afforded in Kelly’s MLS group lesson indicated that she was reflecting on her decisions and reconsidering the value of including calculator technology.” (2185-86)

“Early interviews indicated that faculty was beginning to appreciate the dynamic and complex relationship between content, pedagogy and technology (Koehler, Mishra, Hershey & Peruski, 2004). “It’s not just like finding a way to get this stuff delivered. You’re actually creating a new way, your instructional deliveries, you’re actually creating fundamentally different ways of understanding” (Jim, May 7, 2001). Interviews during the middle and later stages of the design process indicated deeper understanding. We were thinking of the curriculum. What does it require in terms of key buttons or key navigation points or key structures? In terms of the pedagogy, what does that require? I wanted to add the lecture piece. That’s a reflection of the thinking of the pedagogy. I think it’s like how does the pedagogy influence the design? What if a group of people wants clarification so we want to create some avenue or opportunity to do that online (Jim, May 7, 2001)? When Juliet began the design process, she explained that she did not know much about technology and did not have much interest in learning about. However, in later interviews her explanation of her course structure, indicated new understandings about how technology helped her to achieve her pedagogical goals (individual and group learning, finding content online and in texts, providing feedback to students, etc). Each week of the class, they’ll have three units, or days. First, content… they’ll have to buy some texts, and online sites to visit. The second day will be small groups with applications. They’ll work in chat rooms and develop a group product and post them to the whole class. Day three involves individuals looking at what they did in groups and across groups and reflecting individually to me. I’ll then provide group feedback via voiceover to the whole group. In terms of how I make contact with them, every week they get an audio slide show of me previewing the week. I’m going to try to have fun with the pictures. We’re going to superimpose me in different parts of the world (Juliet, September, 26, 2001). Faculty interviews during teaching show the continued progression in understanding. For example, they came to understand the importance of dedicating a “space” or a thread for each of student groups in order to more efficiently mo nitor students’ small group discussions. In person, you can watch the team working and intervene. (Online) even though I was trying my best to watch the different threads, I couldn’t see the progress on a daily basis. I couldn’t intervene fast enough. I think that’s really important in team projects, setting up these communication systems so that the instructor can see the progress on a daily or on an every other day basis and intervene immediately (Mikala, December 7, 2001). Mikala provided an example of how all three faculty members were becoming clearer about affordances and constraints of the technology. It’s almost an iterative process. When I get on line it gives me some limitations like how quickly I can write. But I found that I could do more with it as well. I had different channels of communication so… it also was somewhat liberating. How can I use all these different threads of communication to do different things? I like that a lot (Mikala, December 7, 2001).” (2211-2212)

“In our case, technology can create an environment, SimCity, for students to explore the principles, practices and decisionmaking in economics and land use planning.” (2280) “SimCity4 is a simulation of the development of a city. Users zone land, provide services, and build amenities. Through the use of tools to iteratively create, explore and develop a city, the inherent interdependability of the economics and land use planning considerations are explored and tested. The consequences of the students’ actions are changes in the SimCity landscape and data representations. Based on our conceptual framework for knowledge development, we designed and implemented a continuous adaptation learning process (Fig. 2). The student develops a web of knowledge through a series of negotiations with existing knowledge, the knowledge available in SimCity and the knowledge available in the group. Students iteratively develop an understanding of city planning and balancing budgets. They apply these new understandings to their city decision making and to previous knowledge – which is continuously reevaluated and ‘adapted’. The design emphasized facility with the program, the development of a robust city, the balancing of the budget, and the ability to reflect on the principles and concepts in other environments. Our students managed knowledge as a fluid and dynamic entity. Our role was as facilitator and problem solver, as discussed by Mishra and Koehler (2006). We both engaged in three types of interactions with the students. First, we answered questions on a skills based level on SimCity. Second, we asked questions of the students to support their thinking. These questions were not directive in nature, rather they were to support the students continued interaction with the complex learning environment. The third type of interaction was supportive. None of these students had participated in an open ended assignment like this and some needed reassurance that the process they were engaged in was appropriate.” (2280)

“Participant's TPCK in the early stages of the research study focused more on procedural mathematical knowledge and the use of the technological tool primarily in performing arithmetic calculations. Later in the process, the emphasis was placed on conceptual knowledge and the relationship between the computations and the overall objective of the lesson. A shift in TPCK can also be seen in the specific pedagogical strategies related to the use of the technological tool, primarily in the areas of pacing and sequencing of the lessons. As the participants recognized weaknesses in these areas, modifications were made to enhance the effectiveness of the lesson. An additional shift in TPCK was evidenced in relation to the use of a technological tool in a studentcentered environment. Modifications to the lessons reflected a shift from almost no teacher-led instruction, to an integrated teacher-guided but student-centered approach. Evidence in each of these areas suggests that as the participants worked through the MLS process, their own concepts of what is involved in using a specific technological tool combined with specific technology-related teaching strategies in a manner that enhances student learning began to change, representing changes in their TPCK.” (5217)

“How should a K-12 geography teacher use a geospatial technology such as Google Earth in the classroom? Should they have students pinpoint a series of locations and measure the connecting distances, essentially using the technology as a mere digital representation of the traditional globe? Or, should they encourage learners to harness the powerful data-driven affordances of the technology to make and justify decisions on contemporary issues (for example, where to build a hospital in downtown San Francisco based on factors of seismic activity and population density)? We believe it is the latter scenario. However, there is a necessary level of technological, pedagogical, and content knowledge that an instructor must develop in order to apply this scenario successfully in the classroom.” (2010)

“Consider for example a teacher education class with a mix of digital natives and immigrants. It is important to take deliberate steps in the instructional design to accommodate the needs of both groups. This could involve building technology mediated small group activities into the instruction. By design each group could include both digital natives and digital immigrants on tasks designed to motivate and facilitate the acquisition of skills by the digital immigrants while simultaneously at least minimally challenging digital natives.” (5260)

“A response that incorporated all three types of knowledge would reveal an understanding of the multiple representations of a mathematical concept using technology or how mathematical misconceptions could be overcome with technology.” (5266) “The project was a great experience, both in terms of the valuable information I gained about the process of problem solving as well as the ability to teach problem solving procedures with the use of technology. I feel the portion of the project which benefited me the most, in preparing to create learning objects, was exploring the several approaches students take when solving a problem and being able to represent this with technology.” (5267) “Results from the content analysis revealed that at the end of the project some preservice teachers were able to integrate their mathematics content, pedagogy, and technology knowledge into a connected structure. This structure required evidence of MKT as it relates to representing concepts using technology, finding constructive way to teach math with technology, and knowledge of how technology can address misconceptions. The content analysis also revealed that such connected knowledge was not uniformly distributed among all three types of knowledge. That is, a single response coded as TPCK did not imply that all three components are equally weighted in the response. For example, consider the response: My favorite part of the project was creating the tutorials and sandboxes as part of the learning object for our assigned problem. This allowed each of us to use both our knowledge of the concepts we were teaching as well as our creativity, to create effective learning objects with technology. This TPCK response depicts a more connected knowledge with mathematics and technology, than with pedagogical knowledge.” (5269-5270)

“These in-depth descriptions were developed through triangulation of the data and analyzed by TPACK level resulting in the following extended descriptions that also add a sample teacher comment to illustrate the level: 1. Recognizing Recognizes mathematics ideas displayed with the technology. Views technology activities as focused on learning about the technology within a mathematics context as a tool that does the mathematics rather than teaching the mathematics. Knowledge and beliefs about learning and teaching mathematics describes mathematics as a subject learned through memorization of rules, algorithms and procedures without the use of technologies. Retains fundamental beliefs about how students learn mathematics. Motivation for exploring, experimenting and practicing integrating technologies in learning mathematics is challenged by beliefs about how students learn mathematics. Resists consideration of changes in the curriculum to integrate technology without further investigation about the technology. Instructional strategies for teaching mathematics based on teacher-directed lectures followed by individual student practice and repetition to solidify ideas. Teacher comment: The idea of organizing the information to help them solve math problems is a key to helping students learn math. Another feature that is difficult to learn in its intricacies but easy to start with is graphing. The graphical representation of spreadsheet data is very helpful especially for the visual learners in the class… I can see a student using spreadsheet skills to help them solve a mathematical problem if they already understand the underlying mathematical concepts. But I can see only limited, observational understanding being developed through their use. 2. Accepting Accepts the idea that some technologies can be useful tools for teaching and learning mathematics. Concerns about: o Students’ attention to and learning appropriate mathematics being diverted to a focus on the technology in the activities o Students’ thinking in mathematics when the technology is used as a tool for exploring the mathematics o Technology classroom access and management o The need to teach about the technology as taking away time for teaching mathematics Identically mimics professional development mathematics curricular ideas for incorporating the technologies. More apt to accept the technology as a teaching tool than a learning tool. Expresses desire but demonstrates difficulty in identifying topics in own curriculum for including technology as a tool. Tightly manages and orchestrates instruction with technology with the focus on technology in first lesson and the focus on mathematics in subsequent lessons after students have sufficient knowledge and skill with the technology. Teacher comment: My overall impression of using the spreadsheets in lessons and trying to integrate them with the mathematical concepts is that the students have a very difficult time learning the mathematical concepts when they are attempting to learn about using spreadsheets at the same time. The mechanics of producing the spreadsheets overshadows the mathematical concepts for many of the students. The only ones which seemed successful mastering both were the students that were fairly competent with spreadsheets prior to using them in my class.” 3. Adapting Recognizes some benefits of incorporating technology as a tool for teaching and learning the mathematics curriculum. Discusses desire to explore, experiment and practice integrating technologies as mathematics learning and teaching tools. Considers the technology as a tool to enhance a mathematics lesson, primarily as a means of providing students with a new way to approach the mathematics. Thinks of the technology as enhancing mathematics ideas that students have previously learned prior to using the technology. Expresses questions about student thinking with the technology as a tool in learning mathematics. Identically mimics the simplest professional development activities with the technologies but does attempt adapting lessons for his/her mathematics classes. Actions for implementing technologies in teaching mathematics are restricted by the challenges/barriers for teaching/learning with technologies. Instructional strategies with technologies are primarily deductive, teacher-directed in order to maintain control of the how the activity progresses. Teachers’ comments: Overall, I thought the experience of using Excel for teaching math concepts was worthwhile, both for myself as a teacher and for the students. They were able to see the math concepts we were working on applied in a real problem-solving environment, they felt successful when they applied those concepts in a spreadsheet and got a physical result (immediate feedback), and I was able to monitor their progress at a glance, which is not always obvious when they are working with pencil and paper. The number one barrier I envision would be my own limited abilities in using spreadsheets. While I am teaching the students to use spreadsheets, I will also be learning as I go. Over time as I become more familiar with the programs this won’t be as much of a problem. 4. Exploring Motivated to explore, experiment and practice integrating technologies as mathematics learning and teaching tools. Accepts technologies as tools for learning and teaching specific topics in the mathematics curriculum. Plans, implements, and reflects on teaching and learning in the implementations with concern for guiding students in understanding mathematics using the technology as a tool. Recognizes challenges for teaching mathematics with technologies but willingly explores strategies and ideas for minimizing the impact of the challenges. Explores ideas for placing technology in a more integral role for the development of the mathematics that students are learning. Tentative willingness to engage students in explorations of mathematics with the technology tool where the teacher is in role of guide rather than director of the exploration. Explores various instructional strategies (including both deductive and inductive strategies) with technologies to engage students in thinking about the mathematics. Manages technology-enhanced activities towards directing student engagement in learning the mathematics. Continues to learn and explore ideas for teaching and learning mathematics emphasizing the one technology (such as spreadsheets). Teachers’ comments: I was somewhat anxious to introduce spreadsheets into my curriculum. It was a new concept for me and I wasn’t sure how my students would adapt to it. I was also unsure as to how the marriage of spreadsheets and mathematics would look in my classroom. After the first lesson with my students, I knew I had nothing to worry about. Although none of them had ever used spreadsheets before, most had used the computer before and were very fluent with this technology. By keeping the math skills at a minimum in the beginning, students were able to focus more intently on learning the skills necessary for spreadsheets which later translated into being able to integrate more difficult math concepts with Excel. Even students who had made it very clear that they did not especially enjoy math, found themselves very involved in their learning when spreadsheets were integrated. A second success was seen, as we were able to look more closely at certain topics that required graphing. By being able to quickly change variables that had an immediate effect on the graph, gave students a firsthand look at how each of the parts of the equations play a role. If students had to graph by hand, there would not have been nearly the amount of time and attention given to the changes of variables. 5. Advancing _ Sustained motivation and carry through in exploring, experimenting and practicing integrating technologies as mathematics learning and teaching tools. _ Active, consistent acceptance of technologies as tools for learning and teaching mathematics in ways that accurately translate mathematical concepts and processes into forms understandable by students. _ Plans, implements, and reflects on teaching and learning in the implementations with concern and personal conviction for student thinking and understanding of the mathematics to be enhanced through integration of the various technologies. _ Recognizes challenges in teaching with technology and resolves the challenges through extended planning and preparation for maximizing the use of available resources and tools. _ Technology-integration is integral (rather than in addition) to development of the mathematics students are learning. _ Engages students in high-level thinking activities (such as project-based and problem solving and decision making activities) for learning mathematics using the technology as a learning tool. _ Adapts from a breadth of instructional strategies (including both deductive and inductive strategies) with technologies to engage students in thinking about the mathematics. _ Manages technology-enhanced activities in ways that maintains student engagement in learning the mathematics. _ Continues to learn and explore ideas for teaching and learning mathematics with multiple technologies. Teachers’ comments: I think that many students will feel like they are getting out of doing math by making the computer do it! Little do they know that they actually have to do much higher-level math and higher-level thinking and letting the computer do the basic arithmetic. Also anytime students get to interact with technology, they are engaged. Spreadsheets make students responsible for their learning while keeping them accountable. It’s a relatively easy way to engage students in mathematics learning. Another thing that I think worked out well was you know, the tendency for us to give students answers and I’ve been really trying to watch myself on that, knowing that if I just give answers to somebody, I haven’t really had them learn, I’ve only helped them memorize. So, I had to restrain myself a few times today just giving people the formulas and stuff like that.” (5300-5303)

Technology, Pedagogical, and Content Knowledge (TPaCK) I will provide leadership in helping others to effectively coordinate the use of technology, pedagogy and content knowledge at my school and/or district.

“Participation in GIT Ahead has expanded teachers’ TPCK by enhancing their technological literacy and helping them to integrate their new technological competencies with their pedagogical and content knowledge. The case studies illustrate examples of teachers integrating these three elements of TPCK as they design curricular applications of GIT and then implement, troubleshoot, and evaluate the effectiveness of these lessons. The case studies also provide evidence of growth in TPCK over the course of the year, with teachers reflecting on their increased technical competency and growing awareness of the curricular potential of geospatial tools. Expansion of TPCK is particularly evident when teachers begin viewing geospatial technologies as valuable pedagogical strategies rather than as new topics to be added into their curriculum. For example, case study teacher Matthew concluded that he could fit use of GPS into his highly constrained earth science classes if he treated GPS as a tool for learning about mapping rather than a topic in its own right.” (4803) emerging and crystallizing understandings about the interplay among TPCK.” (Peruski, Mishra, & Koehler, 2007, 2209-2210)

The most noticeable thing about these examples is that nearly all illustrate a unique context in which the teacher used (or considered the use of) technology to enhance students learning of a particular topic. The examples are very context-dependent, meaning that the solutions chosen in these scenarios may not be appropriate for every topic or every group of students or every teaching-learning situation. Also, the technology is being used for a particular purpose, not just for the sake of using technology. However, a degree of complexity is added to the examples as some represent different levels of TPCK, which may make it more difficult to classify examples as representing the TPCK construct.

In looking for examples of TPCK, the essential features must be these: (1) the use of technology (2) in a particular educational context (3) to teach a particular content (4) to fulfill a given educational objective/student need. Questions remaining for the TPCK experts are: (1) whether TPCK must include the use of content-specific pedagogical strategies rather than generic ones (see the technical use analysis of TPK); (2) how much detail must be provided regarding the context in order to classify an example as TPCK (versus TCK or TPK); and (3) how to address the idea of levels in searching for examples of TPCK.

Graphic Organizer

In order to better understand the results of the technical use analysis, the researcher organized the precising definitions and considerations for each construct in a graphic organizer (See Figure X). The major issue that the researcher observes in Koehler and Mishra’s model is that it does not take into account the fact that TPCK, TCK, and TPK overlap. Additionally, it does not elaborate the essential features of each construct.

Figure 4.1. TPCK graphic organizer after the technical use analysis.

Model Cases

The second phase of this conceptual analysis involved finding cases that embodied the essential features of each construct. This was done in three parts. First, examples were gleaned from the resources used in the technical use analysis. Second, TPCK experts and practitioners were interviewed to determine further examples. Finally, journals and trade magazines were searched for examples of technology use outside of the TPCK literature.

Technical use examples

For this portion of the model cases analysis, examples were only used if they were specifically classified by the original researchers as exemplifying one of the constructs as, at this point in the analysis, the purpose was to describe the constructs rather than attempt to categorize examples as belonging to one or another of them.

Technological Content Knowledge

In the technical use analysis, the researcher defined TCK as “An understanding of the technologies that may be utilized in a given discipline and how the use of those technologies interacts with the content of that discipline, particularly with regard to how that content may be represented.” Thus, a model case of TCK should exhibit a consideration of technologies that could be used for the discipline and how those technologies would impact the representation of the content. Kosiak & LeDocq (2008) cite the following as an example of TCK in their study:

“I enjoyed working with a partner and discussing different ideas and techniques of representing the math problem. I[t] was challenging but very helpful to see two different representations of a math idea using the tutorial and sandbox” (p. 5267).

In this example, the focus is on the representation of a concept from the content area using technology. The teachers discuss different technologies and representations that they could utilize to express the content.

Technological Pedagogical Knowledge

The precising definition for TPK derived in the technical use analysis was: “an understanding of the technologies that may be used in a pedagogical context, including the affordances and constraints of those technologies, and how those technologies influence or are influenced by the teacher’s pedagogical strategies.” Thus the essential features of this construct may be a consideration of which technologies might be used in a pedagogical context and how the technology used would impact the pedagogy. A model case of this construct was found in Peruski, Mishra, & Koehler (2007).

“I tried to think about things that would be interesting and how to engage them and how to coerce them to do that. In a classroom, you coerce them by your social persuasion skills. In an online format, your grades are tied to this because they won’t do it unless you provide some sort of incentive to do it because there is more anonymity so I’ve tried to think that through (Juliet, May 2, 2001)” (p. 2210).

Here the focus is on which technologies might be used to improve motivation and how the technology used changes the pedagogical strategies the teacher would normally engage in.

Technological Pedagogical Content Knowledge

As the definition of TPCK is more complex than the other constructs, the model case must also be more complex. The precising definition created by the researcher for this construct is “a way of thinking about the complex relationships between technology, pedagogy, and content in a specific context which is represented through the carefully considered implementation of technology in a classroom setting in order to help students better understand a particular topic.” Therefore, the essential features include a consideration of context, student learning, technologies that might be used to represent the content and how those technologies might change the content, technologies that might be used in the pedagogical context and how those technologies might change the pedagogical strategies. Niess (2008) provides an example of this construct:

“Even students who had made it very clear that they did not especially enjoy math, found themselves very involved in their learning when spreadsheets were integrated. A second success was seen, as we were able to look more closely at certain topics that required graphing. By being able to quickly change variables that had an immediate effect on the graph, gave students a firsthand look at how each of the parts of the equations play a role. If students had to graph by hand, there would not have been nearly the amount of time and attention given to the changes of variables” (p. 5302).

In this example, the teacher had clearly considered the particular students he/she was working with (some did not enjoy math) as well as their learning needs (graphing). Additionally, the teacher selected a technology to assist in representing the content and how that technology changed what was covered in the lesson. The technology was also chosen to support a particular pedagogical strategy and the teacher reflected on how that technology changed the pedagogy (focusing on changes of variables for a longer amount of time). This technology was selected for particular students in a particular context to support specific content and pedagogy.

Williams, D. G., Carr, T. L., & Clifton, N. S. (2006). Technology and urban youth: Emergent issues regarding access. In Tettegah, S. Y. & Hunter, R. C. (Ed.) Technology and Education: Issues in Administration, Policy and Applications in K12 Schools. (Advances in Educational Administration, Volume 8), p. 101-113.