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I am going to look at Sharepoint: Own Cloud for cloud computing this week. I share a lot of data and reports in my position, so I think sharing them through Own Cloud would be the best way to do that. It's a new tool for my company, but I am pretty sure most of them would prefer receiving files through the cloud rather than through email like I had been doing it in the past. I sent out a poll to the people I send reports to, just to double-check their preferences, however, so we will see what I find out! Below is a screenshot of the poll I sent out using Wedgie, my tool from last week.

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Steve Smith - TPACK (Conceptual Framework)

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Steve Smith - TPACK (Conceptual Framework)

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My conceptual framework for Unit 1 is TPACK or Technological Pedagogical Content Knowledge. I believe this is especially important to my job as an English teacher at Brophy College Prep, a 1:1 computing high school in downtown Phoenix. Mishra and Koehler (2006) advocate for the integration of technology, pedagogy, and content knowledge into one practice. No longer are these ideas separate from one another.  This makes technology much less intimidating to me. I don’t have to learn this aspect of technology in a vacuum. I learn this aspect of technology for my content area and my teaching style. Sometimes the best ideas and frameworks are intuitive.  This is certainly the case with Mishra and Koehler and TPACK.
Further, this framework is freeing.  I can see how some elder-statesmen teachers are especially frightened by all the technology that has flooded schools. I see this at my school.  I believe some teachers simply “shut down” due to this deluge. That having been said, if they are presented technology as part of this integrated framework, I believe it would be much less intimidating.  I can see myself going back to my school site and using Mishra and Koehler to help some of the elder teachers at my school slowly but surely interweave technology and content and their overall pedagogy as means of improving classroom instruction and better meeting the needs of 21st century learners.
References
Mishra, P. & Koehler, M.J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge.  The Teachers College Record.

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I also used the FAQs on the Wedgie page.

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I used Twitter to get help with Wedgie. One of their admins actually started following me, and I was able to ask questions!

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Social Networks for Scholarly Research/Education

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Social Networks for Scholarly Research/Education

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Yamaguchi, M. & Maguth, B. (2011). Using social networking in the social studies for global citizenship: A case study of Japan’s 3:11 quake. Society for Information Technology and Teacher Education, (3260-287).

This article explores the use of social media in social studies courses to track primary and secondary sources, access discussions and groups around the world, and find groups to support victims of natural disasters. These researchers looked specifically at the actions of people as they turned to social media following major natural disasters. They analyzed the use of social media and made conclusions, based on the study of education, of how social media could be beneficial in education. They argue that using social media in education is beneficial for two main reasons: the first-person accounts found on social media can rarely be found in textbooks, and when students produce on social media, they are putting their work in front of an authentic audience that can give them real-world experience. This article is pertinent to my workplace in that we are always searching for ways to engage and connect with our students, and social media is a great way to do this. Using social media as a scholarly research tool is something our teachers could use to create connection with students and connection between the students and the material they are studying.

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Using Social Networking in Social Studies for Global Citizenship

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Meishar-Tal H., Kurtz G., & Pieterse E. (2012). Facebook groups as LMS: A case study. The International Review of Research in Open and Distance Learning, 13(4), 33-48.

My company is an LMS creator and provider, so free alternatives to LMS are intriguing to me and something my company of course tries to stay aware of as we are constantly innovating. This article details a case study conducted by professors from the Open University of Israel, for which they evaluated the usefulness of Facebook as an alternative to an LMS. They described their methodology for the study, then detailed the pros and cons of using Facebook as an LMS. Some of the pros include no cost, no technical maintenance, Facebook seems to foster more interaction with content, and more synchronous communication is available. Cons include that Facebook lacks some of the sharing capabilities of most LMS, Facebook dictates the organization of the group, and group members and administrators have many of the same capabilities. The biggest con is that Facebook’s assessment capabilities are virtually null, and it is not possible to store and track grades in Facebook. In the case study, the researchers found that using Facebook as an LMS enhanced collaboration and socially-motivated, active learning. Students did find some difficulty in the organization of material, and in separating their social presence on Facebook with their schoolwork. The researchers concluded that depending on the goals and functions of a course, Facebook can be used as an effective LMS, with the support of some other free tools such as Google Drive.

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Boitshwarelo, B. (2011). Proposing an integrated research framework for connectivism: Utilising theoretical synergies. International Review of Research in Open and Distance Learning, 12(3), 161-179. Athabasca University Press.

The theoretical lens I chose to view my articles through was connectivism. Connectivism looks at learning as heavily influenced by social and cultural context, and looks at ways educators can capitalize on that aspect of learning with their students. This article put forth “a research framework for connectivism that integrates approaches commonly used in online learning environments,” (p. 161) such as social media, LMS, and SIS. The framework “integrates the theories of online communities of practice, design-based research, and activity theory to construct a research framework that is characterised by a synergistic relationship between them” (p. 161). This framework allows researchers to look at the use of social media in educational settings through the lens of how it connects students to the social world around them and leads them to learn better with connectivist principles. The writers of this article propose this framework and ask that researchers who use it report back as to its usefulness so that they may more fully see its use in educational research settings. Reading this article gave me a way to look at different research results with an overall learning goal in mind. I am very interested in connectivism, as I think it applies even more as a learning theory in this digital age. This article gave a cogent argument for their framework as a way to connect studies back to connectivism.

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For whatever reason, my tweets to #techfoulger are not working, so here is the social media tool I plan on using! It is an online polling tool. My company is pretty careful in how they use social media, so I can't publicly post anything I am doing for work. This is a tool that I can use internally that I think will help with my online trainings.

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"What is Technological Pedagogical Content Knowledge?"

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"What is Technological Pedagogical Content Knowledge?"

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This article is a concise and clear explanation of the TPACK model. I appreciated the explanation, as the TPACK model is new for me.

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"Those Who Understand: Knowledge Growth in Teaching"

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"Those Who Understand: Knowledge Growth in Teaching"

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This 1986 article is a very interesting read to understand the history of teacher training : where we have come from and where we are going. It gives a great understanding of why we use frameworks like TPACK.

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I have looked at the standards for teachers many times, but I have never studied the standards for administrators. I enjoyed reading them, and plan to use them in my goals and planning for the year. This is a great resource!

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Hello! I am Heidi Jones. I started out as an English teacher, then I moved to online education as an online teacher for Edgenuity, Inc. I now am an Instructional Supervisor for Edgenuity and I focus on achievement and accountability for the department. I love online learning, and I have enjoyed what I have learned in the ASU Online Learning for K-12 certificate program!

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Kristen Mittal- Help with Exporting Video

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Kristen Mittal- Help with Exporting Video

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Hi all, I have created my video but cannot export it. This is what my screenshot looks like. Any help? It stays at 0% the whole time. If I try to publish it a 3rd time, it says I have to pay money for more than 5 minutes.

Thanks!

Update: Nevermind, I figured it out!

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Kristen Mittal - Interesting Articles for Capability Management

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Kristen Mittal - Interesting Articles for Capability Management

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http://www.wiwiss.fu-berlin.de/forschung/pfadkolleg/downloads/schreyoegg_kliesch.pdf

http://www.emeraldinsight.com/doi/abs/10.1108/02635570610671524

http://www.researchgate.net/profile/Arnoud_De_Meyer/publication/222476379_Lasting_improvements_in_manufacturing_performance_In_search_of_a_new_theory/links/53f6a2010cf22be01c451460.pdf

This is interesting flowchart on how to combat rigidity in capabilities

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Structure of Capability Management

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Lesson Planning using TPACK

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Ginny Saiki- Very Short Article on Future Workplace

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Ginny Saiki- Very Short Article on Future Workplace

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I graduated this May from ASU with my bachelors in biomedical engineering (BME) and now I am finishing my masters in BME through an accelerated program and will graduate this December. I am currently working at Stryker Sustainability Solutions in the Quality Operations department on reprocessed medical devices. I am taking this course to enhance my technological footprint at my workplace.

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In 1986 Lee Shulman launched a new way of thinking about the knowledge teachers need for teaching with a construct that he called pedagogical content knowledge (PCK). This new way of thinking about the knowledge teachers need for teaching called for the integration of content knowledge (the knowledge previously considered the primary knowledge for teachers) and pedagogical knowledge (the knowledge about teaching and learning). The intersection of these two knowledge bases, PCK, was described as the way of representing and formulating subject matter knowledge, the knowledge that makes the subject matter comprehensible to learners (Shulman, 1986, 1987; Wilson, Shulman, & Richert, 1987). More specifically, Shulman (1986) characterized a teacher's PCK as knowledge of

the most regularly taught topics in one's subject area, the most useful forms of representation of those ideas, the most powerful analogies, illustrations, examples, explanations, and demonstrations ... including an understanding of what makes the learning of specific concepts easy or difficult: the concepts and preconceptions that students of different ages and backgrounds bring with them to the learning. ( p. 9)

During those early discussions of the construction of knowledge growth in teaching, teacher preparation programs were challenged to determine how they might guide the development of this teacher knowledge. Some programs honed in on the development of six primary domains of knowledge essential for effective instruction: subject matter knowledge, pedagogical knowledge, knowledge of schools, knowledge of learners, and curricular knowledge, with PCK as the essence of the intersection of these five domains of knowledge (Niess, 2001). The relationship was viewed as a complex and integrated structure where no domain was totally distinct or separate from the other, with the relative amount of overlap and interaction among the domains constantly changing as preservice teachers made sense of and prioritized the multiple factors affecting student learning.

Attention to PCK through research studies provided insight into the preparation of preservice mathematics teachers' development of PCK (Ball, 1988; Civil, 1992; Grossman, 1991; McDiarmid, 1990; Simon & Brobeck, 1993; Simon & Mazza, 1993; Wilcox et al., 1990). Grossman's (1989, 1990) research identified four central components of PCK to focus the description and understanding of the knowledge needing development in the preparation programs: (a) an overarching conception of what it means to teach a particular subject; (b) knowledge of instructional strategies and representations for teaching particular subject matter topics; (c) knowledge of students' understandings, thinking, and learning in the subject area; (d) knowledge of curriculum and curriculum materials with learning subject matter (Borko & Purtnam, 1996).

As this understanding of PCK evolved, modern digital technologies also began to be recognized as useful for teaching and learning. During the late 1970s and 1980s, the focus in mathematics education was on identifying places in mathematics instruction for inserting digital technology applications. A myriad of software programs afforded drill and practice in a variety of environments that were more entertaining than traditional paper-and-pencil worksheets for providing practice with computational skills. Graphing calculators offered capabilities for efficiently generating visuals of graphs useful for demonstrating mathematical ideas such as slope and y-intercept for linear functions and points of intersection for multiple functions.

The primary vision for employing mathematical digital technologies was for demonstration and verification of ideas previously developed in the classroom. Calculators - from limited four-function calculators to scientific calculators - were restricted with the belief that these tools trivialized the mathematics rather than engaging students in learning mathematics. The lack of an in-depth integration of these technologies prompted Kaput's (1992) lament that the "major limitations of computer use in the coming decades are likely to be less a result of technological limitations than a result of limited human imagination and the constraints of old habits and social structures" (p. 515).

An examination of mathematics teachers' PCK in the late 1980s and early 1990s revealed an overarching conception that teachers' beliefs about how to teach mathematics generally were aligned with how they learned mathematics. Although a few teachers embraced the use of graphing calculators, spreadsheets, and software like Logo and Geometric Supposer, many did not. Mathematics teachers' knowledge of instructional strategies and representations for teaching particular mathematical topics relegated the application of such digital technologies to demonstration, verification, and drill and practice. Their knowledge of students' understandings, thinking, and learning in mathematics held to the importance of mastery of skills with paper and pencil prior to using modern digital technologies (Kastberg & Leatham, 2005; Walen, Williams, & Garner, 2003; Yoder, 2000).

Furthermore, access to technology without necessary knowledge of related curriculum materials did not encourage teachers to incorporate the technology in their classroom instruction (Kastberg & Leatham, 2005). "In the absence of professional development on instructional technology and curriculum materials that integrate technology use into the lesson content, teachers are not particularly likely to embed technology-based or technology-rich activities into their courses" (Ferrini-Mundy & Breaux, 2008, p. 437-438).

Fast forward to 2008 to see that many mathematics teachers' PCK lacks a solid and consistent integration of modern digital technologies in mathematics curriculum and instruction. Technologies, such as dynamic geometry tools or advanced graphing calculators with computer algebra systems (CAS), are primarily used for modeling and providing examples, where students imitate the actions and use the technologies for verification, demonstration, and drill and practice. In essence then, while digital technologies have evolved, strategies for their effective integration into the learning of mathematics have not evolved as rapidly.

Mathematics TPACK: The Total Package for Teaching Mathematics

As time shifted and digital technologies became more accessible and incorporated into citizens' work and play, the International Society for Technology and Education (ISTE) challenged teachers to think about the technology skills and knowledge students would need in an increasingly technology savvy society. By the turn of the 21st century, the National Education Technology Standards for Students (NETS-S; ISTE, 2000) were released with the goal of supporting the evolution of effective use of appropriate technologies in school settings.

ISTE recognized that these new standards called for different teacher knowledge than was currently operating in the schools. Within the following 2 years, the National Educational Technology Standards for Teachers (NETS-T; ISTE, 2002) were also released. Although embedded in a rapidly changing digital society, little real instructional change filtered into classrooms. Therefore, ISTE moved to shift the focus of the NETS-S from basic skills and knowledge needed to operate the technology to learning how to effectively use the technology; the NETS-S were updated in 2007. Subsequently, to assist teachers in responding to the call of learning environments supported by multiple technologies, a revision of the teacher standards was released in 2008.

These standards effectively shifted the focus on digital technologies toward a concern about the curriculum and instructional uses of the digital tools and resources. Earle (2002) framed this shift most clearly:

Integrating technology is not about technology - it is primarily about content and effective instructional practices. Technology involves the tools with which we deliver content and implement practices in better ways. Its focus must be on curriculum and learning. Integration is defined not by the amount or type of technology used, but by how and why it is used. (p. 8)

Numerous researchers focused on the integration of technology, content, and pedagogy in much the same way that Shulman described PCK, to gain a broader perspective on the knowledge teachers need for teaching with technology. In essence, they defined technological pedagogical content knowledge (TPCK) as that body of knowledge teachers needed for teaching with and about technology in their assigned subject areas and grade levels. TPCK was presented as the interconnection and intersection of content, pedagogy (teaching and student learning), and technology (Margerum-Leys & Marx, 2002; Mishra & Koehler, 2006; Niess, 2005; Pierson, 2001). The idea of TPCK developed to the point that the American Association of Colleges of Teacher Education supported the collaboration of multiple TPCK authors in the development of The Handbook of Technological Pedagogical Content Knowledge for Educators (AACTE Committee on Technology and Innovation, 2008).

TPCK was proposed as the strict intersection between the three individual knowledge constructs of technology, pedagogy, and subject matter content. The discussion often expanded beyond this intersection to include the overlapping constructs of technological content knowledge (TCK), technological pedagogical knowledge (TPK), and PCK (Koehler & Mishra, 2008). With the importance of the interplay between these constructs, TPCK has, over time, been recast as TPACK, or the total package required for integrating technology, pedagogy, and content knowledge in the design of instruction for thinking and learning mathematics with digital technologies (Niess, 2008; Thompson & Mishra, 2007). As technology, students, teachers, and classroom contexts change, TPACK provides a dynamic framework for viewing teachers' knowledge necessary for the design of curriculum and instruction focused on the preparation of their students for thinking and learning mathematics with digital technologies.

Mathematics Teacher TPACK Standards

The National Council of Teachers of Mathematics (NCTM) supported this new vision of TPACK early in 2000 with its Technology Principle in its standards for a new century, stating that "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning" (NCTM, 2000, p. 24). NCTM recognized and advocated the importance of the types of experiences teachers needed to be prepared to meet this standard. "If teachers are to learn how to create a positive environment that promotes collaborative problem solving, incorporates technology in a meaningful way, invites intellectual exploration, and supports student thinking, they themselves must experience learning in such an environment" (NCTM, 2007, p. 119). Similarly, the Association for Mathematics Teacher Educators (AMTE) advocated for enhancing the preparation of mathematics teachers in their Technology Position Statement: "Mathematics teacher preparation programs must ensure that all mathematics teachers and teacher candidates have opportunities to acquire the knowledge and experiences needed to incorporate technology in the context of teaching and learning mathematics" (AMTE, 2006). Yet, the question remained: What do these recommendations mean for improving the preparation of mathematics teachers?

The AMTE Technology Committee, whose role is to promote the investigation, engagement, and evaluation of uses of technology in mathematics teacher education and to recommend policy related to technology issues pertaining to enhancing mathematics teacher education programs, began addressing this question, initiating work on a set of mathematics-specific standards for TPACK. Given their charge, the AMTE Technology Committee considered the identification of directions and standards for mathematics teaching essential for promoting the improvement of mathematics education in the 21st century.

Beginning in 2007, the Committee focused on the task of creating a set of mathematics teacher standards to promote the implementation of technology in the context of teaching and learning mathematics in grades preK-12 as envisioned in the NETS-T. Although the NETS-T and NETS-S have been revisited and updated, neither set of standards provides content-specific ideas that address what students or teachers should know about using technology for learning mathematics. Therefore, these new mathematics teacher standards are intended to provide a framework for guiding professional practice that supports the improvement of mathematics teaching and learning. The themes in the standards are framed around the TPACK ideas that Niess (2005) adapted from Grossman's four components of PCK. The themes consider the teacher knowledge of incorporating technology in teaching mathematics as the knowledge and beliefs teachers demonstrate consistent with

An overarching conception about the purposes for incorporating technology in teaching mathematics;

Knowledge of students' understandings, thinking, and learning of mathematics with technology;

Knowledge of curriculum and curricular materials that integrate technology in learning and teaching mathematics;

Knowledge of instructional strategies and representations for teaching and learning mathematics with technologies.

A draft of the standards was presented to a working group session at the 12th annual conference of the AMTE in January 2008. Changes were made to the standards reflecting suggestions from the working group session. The updated standards draft was then presented at the 19th annual Society for Information Technology and Teacher Education (SITE) conference. As a followup, the standards were then disseminated to the AMTE Technology Committee, AMTE working group session participants, and SITE panel participants with a request for feedback. Subcommittees of the AMTE Technology Committee were then assigned to revisit other standards documents, such as the new versions of the NETS-S and NETS-T and to further revise the standards draft. Appendix A provides the current proposed draft of mathematics teacher TPACK standards and indicators.

Development of Mathematics Teachers' TPACK

In reviewing the draft version of the Mathematics Teacher TPACK Standards and Indicators, one of the authors interviewed a former undergraduate mathematics education major (called Mary for this discussion). Mary was a student in an undergraduate setting where technology was used in the teaching and learning of mathematics. Specifically, graphing calculators were used in her discrete mathematics course, and Geometer's Sketchpad was used extensively in her modern geometry course. After graduation, Mary taught Algebra I in a large suburban high school and was interviewed at the end of her third year in the classroom. She identified that Geometer's Sketchpad continued to be an important technological tool for her teaching and learning and that it had helped her learn non-Euclidean geometries. Geometer's Sketchpad was available at her school and was used by another teacher in her school. However, Mary chose not to use this software with her Algebra I students and thought that the software was only appropriate for use in a geometry class.

Mary reported that she primarily used graphing calculators for computation but not exploration. In her first 3 years of teaching, Mary indicated using technology only one time to teach a mathematical concept. The lesson she described had the students graph systems of linear equations and discover if and where the lines intersected, an appropriate use of the graphing calculator. Mary's lesson provided evidence of some of the indicators in the TPACK Standards I and II. Specifically, Mary planned a student-centered, technology-based lesson that promoted higher order thinking in her students, but this activity was a one-time occurrence in a 3-year time span.

Mary's case suggests different levels of the integrated knowledge of TPACK. Although the Mathematics Teacher TPACK Standards and Indicators set goals for technology integration, the standards themselves do not provide information on how teachers such as Mary progressively gain this integrated knowledge for appropriately teaching mathematics with suitable technologies. This recognition raises important questions. How does TPACK develop? Is there a process in which teachers gain mathematics TPACK knowledge? Do teachers suddenly display this knowledge in their professional practice? What is needed is a model that captures the progression of mathematics TPACK as teachers integrate technology into the teaching and learning of mathematics.

Niess, Sadri, and Lee (2007) proposed a developmental model for TPACK emanating from Everett Rogers' (1995) model of the innovation-decision process (first introduced in 1962 concerning societal diffusion of innovations). Rogers described a five-stage, sequential process by which a person makes a decision to adopt or reject a new innovation. Niess et al. reframed this process in terms of mathematics teachers learning to integrate a technology that they had not yet integrated in teaching and learning mathematics. Over a 4-year period, they observed many teachers learning about spreadsheets and how to integrate spreadsheets as learning tools in their mathematics classrooms. Analysis of these observations found that teachers progressed through this five-stage developmental process when learning to integrate a particular technology in teaching and learning mathematics:

1. Recognizing (knowledge), where teachers are able to use the technology and recognize the alignment of the technology with mathematics content yet do not integrate the technology in teaching and learning of mathematics.

2. Accepting (persuasion), where teachers form a favorable or unfavorable attitude toward teaching and learning mathematics with an appropriate technology.

3. Adapting (decision), where teachers engage in activities that lead to a choice to adopt or reject teaching and learning mathematics with an appropriate technology.

4. Exploring (implementation), where teachers actively integrate teaching and learning of mathematics with an appropriate technology.

5. Advancing (confirmation), where teachers evaluate the results of the decision to integrate teaching and learning mathematics with an appropriate technology.

Considering these five levels for integrating technology in teaching and learning mathematics relying on the integration of knowledge of technology, pedagogy, and content (TPACK), AMTE's Technology Committee created a visual description for thinking about the TPACK levels. Figure 1 depicts levels in which teachers engage as they develop their knowledge and understandings in ways that merge multiple knowledge bases ― technology, content, and pedagogy. On the left side of the graphic, the figure highlights PCK as the intersection of pedagogy and content. Then, as knowledge of technology expands and begins to intersect with pedagogical and content knowledge, the teacher knowledge base that emerges is the knowledge described as TPACK - where teachers actively engage in guiding student learning of mathematics with appropriate technologies.

Figure 1. Visual description of teacher levels as their thinking and understanding merge toward the interconnected and integrated manner identified by TPACK.

An important caveat when thinking about these levels and the progression toward TPACK is that, while appearing linear with respect to a particular technology, the transition from one level to another does not display a regular, consistently increasing pattern. As with Rogers' innovation-decision process, the emergence of a new technology requires rethinking its acceptance for teaching and learning mathematics. It requires rethinking the content and the pedagogies, as well. Thus, the levels are proposed to display more of an iterative process in the development of TPACK. Some aspects of what is learned about teaching a particular topic with one technology may provide a disposition toward acceptance of another technology, but teachers often challenge an integration that is different from the way they learned specific mathematics concepts.

A Mathematics Teacher TPACK Development Model

While the Mathematics Teacher TPACK Standards provide a lens for considering the actions of teachers who have an integrated knowledge of technology, content, and pedagogy, the recognition of the levels of thinking and understanding as they begin to develop this TPACK calls for clarification. Mishra and Koehler (2006) dissected the basic TPACK framework into its knowledge components beginning with content knowledge (CK), pedagogical knowledge (PK), and pedagogical content knowledge (PCK). As technology knowledge (TK) becomes integrated with these components, additional components emerge: technological content knowledge (TCK) and technological pedagogical knowledge (TPK) are added to PCK as intersections of the content, pedagogical, and technological knowledge. They discussed TCK as follows: "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" (p. 1028). TPK was described as "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" (p. 1028).

These added descriptions explain the various intersections in general terms; however, they are not embedded within the context of developing mathematics TPACK. The AMTE Technology Committee decided to unpack the teacher levels in thinking and understanding in the process of the development of TPACK, as described in the Mathematics Teacher TPACK Standards. Four major themes further framed the Mathematics Teacher TPACK Development Model: Curriculum and Assessment, Learning, Teaching, and Access. Rather than treating Curriculum and Assessment separately, the Technology Committee decided that these themes should be grouped to highlight the connection between the curricular and assessment decision-making process. From this thinking, the Technology Committee developed descriptors as outlined in Table 1.

Table 1
Descriptors for Major Themes in the Mathematics Teacher TPACK Development Model

Curriculum and Assessment

Curriculum, the treatment of the subject matter

Assessment, assessing the students' understandings

Focus on subject matter (i.e., learning of mathematics topics)

Demonstration of conceptions of how students learn (i.e., development of students' thinking skills)

Focus on subject matter (i.e., learning of mathematics topics)

Instructional approaches

Classroom environment

Professional development

Usage (whether or not students are allowed to use technology)

Barriers (how teachers address barriers to technology integration)

Availability (how technology makes higher levels and more mathematics available for investigation for greater numbers of more and more diverse students.

The next step was to expand the descriptors through the TPACK levels and identify specific examples for each descriptor at each of the TPACK levels using detailed descriptions of the levels provided from Niess' (2007) work. Appendix B expands the Mathematics Teacher TPACK Development Model, providing detailed (albeit not exhaustive) actions that teachers may experience and engage in while adapting technology in their teaching in order to enhance student learning.

As an example of how the Curriculum and Assessment theme engages the shift in mathematics subject matter, consider teachers who initially recognize that technology can be used to support mathematical processes such as square root. Teachers' thought processes progress toward an acceptance of the technology as they incorporate it as an alternative for the algorithmic procedure for finding a square root, although they remain concerned about the loss of algorithmic skills for finding square roots.

At the adapting level teachers are willing to try some activities in the classroom that typically mimic activities from their own professional development experiences. Perhaps they focus on estimating square roots and then compare their estimates with calculator results. At some point, these teachers begin to explore their specific mathematics curriculum in search of places to incorporate the calculator square root function as a tool for shifting the subject matter emphasis toward an application of the concept of square roots, where students are allowed to find the results using appropriate technologies such as calculators for identifying the square root results.

Teachers at the advancing level not only incorporate calculators for working on other mathematical topics, they actually challenge the curriculum, looking for how that curriculum might shift as a result of the calculator's capability for finding square roots. These teachers are more willing to make changes in their curriculum, adding and dropping particular topics as a result of the technological capabilities. Now, these teachers no longer focus on teaching the square root algorithm and allow students to use calculators to identify actual square roots, if such a result is needed. With these teacher decisions, the curriculum is shifted toward teaching the concept of square root and estimating square roots, rather than the more procedural emphasis on finding square roots; in fact, a new curriculum component may be introduced to focus on understanding the difference between approximate and exact solutions.

From the Learning theme, teachers might recognize that technology provides an instructional tool for their mathematics classes but at the same time they might perceive that the technology potentially interferes with learning key mathematical ideas. Therefore, the technology is allowed only outside of the regular instructional activities. At the accepting level, teachers see that the technology is here to stay and form their own attitudes and beliefs regarding its use in their instruction. At this level teachers might have concerns that students do not develop appropriate mathematical thinking skills; so technology is used to check their work, first completed with paper and pencil. At the adapting level, teachers start experimenting with the technology to determine whether to adopt or reject it. They might consider it to be useful but still express questions about students developing appropriate mathematical thinking skills. Therefore, although students use technology for most topics, testing remains mostly technology free.

At the exploring level, teachers who decide to adopt the technology in their classrooms start integrating teaching and learning of mathematics with appropriate technologies; they plan, implement, and reflect on teaching and learning with a possible concern for guiding students in understanding mathematics using the technology as a tool for learning. At the last level, advancing, teachers are likely to evaluate the results of the decision to integrate technology in teaching and learning mathematics. As a result, technology integration becomes integral (rather than in addition) to the development of the mathematics students are learning.

TPACK Next Steps

This description of the overarching construct of TPACK provides specific and identifiable constructs of teacher knowledge associated with TPACK, accompanied with a model or a framework that supplies context for the constructs. The themes, levels, and descriptors provide structured detail to permit various groups to use the model independently. The five levels (recognizing, accepting, adapting, exploring, and advancing) expand upon the themes of Curriculum and Assessment, Learning, Teaching, and Access. The descriptors for each level and the mathematics examples provide further delineation of the themes and levels. This structure may be useful for teachers, researchers, teacher educators, professional development consultants, and school administrators to guide development and evaluation of professional development activities, mathematics education programs, and school mathematics programs.

Teachers may find the model useful in assessing their level of mathematics TPACK using the descriptors and examples, and then plan their individual professional development in mathematics instructional technology. Principals and professional development consultants, with specific work guided by TPACK, are able to plan more informed and directed professional development for groups of teachers, as well as evaluate the effectiveness of their programs. Teacher educators might find the TPACK levels helpful in evaluating and planning the technology preparation of their preservice and in-service students. The Mathematics Teacher TPACK Developmental Model establishes common constructs and language that should help researchers connect their work to that of others and within a larger context.

A number of questions remain about the model. For example, a mathematics teacher may be at different levels for different themes and descriptors ( Appendix B). That is, in the Curriculum and Assessment theme, one might be at the exploring level by demonstrating a willingness to develop personal ideas for using technologies in instruction, yet at the recognizing level when it comes to allowing students to use technologies during assessments. This proposal must be tested. Moreover, moving from one level to another may require different sets of experiences for different levels and for different teachers. What are these sets of experiences? Do experiences exist that cause teachers to regress from one level to a previous one? Do teachers skip levels?

This model generates a number of new questions for mathematics educators; however, these questions are much more focused and specific than what typically emerge without such a model. Moreover, the answers to these questions, should they be answered, will have a ready-made framework for a mathematics context. In this way, mathematics education moves forward in the understanding of the impact of technology on the learning of mathematics.

The Mathematics Teacher TPACK Standards and the corresponding TPACK Development Model are works in progress that may change as new technologies are introduced into mathematics classrooms and as more research is conducted in classrooms that carefully examine and describe the teaching and learning. A directed focus on understanding mathematics teachers' TPACK will continue to push the uses of technology in the mathematics classroom, as well as outside of our current limited human imagination.

References

AACTE Committee on Innovation and Technology (Eds). (2008). Handbook of technological pedagogical content knowledge (TPCK) for educators. New York: Routledge

Association of Mathematics Teacher Educators. (2006). Preparing teachers to use technology to enhance the learning of mathematics. Retrieved from http://www.amte.net/

Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Unpublished doctoral dissertation, Michigan State University, East Lansing.

Borko, H., & Putnam, T. (1996). Learning to teach. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 673-708), New York: Simon & Schuster Macmillan.

Civil, M. (1992, April). Prospective elementary teachers' thinking about mathematics. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA.

Earle, R.S. (2002). The integration of instructional technology into public education: Promises and challenges. ET Magazine, 42(1), 5-13.

Ferrini-Mundy, J., & Breaux, G. A. (2008). Perspectives on research, policy, and the use of technology in mathematics teaching and learning in the United States. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Volume 2. Cases and perspectives (pp. 427-448). Charlotte, NC: Information Age Publishing.

Grossman, P. L. (1989). A study in contrast: Sources of pedagogical content knowledge for secondary English. Journal of Teacher Education, 40(5), 24-31.

Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.

Grossman, P. L. (1991). Overcoming the apprenticeship of observation in teacher education coursework. Teaching and Teacher Education, 7, 245-257.

International Society for Technology in Education. (2000). National educational technology standards for students: Connecting curriculum and technology. Eugene, OR: International Society for Technology in Education.

International Society for Technology in Education. (2002). National educational technology standards for teachers: Preparing teachers to use technology. Eugene, OR: International Society for Technology in Education.

International Society for Technology in Education. (2007). National educational technology standards and performance indicators for students. Eugene, OR: International Society for Technology in Education.

International Society for Technology in Education. (2008). National educational technology standards and performance indicators for teachers. Eugene, OR: International Society for Technology in Education.

Kaput, J. (1992). Technology and mathematics education. In. D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 515-556).New York: MacMillan Publishing.

Kastberg, S., & Leatham, K. (2005). Research on graphing calculators at the secondary level: Implications for mathematics teacher education. C ontemporary Issues in Technology and Teacher Education, 5(1). Retrieved from http://www.citejournal.org/vol5/iss1/mathematics/article1.cfm

Koehler, M. J. & Mishra, P. (2008). Introducing technological pedagogical content knowledge. In AACTE Committee on Innovation and Technology (Eds)., Handbook of technological pedagogical content knowledge (TPCK) for educators (pp. 3-29). New York: Routledge.

Margerum-Leys, J., & Marx, R. W. (2002). Teacher knowledge of educational technology: A study of student teacher/mentor teacher pairs. Journal of Educational Computing Research, 26(4), 427-462.

McDiarmid, G. W. (1990). Challenging prospective teachers' beliefs during early field experience: A quixotic undertaking? Journal of Teacher Education, 41(3), 12-20.

Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017-1054.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (2007). Mathematics teaching today: Improving practice, improving student learning (2nd ed.). Reston, VA: Author.

Niess, M. L. (2001). Research into practice: A model for integrating technology in preservice science and mathematics content-specific teacher preparation. School Science and Mathematics, 101(2), 102-109.

Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge. Teaching and Teacher Education, 21, 509-523.

Niess, M. L. (2007, June). Mathematics teachers developing technological pedagogical content knowledge (TPCK). Paper presented at IMICT2007, Boston, MA.

Niess, M. L. (2008). Knowledge needed for teaching with technologies - Call it TPACK. AMTE Connections, 17(2), 9-10.

Niess, M. L., Sadri, P., & Lee, K. (2007, April). Dynamic spreadsheets as learning technology tools: Developing teachers' technology pedagogical content knowledge (TPCK). Paper presented at the meeting of the American Educational Research Association Annual Conference, Chicago, IL.

Pierson, M. E. (2001). Technology integration practices as a function of pedagogical expertise. Journal of Research on Computing in Education, 33(4), 413-429.

Rogers, E. M. (1995). Diffusion of innovations. New York, Free Press.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4-14.

Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57, 1-22.

Simon, M. A., & Brobeck, S. (1993, March). Changing views of mathematics learning: A case study of a prospective elementary teacher. Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NW), Monterey, CA.

Simon, M. A., & Mazza, W. (1993, October). From learning mathematics to teaching mathematics: A case study of a prospective teacher in a reform-oriented program. Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA), Monterey, CA.

Thompson, A. D., & Mishra, P. (2007). Breaking news: TPCK becomes TPACK! Journal of Computing in Teacher Education, 24(2), 38, 64.

Walen, S. B., Williams, S. R., & Garner, B. E. (2003). Pre-service teachers learning mathematics using calculators: A failure to connect current and future practice. Teaching and Teacher Education, 19, 445-462.

Wilcox, S., Schram, P., Lappan, G., & Lanier, P., et al. (1990, April). The role of a learning community in changing preservice teachers' knowledge and beliefs about mathematics education. Paper presented at the annual meeting of the American Educational Research Association, Boston, MA.

Wilson, S. M., Shulman, L. S., & Richert, A. E. (1987). '150 different ways' of knowing: Representation of knowledge in teaching. In J. Calderhead (Ed.), Exploring teachers' thinking (pp. 104-124). London: Cassell.

Yoder, A. J. (2000, October). The relationship between graphing calculator use and teachers' beliefs about learning algebra. Paper presented at the annual meeting of the Mid-Western Educational Research Association, Chicago, IL.

Author Note:

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Mathematics Teacher TPACK Standards and Development Model

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In 1986 Lee Shulman launched a new way of thinking about the knowledge teachers need for teaching with a construct that he called pedagogical content knowledge (PCK). This new way of thinking about the knowledge teachers need for teaching called for the integration of content knowledge (the knowledge previously considered the primary knowledge for teachers) and pedagogical knowledge (the knowledge about teaching and learning).

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Having a little fun with TPaCK

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Ginny Saiki--Standards for my area of study (Instructional Design).

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Ginny Saiki--Standards for my area of study (Instructional Design).

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Ginny Saiki--Short and sweet explanation of TPACK.

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Ginny Saiki--Short and sweet explanation of TPACK.

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Technological Pedagogical and Content Knowledge

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Ginny Saiki--TPACK article found in ASU Library search

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Ginny Saiki--TPACK article found in ASU Library search

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This looks exciting, and it says you can try it for free (sounds dubious). Regardless, it looks like a fun way to organize a flipped classroom. Posted by Steve Smith.

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Hello. My name is Steve Smith, and I teach at Brophy College Prep in downtown Phoenix. I'm so excited for all the new things I'll learn in this class.

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 Hi Everyone!  My name is Ginny Saiki and I am originally from North Dakota.  I have lived in AZ for almost 10 years, and am an Instructor for ASU Academic Success Programs.  (I guess now I get to see if I can walk the talk!)    I am working on my Master's in Ed Tech, and looking forward to learning what is necessary to keep up with my students!

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 Hi Everyone!  My name is Ginny Saiki and I am originally from North Dakota.  I have lived in AZ for almost 10 years, and am an Instructor for ASU Academic Success Programs.  (I guess now I get to see if I can walk the talk!)    I am working on my Master's in Ed Tech, and looking forward to learning what is necessary to keep up with my students!

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Hi, my name is Shaun Bennison.  I'm originally from Indiana, but have been living out here in Phoenix since 2003.  I received a Business Management Degree from Purdue University.  Changed careers and got my teaching certification from ASU.  I earned my Masters degree in from NAU in Multicultural/Bilingual Education.  I've been teaching 5th grade at Rio Vista in the Pendergast District in Avondale for 10 years.  I'm married and have a little girl that is turning 1 this month.  I've been to ISTE 3 times and love trying to implement new technology in the classroom whenever I can.  It's nice meeting everyone.  

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Hi, my name is Shaun Bennison.  I'm originally from Indiana, but have been living out here in Phoenix since 2003.  I received a Business Management Degree from Purdue University.  Changed careers and got my teaching certification from ASU.  I earned my Masters degree in from NAU in Multicultural/Bilingual Education.  I've been teaching 5th grade at Rio Vista in the Pendergast District in Avondale for 10 years.  I'm married and have a little girl that is turning 1 this month.  I've been to ISTE 3 times and love trying to implement new technology in the classroom whenever I can.  It's nice meeting everyone.  

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Charisa Dickson---A Prezi on SAMR, TPACK, and 21st Century Skills 

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Charisa Dickson---A Prezi on SAMR, TPACK, and 21st Century Skills 

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Also found this during my TPACK twitter search.

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After doing a twitter search for TPACK, I kept coming across comparisons between TPACK and SAMR. Interesting...

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I shared about the infographic that Rebecca Cissel of 21st Century Tekkie and I created. Now it is even better because Rebecca app smashed and used ThingLink to add links to our infographic. Here it is in all its link love glory.

I shared about reading the new to be out book, Power Up: Making the Shift to 1:1 Teaching and Learning, and one of the AUTHORS, Jen Roberts, shared two links related to SAMR and TPACK.

@harristeaches Thank you! I looked at some of your other posts. I think you'll like http://t.co/GwxiDImFpv and http://t.co/6ewjuv00QW

- Jen Roberts (@JenRoberts1) June 18, 2015

For SAMR, she took the focus of the tasks and placed it back on students and teachers.

For TPACK, she took a similar approach and added an "S" for students.

P.S. Summer (for me) is officially here! Have you read this article about 16 ways summer improves teachers' lives? #14 is one of my favs!

8,069 total views, 5 views today

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I shared about the infographic that Rebecca Cissel of 21st Century Tekkie and I created. Now it is even better because Rebecca app smashed and used ThingLink to add links to our infographic. Here it is in all its link love glory.

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Hello! My name is Stephen Cowart. I teach high school math at the Phoenix Union High School District. This is my third year at this school and my fifth year teaching. I am currently in the Accomplished Teaching - Educational Technology degree and I will be finished with that in one more semester. My goals after this course are to implement more technology into my own classroom and eventually teach online. A fun fact about me is that I started playing tabletop board games a lot about a year ago and I own about 50 different board games. I look forward to working with everyone this semester!

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Hello! My name is Stephen Cowart. I teach high school math at the Phoenix Union High School District. This is my third year at this school and my fifth year teaching. I am currently in the Accomplished Teaching - Educational Technology degree and I will be finished with that in one more semester. My goals after this course are to implement more technology into my own classroom and eventually teach online. A fun fact about me is that I started playing tabletop board games a lot about a year ago and I own about 50 different board games. I look forward to working with everyone this semester!

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Stephen Cowart - TPACK in 2 minutes video

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Stephen Cowart - TPACK in 2 minutes video

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A video from youtube that explains the basics of TPACK in 2 minutes. Quite helpful to get a general understanding of what TPACK is.

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Charisa Dickson---- What Is Technological Pedagogical Content
Knowledge?

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Charisa Dickson---- What Is Technological Pedagogical Content
Knowledge?

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In this article, Koehler and Mishra discuss the framework for teacher knowledge on technology integration, known as TPACK (technology, pedagogy, and content knowledge). Koehler and Mishra begin by comparing traditional technologies, such as a pencil and paper, to digital technologies, such as computers and smartphones. They tell about how traditional technologies are no longer considered “technologies,” as they have become commonplace. Therefore, these traditional technologies are characterized by their specificity, stability, and transparency of function. Digital technologies however, are not so commonplace, as they are constantly evolving; these digital technologies are characterized by protean (usable in many different ways), unstable (rapidly changing), and opaque (their inner workings invisible to its users). Because of these versatile, rapidly changing, and obscure digital technologies, it makes it more difficult for teachers to always use them in the classroom. This is where TPACK enters. In TPACK’s model, there are three main components of a teachers’ knowledge: Content, Pedagogy, and Technology. Within these three main components, are important bodies of knowledge: Pedagogical Content Knowledge (PCK), Technological Content Knowledge (TCK), and Technological Pedagogical Knowledge (TPK). Combining all components creates Technological Pedagogical Content Knowledge (TPACK). Koehler and Mishra go on to describe each component in length, ending with the emergent form of knowledge: TPACK.

Reference:

Koehler, M. J., & Mishra, P. (2009). What is technological pedagogical content knowledge?, Contemporary Issues in Technology and Teacher Education, 9(1), 60-70.

http://www.citejournal.org/vol9/iss1/general/article1.cfm

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What Is Technological Pedagogical Content Knowledge?

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Hi, I'm Charisa Dickson. (I'm currently sitting at the airport...fun stuff! Haha) I worked in the Tempe Elem. school district for five years, and currently I am going into my second year teaching at Connections Academy---an online K-12 school. I teach 2nd grade and love it! :) I am getting my masters in Instructional Design and I am excited to learn more in this class about Emerging Technologies in schools! I hope to use the information I learn in this class and apply it to my current career and my future professional agenda.

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Hi, I'm Charisa Dickson. (I'm currently sitting at the airport...fun stuff! Haha) I worked in the Tempe Elem. school district for five years, and currently I am going into my second year teaching at Connections Academy---an online K-12 school. I teach 2nd grade and love it! :) I am getting my masters in Instructional Design and I am excited to learn more in this class about Emerging Technologies in schools! I hope to use the information I learn in this class and apply it to my current career and my future professional agenda.

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Hi I'm Dr. Foulger. I will be your facilitator through this course. I thought it might be fun for us to share our resources here, in padlet. This particular padlet is dedicated to Unit 1. Please contribute to the knowledge bank here by adding resources that you use for your video. You'll want to do this in a timely manner so you can be helpful to others, and visa versa. For practice, please create a welcome message of your own on this page by clicking on the edit (pencil) icon in the lower left of this window. Tell your classmates about you and add a photo by clicking on the camera icon in the new field. That way we can see your face on this page

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Hi I'm Dr. Foulger. I will be your facilitator through this course. I thought it might be fun for us to share our resources here, in padlet. This particular padlet is dedicated to Unit 1. Please contribute to the knowledge bank here by adding resources that you use for your video. You'll want to do this in a timely manner so you can be helpful to others, and visa versa. For practice, please create a welcome message of your own on this page by clicking on the edit (pencil) icon in the lower left of this window. Tell your classmates about you and add a photo by clicking on the camera icon in the new field. That way we can see your face on this page

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Watch this orientation to padlet.com, our knowledge bank tool, created by Dr. Foulger: http://screencast.com/t/XQW9HUvx0lC

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Free online storage and sharing with Screencast.com. 2 GB of storage and 2 GB of bandwidth per month for free. We won't compress, alter or take ownership of your content.

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Technology Standards (most appropriate for PreK-12 professionals): The course objectives and activities are aligned with the International Society for Technology in Education (ISTE) Educational Technology Standards, meant to support the integration of technology in learning situations.The standards can be viewed at http://www.iste.org/standards .Pick the standard set(s) that apply directly to you,within your professional setting.

Standards for Professional Learning (appropriate for any professional): Improving the performance of educators, with the bottom line of impacting student achievement, is addressed by professional standards created by 40 professional associations and education organizations. These standards do not address how to improve performance; instead, they focus on professional learning. Those who are not “teachers” and are good at adapting frameworks to other contexts will find these helpful.
See http://learningforward.org/standards#.U2qLC8cZfQA and http://learningforward.org/standardsfor-professional-learning#.U2qOyMcZfQA