Niess, M. L., Ronau, R. N., Shafer, K. G., Driskell, S. O., Harper S. R., Johnston, C., Browning, C., ÖzgünKoca, S. A., & Kersaint, G. (2009). Mathematics teacher TPACK standards and development model. Contemporary Issues in Technology and Teacher Education [Online serial], 9(1). Retrieved from http://www.citejournal.org/vol9/iss1/mathematics/article1.cfm
Mathematics Teacher TPACK Standards and Development Model
Margaret L. Niess
Oregon State University
Robert N. Ronau
University of Louisville
Kathryn G. Shafer
Ball State University
Shannon O. Driskell
University of Dayton
Suzanne R. Harper
Miami University
Christopher Johnston
George Mason University
Christine Browning
Western Michigan University
S. Asli ÖzgünKoca
Wayne State University
Gladis Kersaint
University of South Florida
Abstract
What knowledge is needed to teach mathematics with digital
technologies? The overarching construct, called technology, pedagogy, and content
knowledge (TPACK), has been proposed as the interconnection and intersection of
technology, pedagogy, and content knowledge. Mathematics Teacher TPACK
Standards offer guidelines for thinking about this construct. A Mathematics
Teacher Development Model describes the development of TPACK toward meeting
these standards. The standards and model provide structured detail to further
the work of various groups. The proposals may guide teachers, researchers,
teacher educators, professional development consultants, and school
administrators in the development and evaluation of professional development
activities, mathematics education programs, and school mathematics programs.
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 paperandpencil
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 yintercept 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 fourfunction
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 indepth 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 technologybased
or technologyrich activities into their courses” (FerriniMundy & Breaux,
2008, p. 437438).
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 (NETSS; 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 (NETST; 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 NETSS from basic skills and knowledge needed to operate the
technology to learning how to effectively use the technology; the NETSS 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 (MargerumLeys & 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 mathematicsspecific
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
preK12 as envisioned in the NETST. Although the NETST and NETSS
have been revisited and updated, neither set of standards provides
contentspecific 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 NETSS and NETST
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 nonEuclidean 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 studentcentered,
technologybased lesson that promoted higher order thinking in her students,
but this activity was a onetime occurrence in a 3year 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
innovationdecision process (first introduced in 1962 concerning societal
diffusion of innovations). Rogers described a fivestage, 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 4year 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 fivestage developmental process when learning
to integrate a particular technology in teaching and learning mathematics:
 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.
 Accepting (persuasion), where teachers form a
favorable or unfavorable attitude toward teaching and learning mathematics
with an appropriate technology.
 Adapting (decision), where teachers engage in
activities that lead to a choice to adopt or reject teaching and learning
mathematics with an appropriate technology.
 Exploring (implementation), where teachers actively
integrate teaching and learning of mathematics with an appropriate
technology.
 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’
innovationdecision 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 decisionmaking 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
Theme 
Descriptors 
Curriculum and Assessment 
 Curriculum, the treatment of the subject matter
 Assessment, assessing the students’ understandings

Learning 
 Focus on subject matter (i.e., learning of mathematics topics)
 Demonstration of conceptions of how students learn (i.e., development of students’ thinking skills)

Teaching 
 Focus on subject matter (i.e., learning of mathematics topics)
 Instructional approaches
 Classroom environment
 Professional development

Access 
 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 inservice 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 readymade 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.
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Author Note:
Margaret L. Niess
Oregon State University
niessm@onid.orst.edu
Robert N. Ronau
University of Louisville
bob@louisville.edu
Kathryn G. Shafer
Ball State University
kgshafer@bsu.edu
Shannon O. Driskell
University of Dayton
Shannon.Driskell@notes.udayton.edu
Suzanne R. Harper
Miami University
harpersr@muohio.edu
Christopher Johnston
George Mason University
cjohnst2@gmu.edu
Christine Browning
Western Michigan University
christine.browning@wmich.edu
S. Asli ÖzgünKoca
Wayne State University
aokoca@wayne.edu
Gladis Kersaint
University of South Florida
kersaint@coedu.usf.edu
