Dynamic Spreadsheets as Learning Technology Tools: Developing Teachers’ Technology Pedagogical Content Knowledge (TPCK)

Dynamic Spreadsheets as Learning Technology Tools:  Developing Teachers’ Technology Pedagogical Content Knowledge (TPCK)

Margaret Niess, Pejmon Sadri and KwangHo Lee

Department of Science and Mathematics Education

Oregon State University

Corvallis, OR 97331 USA

niessm@onid.orst.edu, sadrip@onid.orst.edu, leekw@onid.orst.edu

Abstract: Few mathematics or science teachers have incorporated spreadsheets as dynamic learning tools with unique capabilities for supporting students in engaging in problem solving and decision making leading to increased science/mathematics content knowledge, skills and dispositions.  These teachers have neither learned their content with this tool nor been prepared to teach with dynamic spreadsheets in ways that developed their technology pedagogical content knowledge (TPCK) to an activation level.  The professional development program emphasized integrating teaching their content with designing dynamic spreadsheets through an intensive summer workshop.  This paper focuses on this emphasizing inquiry-based/decision-making teaching of science/mathematics while concurrently learning about designing dynamic spreadsheets within a science/mathematics curriculum. Multiple case studies of teachers’ development of TPCK expose ideas for meaningful in-service programs for practicing teachers to integrate innovative technologies in learning in their content. Implications describe considerations for guiding teachers toward more advanced, action-oriented levels of TPCK where they willingly test and expand on their ideas in technology-enhanced classroom environments.

Spreadsheets are readily available among classroom technologies with potential for engaging students in higher-level content objectives in both the mathematics and science. In particular, when students develop skills in using dynamic spreadsheets to investigate problems, they also acquire skills that support them in learning important science/mathematics concepts and processes while modeling and extending problems beyond their original conditions.  Unfortunately, spreadsheet technology use is limited or almost nonexistent in science/mathematics classrooms.  The teachers have not learned their content with these technology tools nor have they had teacher preparation experiences to challenge their thinking and visioning about how students might learn science or mathematics with dynamic spreadsheet technologies. In short, they have not been prepared to integrate dynamic spreadsheets as teaching and learning tools. These teachers need educational experiences directed at (1) expanding their own conceptions of teaching science/mathematics with spreadsheets, (2) investigating and expanding their knowledge of instructional strategies for integrating spreadsheet learning activities, (3) developing their own knowledge and skills of spreadsheets as tools for exploring and learning science/mathematics, and (4) exploring curricular materials that support learning with and about spreadsheets over an extended period of time.  These teachers need in-service educational programs that support them in developing a technological pedagogical content knowledge (TPCK) for integrating dynamic spreadsheets with teaching science/mathematics. What type of experiences do they need?  Can they simply focus on learning about spreadsheet capabilities?  Much evidence about the preparation of teachers to teach mathematics/science suggests that simply learning about spreadsheets is not sufficient preparation for engaging students in learning mathematics/science with spreadsheets.  Such preparation does not deal with content area topics that might benefit from dynamic spreadsheet explorations.  Also, current thinking suggests that the knowledge for teaching specific content requires attention to more than the technology and the content. TPCK, the interconnection and intersection of content (mathematics), pedagogy (teaching and student learning), and technology (spreadsheets) (Margerum-Leys & Marx, 2002; Mishra, & Koehler, 2006; Niess, 2005; Pierson, 2001; Zhao, 2003), is a mode of thinking that integrates these multiple domains of knowledge in ways that rely on planning, organizing, critiquing and abstracting ways to integrate technologies such as spreadsheets with specific subject matter content while also attending to specific student needs.  

Optimally, teachers need opportunities for learning and building their TPCK while they are teaching. However, few school systems have capacities for on-going professional development.  Reality suggests that teachers must rely on summer workshops for intensive instruction directed toward developing their TPCK. Yet, an experience in a summer workshop does not result in teachers who either have TPCK or who do not.  From prior professional development program research, Niess et al. (2006) identified and described five increasing ability TPCK levels for teaching with spreadsheets:

• Recognition: The teacher considers spreadsheets as tools for teaching and learning their content.
• Accepting: The teacher accepts the idea of teaching and learning their content with spreadsheets.
• Adapting: The teacher adapts experiences with learning about the technology within their curriculum for teaching and learning with spreadsheet.
• Exploring: The teacher actively investigates and explores the curriculum, trying new ideas for teaching and learning their curricula with spreadsheets.
• Advancing: The teacher advances the curriculum integrating learning with and about spreadsheets as learning tools where appropriate, evaluating their students’ knowledge of mathematics within a spreadsheet context.

While the first two levels point toward teachers who are considering teaching with spreadsheets, the other three levels identify teachers who actually act upon their thoughts, testing and reflecting on their developing TPCK knowledge and skills about teaching science or mathematics with spreadsheets.

A.    Objectives

The goal of this professional development program focused on preparing science and mathematics teachers for integrating dynamic spreadsheets as learning tools that ultimately supports them in reaching the action levels of TPCK.  While the full professional development program is completed during the school year, the purpose of this study was to describe and interpret the impact of the program on the nature of the teachers’ developing TPCK for teaching science/mathematics using dynamic spreadsheets as learning tools throughout summer workshop specifically designed around:

• Learning about designing dynamic spreadsheets while focused on mathematics or science concepts and processes;
• Modeling instructional strategies for integrating spreadsheets when teaching science/mathematics;
• Investigating curriculum topics and strategies for integrating dynamic spreadsheets as learning tools;
• Planning for integrating student learning about dynamic spreadsheets within the context of learning science or mathematics;

The over-riding challenge was to differentiate factors that lead teachers to TPCK action levels for effectively teaching content with the technology and to identify challenges, actions, and questions that need attention when planning to guide teachers to action levels of TPCK through summer workshops.

B.     Theoretical Perspective for Defining the Professional Development Program

Extending Grossman’s (1989, 1991) four central components of pedagogical content knowledge to incorporate technology in teaching their content, Niess (2005) framed important components of TPCK that described the knowledge teachers need for teaching with technology; they need: (1) an overarching conception of teaching their subject with technology; (2) knowledge of instructional strategies and representations for teaching with technologies; (3) knowledge of students’ understandings, thinking, and learning the content with technology; and (4) knowledge of curriculum and curricular materials that integrate technology.  From this perspective, the professional development of science/mathematics teachers must guide the development of their knowledge and thinking in ways that consider the knowledge required for guiding students in learning the content using the technology.  Teachers need to develop their knowledge, skills and dispositions to support them in teaching their students about the technology as they learn with the technology.  Ultimately, the professional development must challenge experienced teachers to reconsider their subject matter content and to develop their knowledge of the technology along with its impact on the comprehension of the subject itself as well as on teaching and learning the subject.  This attention must recognize the importance of the process of learning to teach - a “constructive and iterative” process during which teachers must interpret “events on the basis of existing knowledge, beliefs, and dispositions” (Borko & Putnam, 1996, p. 674).  

Shreiter and Ammon (1989) have argued that teachers’ adaptation of new instructional practices is a process of assimilation and accommodation that results in changes in their thinking.   This perspective suggests that the professional development program must be ongoing and provide numerous experiences to engage teachers in investigating, thinking, planning, practicing and reflecting on their learning and teaching.  Numerous studies have yielded consistent findings on differences in the thoughts and instructional practices of experienced versus novice teachers (Borko & Livingston, 1989; Leinhardt, 1989; Livingston & Borko, 1990; Westerman, 1992).  With respect to the development of TPCK, many experienced science/mathematics teachers are novices.  Their teacher actions largely grow from an understanding based on having been taught science/mathematics without the use of technology; they need a professional development program that provides experiences and instructional practices that encourage and allow their TPCK beliefs, knowledge and thinking to develop and mature. In essence then, professional development that aims at guiding experienced teachers in developing TPCK must include active learning - not only about the technology but also about teaching and learning science/mathematics with technologies such as dynamic spreadsheets.  And, if teachers are to develop their actions described in the adapting, exploring, and advancing levels, professional development programs must prepare them for implementing their instructional plans while dealing with school-based barriers to technology implementation and for adapting their curriculum and instructional strategies for guiding student learning of mathematics/science with technologies such as spreadsheets (Brzycki & Dudt, 2005; Feist, 2003).

C.  The Professional Development Program

This professional development program for the science and mathematics teachers was framed around preparing them to teach their content with the aid of dynamic spreadsheets as learning tools.  The program began with a 30-instructional hour workshop over one week (3 graduate credits) that was followed by a field practicum (2 graduate credits) for followed the teachers to their teaching assignment.  Six mathematics teachers (4 from grades 6-8, 1 high school, and 1 community college) and five science teachers (2 middle school and 3 high school) were supported through an NSF grant for their participation in the program. The program emphasized helping teachers develop their TPCK, along with guiding them in identifying and preparing to integrate spreadsheet instruction in their day-to-day teaching.  Another related issue of interest in the design of the program had been the adoption of an instructional approach that scaffolded learning experiences about spreadsheets while also attending to both instructional and assessment strategies in their planning. The instruction began with activities for developing skills and abilities to design dynamics spreadsheets.  Teachers were engaged in these interactive, hands-on activities based within learning science and mathematics concepts while also experiencing important instructional modeling of effective strategies for integrating spreadsheets as learning tools.  Previous research (Niess, et al., 2006) in preparing teachers to teach with spreadsheets highlighted that a significant barrier affecting a teachers’ capacities for integrating spreadsheets in the curriculum was the difficulty in identifying appropriate topics and content in their own curriculum. Therefore, the program engaged the teachers in collaborative investigations of their science or mathematic curriculum (with teams formed by content (science/mathematics) and further by grades levels (middle or high school/community college) with the expectation that they plan their content area curriculum to support students in building their knowledge and skills with spreadsheets concurrently with their science/mathematics knowledge and skills. The final expectation in the program was that each teacher would personalize the developed plans for the students they would be teaching during the subsequent school year.

The second phase of the program is following the teachers to their classrooms during this school year where they were expected to design and integrate dynamic spreadsheets in their curriculum.  A minimum of two extended plans, videos or audios of instruction, pre- and post lesson interviews, and reflections of the teachers on their learning and teaching effects of integrating spreadsheets over the school year will provide a means to assess and document their developing TPCK for teaching with spreadsheets.

D.  Methodology

A descriptive multiple case study design was selected for this study since the purpose was to describe and interpret the nature of the teachers’ developing TPCK for teaching science/mathematics using dynamic spreadsheets as learning tools throughout the specifically designed professional development program. The over-riding challenge was to differentiate factors that lead teachers to TPCK action levels (adapting, exploring and advancing) for effectively teaching content with technology and to identify challenges, actions, questions and needs requiring attention in programs directed at guiding teachers to action levels of TPCK.  Cases were purposely selected for building an understanding that supported an increased comprehension of the impact of the professional development activities on their developing TPCK. These case studies were used for building hypotheses with implications for dealing with the complexities of this phenomenon.

Five of the eleven teachers in the program were selected for the in-depth case studies since they were in appropriate positions for integrating spreadsheets in their science/mathematics classes and for following their actions during the school year.  Two teachers were teaching middle school mathematics, two were teaching middle school science, and one was teaching high school science.

Multiple data sources were used to gather information throughout the program. To investigate the impact of the program on their developing TPCK, in-depth descriptions of the science/mathematics knowledge, beliefs and dispositions of the five teachers were gathered and analyzed from background questionnaires, pre- and post-attitude surveys (Appendix A), daily journal prompts, and classroom assignments (resource ideas, lesson plans and final projects).

Assuming that teachers’ self efficacies (beliefs in their own abilities with spreadsheets) and outcome expectancies (outcomes they believed possible given effective teaching behavior) would be affected during the summer workshop, a survey was adapted from the Microcomputer Beliefs Inventory developed by Riggs and Enochs (1993).  The adaptation substituted the word spreadsheet for the word computers; for the outcome expectancies, the statements reflected a teaching and learning mathematics with spreadsheets outcome rather than a career/future outcome. Cronbach’s alpha reliabilities for this instrument were a=0.89 (pretest) and a=0.85 (posttest) for the full inventory, a=0.89 (pretest) and a=0.81 (posttest) for the self-efficacy subscale and a=0.80 (pretest) and a=0.81 (posttest) for the outcome expectancy subscale. 

For the second phase of the research, extensive observations and interviews of teachers prior to and after teaching with spreadsheets will provide views of their TPCK as they implemented their plans for teaching with spreadsheets in their own classrooms.  Interviews will gather teachers’ reflections both before and after teaching their lessons.  These interviews will gather data on the their planning and preparation for the lessons, their goals and objectives for the lessons, details about their work during the lessons including classroom management of students with the technology, reflections on student learning in the lesson, the use of spreadsheets as a learning tool for students, and the impact of the professional development in their planning and implementation of their plans.

At the end of each stage of the program, teachers’ TPCK is assessed using the five hierarchical levels of: 1) recognizing, 2) accepting, 3) adapting, 4) exploring, and 5) advancing. This paper describes the cases based on the first stage of the program.

E. Results

Despite the limited yet intensive nature of the workshop, shifts in the teachers’ TPCK were evident.  All five teachers demonstrated a strong pedagogical content knowledge (PCK), a necessary foundation for TPCK, prior to the summer workshop in that they had clear conceptions for strategies for motivating and encouraging students to think and learn about the subject matter content.  However, for all, their TPCK was at best described as novice.  Even though three of the five teachers had prior experiences with spreadsheets, information from the demographic questionnaire indicated that their knowledge was limited to spreadsheet operation for personal use, rather than an integration of spreadsheets with teaching and learning science/mathematics.

Only the first three TPCK levels were needed for articulating the five teachers’ developing TPCK.  They were, at best, described at the adapting level where they took ideas that they had experienced with spreadsheets and designed lessons they might use in their teaching but they had not yet had the opportunity to explore student thinking in a spreadsheet learning environment.  Since two of the teachers were just beginning to learn about spreadsheets (Ms. B and Mr. R), they had difficulty comprehending topics in their curriculum where spreadsheets might be useful for learning as well as the impact of integrating such activities with their own students.  Since the summer workshop was directed toward developing the teachers’ spreadsheet knowledge and their knowledge of integrating spreadsheets in teaching and learning, this first analysis focused on their spreadsheet knowledge (TK or technology knowledge described by Koehler and Mishra (in press) as a disposition towards the continuing evolution of an understanding and mastery of spreadsheets) and their technological pedagogical knowledge (TPK described by Koehler and Mishar (in press) as teachers’ understanding of how teaching and learning change with technologies such as spreadsheets). The teachers’ end-products from the course were used to describe their TK and TPK.  The results of the teachers’ pre-post survey results delineated their’ expressed beliefs about their knowledge of spreadsheet technologies (self-efficacy) and their beliefs about what was possible in teaching and learning with spreadsheets (outcome expectancy). The descriptive analysis for TK and TPK provided a descriptive lens to make more sense of positive versus negative changes in the teachers’ beliefs.  Table 1 presents a summary of these analyses.

Table 1.  Spreadsheets and teaching science/with spreadsheets

	Ms. A (math)		Ms. B (science)		Mr. R (science)		Mr. W (science)		Mr. C (math)
TK	Moderate		Limited		Limited		Proficient		Proficient
TPK	Recognizing		Adapting		Adapting		Adapting		Adapting
	Pre/Post	Change	Pre/Post	Change	Pre/Post	Change	Pre/Post	Change	Pre/Post	Change
Self Efficacy	0.58/0.17	-0.41	0.17/0.5	0.33	-0.58/0.92	1.5	0.83/1.08	0.25	0.5/1.33	0.83
Outcome Expectancy	0.5/0.07	-0.43	1.43/0.57	-0.86	0.07/0.57	0.50	0.79/0.93	0.14	0.71/1.5	0.79

For TK, the teachers’ knowledge of spreadsheets was assessed as limited, moderate, or proficient.  Ms. B’s and Mr. R’s knowledge and understanding were limited because both were new to using spreadsheets, however, both increased their beliefs about their own abilities to work with spreadsheets. Mr. R had the benefit of a colleague in the program; this colleague had previous experiences with teaching mathematics with spreadsheets and had encouraged him to come to the program. Thus, Mr. R had consistent private mentoring for guiding his learning about spreadsheets that appeared to have a significant positive effect on his beliefs about his ability with spreadsheets. Ms. A’s TK was described as moderate in that she was comfortable designing spreadsheets to solve problems. She was at ease exploring the various functions and capabilities of the spreadsheet to test whether the results were what she expected; yet, over the course of the week her beliefs about her ability with spreadsheet reduced.  Mr. W and Mr. C were assessed as proficient. Both entered the program with several years of experiences in designing spreadsheets for their personal and professional uses. When designing spreadsheets for either science or mathematics applications, they relied on their previous knowledge and experiences.

With respect to the teachers’ understanding of how teaching and learning changed with technologies such as spreadsheets (TPK), only Mr. W had previously incorporated integrating spreadsheets in teaching/learning science/mathematics in his physics and chemistry classes. However, the notion of preparing students to design dynamic spreadsheets in the process of learning their subject was new to him; he had mostly provided his students with pre-prepared spreadsheets to use for analyzing the data they collected.  Both Mr. W and Mr. C both clearly described the spreadsheets they wanted to create for exploring their content area problems and worked with ease in accomplishing their visions. The highest level during this summer was that of adapting where the teachers were adapting the ideas they experienced in the program for teaching and learning mathematics with spreadsheets.  Mr. W and Mr. C gave indications that they might be at the exploring level but were labeled as adapting since they had not yet experienced teaching students to design dynamic spreadsheets and to use those spreadsheets in exploring the science/mathematics content.  Both clearly prepared and described lessons and units that they planned for integrating spreadsheets in their curricula during the coming year.

I envision using dynamic spreadsheets to assist students with: (1) Verification of mathematical problem solving and reasoning; (2) Testing and proving mathematical theorems, properties and operations; (3) Motivation issues by allowing students to extend their learning through the use of a spreadsheet after completing activities with paper and pencil.  (Mr. C)

This week, one of the key concepts for me was seeing how to use the spreadsheets to scaffold the intermediate knowledge required to achieve certain end results.  This program has shown how to use examples that are more aligned with student experiences to scaffold the stepping stones that reach more difficult concepts that may be more unfamiliar to students.  (Mr. W)

Ms. B initially had difficulty adapting her lessons but by the end of the workshop had gained confidence for planning lessons where she considered adapting ideas from the workshop.  She was not as certain about her abilities as either Mr. W or Mr. C (as noted by her decreasing outcome expectancy) but she had shifted her thinking to the adapting level.

I feel that I have a stronger understanding of how spreadsheets can be applied to lessons in my classes.  There were several examples introduced throughout the weeklong course that will help me in developing my own lessons.  I especially liked the M&M lab and have thought of several lessons that I can relate this to. (Ms. B)

Mr. R was also described at the adapting.  He verbally accepted the idea that spreadsheets can be useful for teaching science but he questioned the amount of spreadsheet knowledge students needed to learn in order to use them as learning tools in science. 

I think that at this point my main focus will be to get students excited about doing basic spreadsheets and graphs.  I do see in the future once I start getting into experiments that a dynamic spreadsheet could be used… I will try to integrate spreadsheets whenever my students are doing data collecting where spreadsheets and graphing are involved. (Mr. R)

As the days progressed, Ms. A grew increasingly resistant to creating lessons that integrated spreadsheets even though she initially voiced her approval for spreadsheets as useful tools for problem solving.  She was labeled at the recognizing level rather than the accepting level because she was unable to complete any lessons that integrated spreadsheet learning.  She did talk about using the spreadsheet as a “teaching tool” where she “walked through problems” to show students “how changing parameters or variables … can affect the results.” Her reluctance was based in her firm belief that students needed to initially learn the mathematics in more traditional ways and then only use spreadsheets for applications of the mathematical ideas.

An important consideration for the attitude survey was that it represented the teachers’ beliefs in their abilities with spreadsheets (self efficacy subscale) and their abilities to achieve the outcome of teaching mathematics with spreadsheets.  In analyzing this Likert scale, strongly agree was 2, agree was 1 and neutral was 0; values for negatively worded items were reversed so that the computed average showed the teacher’s level of agreement. The changes in the pre- to post-survey described the shift in their beliefs over the course. The interpretation of the results benefited with the TK and TPK classifications considering actual teacher actions. Ms. A posted a large negative change in her beliefs about her abilities even though she had previous experiences with spreadsheets; her shift perhaps was related to designing dynamic spreadsheets and to her reluctance to the use of spreadsheets in learning mathematics as noted in her TPK classification. Ms. B’s outcome expectancy was initially the most positive of all five of the teachers.  However, as she began to work with her curriculum, the reality of the work involved in designing new problems seemed to change her opinion.  Perhaps part of the reason for this decrease might also have been related to her own learning curve for creating dynamic spreadsheets to solve problems in the workshop.  Mr. R had the greatest change in his beliefs about his own ability to create spreadsheets.  This increase was viewed related to the consistent mentoring from his colleague.  Mr. W and Mr. C posted positive changes in their beliefs in their abilities with spreadsheets, suggesting that their comfort with computer technologies. Mr. C had increasingly strong agreement in his beliefs in his ability to support teaching and learning mathematics with spreadsheets while Ms. A had a negative belief about this outcome, both reflected in their TPK classifications.

By the end of the summer workshop, the teachers were able to describe and discuss scaffolding ideas for developing spreadsheet skills in science/mathematics lessons.  They recognized advantages of using dynamic spreadsheets for solving complicated problems, motivating students, and providing opportunities for students to extend problems for additional hypothetical situations.  Their plans for teaching with spreadsheets were sketchy, much as novice instructional planners, despite their strength in PCK.  While some of them clearly had strong content knowledge of spreadsheets, they were still developing their knowledge of teaching science/mathematics with spreadsheets. 

F.  Implication and Significance of the Study

In this study, the intersection of the capabilities of dynamic spreadsheets for teaching in science versus mathematics provided an interesting consideration about the importance of the content in TPCK.  The mathematics teachers were challenged by issues of where, when and how the spreadsheet should be used in their classes.  Should students learn paper and pencil algorithms before using the spreadsheet as a tool in mathematics? The argument was similar to the well-documented challenges for integrating calculators in mathematics instruction.  In this study, the mathematics teachers’ views about integrating spreadsheets as learning tools were connected with their views of learning mathematics.  As Borko and Putnam (1996) described, the conception of what it means to teach a particular subject was “related more specifically to how the teacher thinks about the subject matter domain for students – what it is that students should learn about … the nature of those subjects” (p. 690).  Both Ms. A and Mr. C taught middle school mathematics, yet they had significantly different views about integrating of spreadsheets.  Ms. A held a view that these students’ needed to master traditional paper and pencil algorithms first, reserving spreadsheet work for after the mathematical concepts were developed. This conception restricted her from considering integrating building skills with spreadsheets concurrently with building skills in mathematics.  Mr. C held a broader perception of the knowledge his students needed to gain in mathematics; he was less concerned about the paper and pencil algorithms and valued the time to focus students on problem solving and decision making through the use of dynamic spreadsheets. He had prior experiences in exploring mathematics with graphing calculators and viewed spreadsheets as a similar tool – a tool that concurrently provided symbolic, graphical, and tabular representations.  He quickly saw the value of connecting the multiple representations for helping his students gain mathematical knowledge.

On the other hand, the science teachers did not engage in such a debate for learning science with spreadsheets. They easily recognized the spreadsheet capabilities for analyzing and graphically displaying the results as important capabilities for science investigations.  All noted the graphical capabilities as providing their students with a valuable tool that would support their students in learning and communicating their ideas in science.  As Ms. B noted, for science classes “Student's have a misconception that their data they collected in the field is static but nature isn't static it's dynamic.  Being able to show student's "what if" situations is very helpful in dealing with this misconception.”    Therefore, the nature of what it means to know the specific content is an important consideration in guiding teachers in developing their TPCK.   Does the availability of the technology as a tool for learning change the nature of the curriculum that teachers are expected to teach?

A major focus in this study was to model curricular and instructional approaches for integrating dynamic spreadsheets in teaching mathematics/science. The program emphasized backward design where the teachers began by identifying problems they wanted their students to solve at the end of their units.  Then they analyzed the mathematics/science and the spreadsheet knowledge and skills that were needed to effectively explore the problems.  With this information, they were guided in designing plans for supporting their students in developing the spreadsheet skills along with the content concepts and processes as a means of preparing students for using spreadsheets as a tool for problem solving. Ultimately, they were engaged in curriculum design that integrated spreadsheets throughout the curriculum.  Again, all but Ms. A seemed to increase their positive beliefs about integrating spreadsheets in teaching their content.  This approach focused the teachers’ thinking toward the intersection of content, pedagogy (teaching and learning) and the technology – the integral heart of the development of TPCK.  Modeling the teaching and learning in the content area with attention to the development of skills of using the technology as a learning tool was an essential component of this workshop for two primary reasons: (1) the teachers had not had previous experiences in learning their subject with the technology as a learning tool and (2) the content curriculum provided little support for integrating dynamic spreadsheets as a learning tool.  An emphasis on learning with the technology while also learning about the technology maximized the teachers’ experiences supporting their TPCK development as they considered important questions.  How is a student’s proficiency with the technology developed within their developing knowledge and skills in the content area? What curricular topics are supported through exploration with the technology?  What instructional strategies best guide students in learning the concepts and processes in a technology-enhanced classroom environment?

All five of the teachers recognized the value of displaying covariation of variables in problem solving and decision making. But this recognition led to debates about whether students needed to engage in the design of the dynamic spreadsheets.  Could the content area value be achieved by simply exploring variation of the data through the use of pre-prepared spreadsheets?  Should teachers just use these spreadsheets as a teaching tool, to demonstrate how variables covaried and how that covariation could lead to different decisions?  This concern lies at the intersection of the multiple domains in TPCK leading to important questions for teachers in many different content areas.  What value do students gain by developing knowledge, skills and dispositions for designing content area solutions using a particular technology?  Do they need to be creators or users of the products of the technology?

It was never expected that this summer course would fully develop the teachers’ TPCK for teaching science/mathematics with dynamic spreadsheets.  With the focused look at their knowledge, beliefs and dispositions for teaching with a technology such as the spreadsheet, the summer pointed to concerns and questions that must be considered in the development of professional activities directed at the development of their TPCK.  Teachers need opportunities to experience learning about the technology’s capabilities through problems that promote an investigation of content area concepts and processes and to explore and challenge their curricula toward a consideration of how they might scaffold students learning about the technology in ways that they also gain knowledge and skills in the content.  Professional development work has notoriously been considered only motivational and likely to decrease with the realities of returning to school-based environments.  Regardless of the teachers’ progress in developing ideas for teaching and learning with the technology, the continuing field practicum is important for providing them with opportunities to test their ideas, experience interactions with students’ thinking, reflecting on their students’ learning in the technology-enhanced lessons, dealing with school-based technological issues, interacting with parents who challenge the time spent with the technology as time taken away from the content instruction, and dealing with the realities of school cultures – the time, curriculum, access, infrastructure, and culture issues.

The challenge for this professional development program was to extend the initial knowledge, beliefs and dispositions for teaching with the technology by guiding their development of plans to implement what they learned in their own classrooms.  Further investigation must extend these initial descriptions of the impact of teachers’ knowledge, skills and dispositions on their developing TPCK as they learn to integrate various technologies as tools for learning. Such an investigation must carefully envision building on the interactions of their knowledge of the content and the pedagogy with the technology.

Acknowledgements

This work was partially supported by the National Science Foundation under the grant IRT-0324273 and by the EUSES Consortium (http://eecs.oregonstate.edu/EUSES/).

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Appendix A

Self-Efficacy/Outcome Survey *

(Shaded numbers identify self-efficacy items/ clear numbers identify outcome items.)

1	I know how to use spreadsheets.	SA	A	UN	D	SD
2	I am always finding better ways to use spreadsheets.	SA	A	UN	D	SD
3	If I got better in using spreadsheets, it would improve my teaching of math.	SA	A	UN	D	SD
4	I am not very good at using spreadsheets for explorations in math.	SA	A	UN	D	SD
5	Learning math with spreadsheets improves students’ attitude toward math.	SA	A	UN	D	SD
6	Even when I try hard, I do not use spreadsheets as well as others do.	SA	A	UN	D	SD
7	I generally use spreadsheets poorly.	SA	A	UN	D	SD
8	Learning how to use spreadsheets well would help me in teaching my math classes.	SA	A	UN	D	SD
9	I understand what spreadsheets can do well enough to use them correctly.	SA	A	UN	D	SD
10	My success in teaching mathematics/science is related to how well I can use spreadsheets for learning math.	SA	A	UN	D	SD
11	I know how to use spreadsheets as well as most math teachers.	SA	A	UN	D	SD
12	Learning how to use spreadsheets can help me teach math.	SA	A	UN	D	SD
13	I m comfortable using spreadsheets.	SA	A	UN	D	SD
14	Learning to use spreadsheets will not help my future teaching of math.	SA	A	UN	D	SD
15	It is not worth my time to use spreadsheets in teaching math.	SA	A	UN	D	SD
16	I will probably never use spreadsheets once I return to the classroom to teach.	SA	A	UN	D	SD
17	Given a choice, I would not want to grade students using spreadsheets to solve math problems.	SA	A	UN	D	SD
18	It is really not necessary for students to use spreadsheets for learning math.	SA	A	UN	D	SD
19	When I recognize a math problem that might benefit from a spreadsheet solution, I am usually at a loss as to how to implement it in my teaching.	SA	A	UN	D	SD
20	Spreadsheets can help students in learning math.	SA	A	UN	D	SD
21	I might be a more successful teacher if I learn to integrate in my instruction the use of spreadsheets as tools for learning math.	SA	A	UN	D	SD
22	I feel comfortable when I teach with spreadsheets.	SA	A	UN	D	SD
23	Most good teachers do not need spreadsheet skills to teach mathematics.	SA	A	UN	D	SD
24	I do not know how to use spreadsheets well.	SA	A	UN	D	SD
25	Whenever I can, I would avoid using spreadsheets.	SA	A	UN	D	SD
26	Student’s success in learning math has nothing to do with being able to use spreadsheets.	SA	A	UN	D	SD

* Adapted from the Microcomputer Beliefs Inventory developed by Riggs and Enochs (1993)