It's TIME for Technology: The Technology in Mathematics Education ...

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to integrate technology into their instruction (CEO Forum, 1999; Interna- tional Society for Technology in Education [ISTE], 2002; National Council of Teachers of ...
Jl. of Comput Computers in Mathemat ematics and Science Teaching (2008) 27(2), 221-237

It’s TIME for Technology: The Technology in Mathematics Education Project MICHAEL HARDY Saint Xavier University USA [email protected] This article describes the impact that the Technology in Mathematics Education (TIME) Project had on participating middle level and secondary mathematics teachers’ preparedness to teach through technology. Results indicate that the TIME Project positively impacted participants’ perceptions of their knowledge of technological resources and methods of using such resources to teach mathematics. Accordingly, the methods employed in the TIME Project appear to be viable avenues for preparing middle level and secondary mathematics teachers to infuse technology into their instructional practice. Further, engaging middle level and secondary mathematics teachers in activities in which they use a variety of resources to explore a variety of topics that might be encountered at the relevant level of mathematics seems to be of particular value.

Over the past twenty years or so, mathematics teachers have been urged to integrate technology into their instruction (CEO Forum, 1999; International Society for Technology in Education [ISTE], 2002; National Council of Teachers of Mathematics [NCTM], 1989, 2000). Unfortunately, a literature review reveals that many in- and preservice teachers either are not or do not perceive themselves to be well prepared to infuse technology into their pedagogy (CEO Forum, 1999; Doering, Hughes, & Huffman, 2003; National School Board Foundation (NSBF), 2002; Jennings, 1999; Office of Technology Assessment (OTA), 1995). In- and preservice teachers have often criticized how their teacher education programs sought to prepare them to teach with technology. They tend to note that teacher educators endorse

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teaching with technology but frequently do not do so themselves (Beaver, 1990; CEO Forum, 1999; Hardy 2003; Topp, 1996). This is especially unfortunate because observing instructors who effectively teach with technology can enhance in- and preservice teachers’ attitudes and confidence concerning teaching through technology, which can increase the frequency and fluency with which the observers so teach (Mills & Tincher, 2003; Pope, Hare, & Howard, 2002). Teachers and teacher candidates have also asserted that a single educational technology course was insufficient to prepare them to teach with technology. One reason for this is that such courses have typically taught teachers about technology rather than how to teach with technology (Duhaney, 2001; Grabe & Grabe, 1998; OTA, 1995; Pope et al., 2002). More specifically, educational technology courses have often focused on computer literacy, putting data into spreadsheets, use of grading programs, and creating multi-media presentations (CEO Forum, 1999; OTA, 1995; Topp, 1996). These are certainly valuable skills, but they are insufficient to adequately prepare teachers to teach by way of technology. In light of what’s been mentioned, there is a need for teacher education programs that focus on how to teach with technology (Conference Board of the Mathematical Sciences (CBMS), 2001; Halpin & Kossegi, 1996; OTA, 1995; Pope et al., 2002; Topp, 1996). Moreover, the instructional activities used in such programs should be set within a context of teaching and learning that is relevant to the participants (Doering et al., 2003; Duhaney, 2001; Halpin & Kossegi, 1996; Martin, Hupert, Amon, & Gonzales, 2003; Roblyer & Erlanger, 1999). Accordingly, the Technology in Mathematics Education (TIME) Project was developed to help middle and secondary mathematics teachers broaden their knowledge of technological resources and methods of using them to teach mathematics. It was anticipated that such learning would facilitate attainment of the Project’s other goals, which were to significantly improve participants’ perceptions of their knowledge of methods and resources for teaching mathematics with technology as well as the frequency with which the participants did so. THEORETICAL FRAMEWORK The TIME Project directly concerned participating teachers’ pedagogical knowledge (Shulman, 1987) related to the infusion of technology into their mathematics instruction. More specifically, the TIME Project concerned teachers’ learning to interweave technology into their instructional practice. Thus, a constructivist lens was used to structure the methods

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through which learning was facilitated. For that reason, instructional activities were designed to allow participants to construct knowledge through their experiences (von Glasersfeld, 1991; Vygotsky, 1978). The Project was also implicitly informed by the critical or emancipatory interest (Habermas, 1978) in that it questioned the adequacy of professional development programs intended to prepare teachers to teach by way of technology as well as the current state of many teachers’ preparedness to do so. Finally, the TIME Project focused on meeting the needs that teachers had in learning to teach with technology. Bailey and Pownell (1998, p. 48) used Abraham Maslow’s hierarchy of needs as the basis for a hierarchy of “basic technology-related needs that must be met before higher levels of technology integration can be achieved.” Like Maslow’s needs hierarchy, Bailey and Pownell’s model had five categories of needs: (a) physiological needs, (b) safety needs, (c) belonging needs, (d) esteem needs, and (e) self-actualization needs. Hence, activities and components of the Project were designed to meet the various types of participants’ technology-related needs. PARTICIPANTS Nineteen middle level or secondary mathematics teachers participated in the TIME Project. Four of the participants were certified (1) or seeking certification (3) in middle level mathematics, one (1) was certified in elementary education but taught at the middle level (4th grade), and 14 were certified in secondary (7-12) mathematics. Eleven of the participants had at least five years of teaching experience, five had from one to four years of experience, and three were preservice teachers with no experience. One participant held a doctorate, but not in mathematics or education. Eight participants held master’s degrees, seven held bachelor’s degrees, and three were in the last year of their undergraduate program. Finally, the participants represented three urban school districts and seven rural, high poverty level districts. THE CONTEXT General Information The participating teachers completed a course that focused on exploring resources and methods for teaching mathematics with technology. Eleven of

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the secondary participants completed an intensive five-day course of 35-40 contact hours during the summer of 2003. The middle level and remaining secondary teachers completed a 12-week course of 35-40 contact hours during the fall of 2003. Both courses focused on methods of teaching mathematics by way of technology, but some activities were different in order to better meet the varying needs of the middle and secondary teachers. The principal investigator was the sole instructor for the fall course. However, for the summer course, another instructor did teach one topic and was usually present to assist participants with technical problems. This was immensely valuable in maintaining the flow of the class. Hence, having a second instructor present who can assist students with technical problems is highly recommended for technological methods courses. The instructional practices employed in the TIME Project were based on constructivist epistemology. Learning was therefore facilitated by providing participants with numerous opportunities to learn by doing. Accordingly, heavy emphasis was placed on engaging participants in activities through which they could use a variety of technological resources to independently and collaboratively explore a variety of mathematical topics and problems relevant to the levels at which the participants taught. This afforded participants ample time to explore how different technological resources could be used to teach the same topic, to become familiar with resources, and to experience the use of those resources from the perspective of a learner. Participants were thereby better prepared to overcome any doubts about their ability to use the resources and to anticipate and empathize with problems their pupils might have. Further, these approaches allowed the course instructors to model effective technological pedagogy while teaching both about and how to teach with technology. All of these benefits and points of emphasis were of practical value in preparing participants to teach through technology. This was both a key consideration in selecting course activities and consistent with the previously noted recommendations for such courses (Doering et al., 2003; Duhaney, 2001; Dusick, 1998; Halpin & Kossegi, 1996; Martin et al., 2003; Roblyer & Erlanger, 1999). Content and Activities The mathematical topics addressed in the courses included probability, patterns, sequences, linear regression, data representation, distance-ratetime problems, limits, and mathematical modeling. The technology-related topics explored in the courses included using videos to motivate or elabo-

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rate on instruction; using PowerPoint to enhance lectures; using Geometer’s Sketchpad, graphing calculators, and spreadsheets to solve problems, teach concepts, and link mathematics to realistic contexts; locating and using internet resources; writing plans for technology-infused lessons (Doering et al., 2003; Martin et al., 2003); exploring criteria for evaluating software; and critiquing software or other technological resources. Each critique focused on whether or not a resource would positively impact students’ computational skill, retention, understanding, and appreciation of mathematics as well as their motivation to learn it. It was also required that claims be justified. It was believed that such critiques would help participants become critical consumers of technology, which would better prepare them to wisely select and use technology to facilitate learning (Hoffman, 1997; Martin et al., 2003; Snider, 2002). As previously noted, class activities were intended to provide participants with hands-on experience using technology to explore mathematical topics and problems that might be encountered at the middle or secondary levels. To yield greater insight into the nature of such experiences, the following descriptions of two class activities are provided. One exploration conducted in class asked participants to wind motorized, toy cars various distances, set them off, and measure the distance traveled. Participants then entered their data into both spreadsheets and graphing calculators, and both tools were used to generate a scatter plot of the data and to insert a regression line into the plot. Next, participants interpreted the slope of that line and used both its graph and equation to predict how far the car would travel for a given wind distance. The predicted and actual distances traveled were then compared. In another activity, each participant was assigned a theorem from Euclidean geometry and required to develop an independent investigation using Geometer’s Sketchpad that would allow students to infer the theorem. The inclusion of a set of instructions for constructing objects was required, and the use of diagrams to clarify directions was encouraged. It was also required that at some point in the investigation students be asked to drag an object in the sketch, observe the results, and on the basis of their observations, write a conjecture that they believed to be true. Support Mechanisms In addition to the course, participants attended follow-up meetings interspersed over the 2003-04 school year. The summer participants attended four follow-up sessions, but due to scheduling constraints, fall participants

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only completed three sessions. The follow-up meetings were intended to help the participating teachers sustain their efforts to teach with technology (Jennings, 1999; Lewis, et al., 1991; Shaw & Jakubowski, 1991). Further, the follow-up sessions were believed to be an essential component of the Project since it takes an extended period of time (up to five or six years) for teachers to infuse technology into their pedagogy (Hoffman, 1997; Hadley & Sheingold, 1993). Support was provided by affording participants a community of learners with which and a forum in which they could share, model, and reflect on their endeavors to incorporate technology into their instruction (Bailey & Pownell, 1999; CEO Forum, 1999; Martin et al.; 2003). Support was also provided by exposing participants to additional activities and resources for teaching mathematics through technology. This was accomplished by modeling the use of the resources while providing participants first hand experience using the technology within the context of activities that they could use with their pupils. Additional support structures included a technological resource library from which participants were able to borrow software, videos, or reference books, a CD for each course containing a copy of all the lesson plans created for the course, and a website at which all of the teachers’ lesson plans and various activities and course artifacts were posted. Finally, each participant received $150-$250 worth of technological resources that were of the participant’s choosing. Participants from districts partnering in the Project received $250 worth of resources and participants from other districts received $150 worth of resources. It should be noted that by the employing the methods described herein, the TIME Project met multiple needs from each level of Bailey and Pownell’s (1998) technology-related needs hierarchy. The Project helped meet participants’ physiological needs by providing them with time devoted to learning to teach by way of technology as well as professional development designed to attain that goal. Participants’ safety needs were met through administrative support demonstrated by the partner districts’ financial contributions to both the purchase of technological resources and the Project’s participation costs. Safety needs were also met through the time spent exploring resources and methods of teaching mathematics through technology, which helped to alleviate any “technophobia” (Bailey & Pownell, 1998, p. 48) the participants may have had. The teachers’ belonging needs were addressed by providing a community of peers that were all striving to integrate technology into their teaching. Esteem needs were met by enhancing the participants’ sense of self-efficacy for teaching with technology, which was accomplished through the exploration of technological resources and

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methods of teaching mathematics with them. Esteem needs were also met through the extrinsic reward provided in the resources participants were allowed to purchase. Finally, the ongoing exploration of resources that took place in both the courses and follow-up sessions, the teachers’ creation of lessons incorporating the use of technology, and the sense of empowerment such experiences were intended to generate served to meet the participants’ self-actualization needs. Aggregately all of the support mechanisms noted herein served to help participants sustain their efforts to integrate technology into their pedagogy. METHODS AND DATA SOURCES Both quantitative and qualitative data were collected and analyzed. The primary data collection instrument was a questionnaire developed by the investigator with about half of the items being adapted from the Flashlight Current Student Inventory (Ehrmann, 1995). The survey contained both open-response and five-point Likert scale items. On Likert scale items, participants could choose from a standard five-point scale of responses ranging from strongly agree (5) to strongly disagree (1). The survey was completed on the first and last days of the course and several months after the end of the course, five months for the fall participants and eight months for the summer participants. However, three of the participants took both the summer and fall courses. This was viewed as a confounding factor that exacerbated limitations due to the small sample size and prevented valid analysis of the data from the survey administered several months after completion of the course. Accordingly, it was not possible to quantitatively assess whether or not the Project achieved its goal of significantly increasing the frequency with which participants taught with technology. Likert scale items focused on the frequency with which the participants integrated technology into their instruction, their perceptions of their knowledge of and preparedness to teach with various technological resources, and their perceptions of how the TIME Project impacted their ability to teach by way of technology. Chi-square tests were conducted to determine if significant differences across pre-and posttests existed in the frequency of responses to Likert-scale items. Similarly, one-sample tests of population proportion were used to determine if significantly more than 50% of the participants chose strongly agree or agree on three posttest questions that were inappropriate for the pretest. An alpha level of .05 was used in all quantitative analyses.

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As a check on the participants’ perceptions of their knowledge of technological resources, one open-ended item asked the teachers to list broad categories of technological resources that could be used to teach mathematics. Another item asked participants to list five titles of technological resources and for each title, a specific mathematical topic the resource could be used to teach. Finally, the teachers were asked to explain how the TIME Project impacted their ability to teach with technology and how the Project could be improved. Data from the open-ended questions on both pre- and posttests were coded to identify themes in the participants’ responses. One-time observations of three participants’ efforts to use technology as a teaching tool were also conducted to verify that participants were teaching with technology in ways that were consistent with the vision of the Project. Finally, each observation was augmented with a semi-formal interview that focused on the observed lesson. However, the interview data did not yield any justifiable insights and will not be addressed herein. This may be due to the interview’s focus on a single lesson. Thus, it is recommended that future research of such issues employ case study methodology to generate larger pools of qualitative data that may reveal themes that could support a grounded theory concerning the process of learning to teach with technology. RESULTS AND IMPLICATIONS Quantitative Analysis The first point of interest concerns participants’ responses to the following statements. 1. The TIME Project positively impacted my ability to teach by way of technology. 2. I would recommend the TIME Project to other teachers. All of the participants indicated that participation in the Project enhanced their ability to teach with technology, and 95% asserted that they would recommend the Project to other teachers. The mean for the first item was 4.48, and the mean for the second was 4.52. A one-sample test of population proportion revealed that participants reported the Project had a positive impact and would recommend the Project to others at rates that were significantly greater than 50% ((p < 0.0001 in both cases, n = 19). With regard to the frequency with which participants taught with technology, it is only possible to report descriptive statistics for the posttest completed several months after the course. This is due to a confounding

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factor arising from the fact that three of the participants took both the fall and summer courses, which magnified limitations due to the small sample size. When the survey was administered several months after completing the course, three in- and one preservice teacher had dropped out of the Project, and two of the remaining participants were preservice teachers. Thus, the number of potential respondents was reduced to13, and three of those had taken both courses associated with the Project. Of the 13 participants that responded to the claim, “I have taught with technology or used technology to support my instruction more this year than in the past,” 12 indicated that they had. The mean response was four, but as previously noted, no further analysis could be conducted. It should be noted that all other findings discussed herein concern administrations of the survey conducted at the beginning and end of the course. Further, for the participants that completed both courses, only their data from the first course completed were included in the analysis. Two-way chi-square analysis across pre- and postcourse surveys of participants’ responses also revealed significant positive differences in the frequency with which participants chose SA or A versus all other responses on each of the following items. • At this point in time, I am familiar with a wide variety of technological resources ((p = 0.0009). • At this point in time, I am familiar with a wide variety of methods of teaching mathematics through the use of technological resources ( < 0.0001). (p • I am prepared to use technology as a tool for fostering learning or conducting an investigation of mathematics with my students ((p =.0375 § Warning 50% of cells had counts less than 5). • I can use the Internet to locate a class with whom my class can interact through email or a video package that can be used in conjunction with the Internet ((p = 0.0009). • I can create a multi-media presentation by using software such as PowerPoint or HyperStudio ((p = 0.0032). • I can effectively incorporate the use of spreadsheets into my instruction ( = 0.0001). (p • I can effectively use computer software as a major component of a lesson ( = 0.0001). (p • I can effectively incorporate the use of databases into my instruction ((p = 0.0368).

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The improvement on the last item is of particular interest because little emphasis was placed on the use of databases. Thus, the increase in the frequency of choosing SA or A versus all other options on the database item could reflect a general increase participants’ confidence in their ability to teach with technology. In any case, the statistically significant results previously noted consistently implied that the TIME Project was successful in enhancing participants’ knowledge of technological resources and methods of using them to teach mathematics. As a check on their assessment of their knowledge of technological resources and methods for teaching mathematics, participants were asked to list five software titles and for each title, a mathematical topic the resource could be used to teach. Two-way chi-square tests indicated that on the posttest, participants listed three to five titles of resources and three to five mathematical topics that could be taught with those resources significantly more frequently than on the pretest ((p < 0.0005; Note that due to a copying error, data from the three undergraduates could not be analyzed, so n = 16). Accordingly, it appears that the previously noted results did represent an increase in familiarity with resources and methods for infusing technology into mathematics instruction. However, there was no significant difference across pre- and posttests in the frequencies of listing zero to two and three to five broad classes of technological resources that could be used to teach mathematics (again, n = 16 due to the noted copying error). This result was interpreted as indicating that prior to beginning the Project, the participating teachers were aware of categories of resources that could be employed as instructional aids, but lacked knowledge both of the resources’ capabilities and of methods for teaching mathematics with them. This interpretation was reasonable in light of the prevalence of other data supporting the TIME Project’s positive impact on participants’ knowledge of methods and resources for teaching mathematics by way of technology. Qualitative Analysis Impact of the project. The qualitative data collected also indicated that the TIME Project fulfilled its primary purpose. As previously noted, participants’ responses to open-ended questions were coded to identify common themes. The code categories into which participants’ responses most frequently fell and their associated frequencies are highlighted in the following list. Further the frequencies reflect only the postcourse responses for the

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first course completed by the participants who took both the summer and fall courses. • Enhanced knowledge of resources and/or methods (16). • Enhanced confidence (4). Based solely on the noted frequencies, participation in the TIME Project helped 21% of the teachers enhance their confidence in using technology as an instructional tool. Moreover, 84% of the participants cited increased knowledge of methods and resources for teaching mathematics with technology as a benefit of participating in the Project. This is also exemplified in the following representative responses to the question, “How has participation in the TIME Project helped prepare you to use technology as a teaching tool?” The participant category and codes attributed to the response are shown in parenthesis. • It made me familiar with the TI-83 calculators, CBR, and CBL’s in my room. I can now find many technology lessons on the Internet. I can send email with attachments (Fall, Inservice; knowledge of resources and/or methods). • It has shown me what technology is available, how to use it, and ideas on how to incorporate it into the classroom (Fall, Preservice; knowledge of methods & resources). • I knew almost nothing about the TI-83, Sketchpad, Power Point, and spreadsheets. Now, I feel confident to use any of these in teaching a lesson (Summer, Inservice; knowledge of resources and/ or methods, enhanced confidence). The preceding responses highlight the teachers’ belief that participating in the TIME Project enhanced their knowledge of resources and methods of using technology to teach mathematics. Further, the teachers found the Project especially useful in learning how to teach mathematics through Geometer’s Sketchpad, spreadsheets, PowerPoint, and graphing calculators, which were heavily emphasized in both courses. Observations. Observations indicated that participants were teaching with technology through methods that were consistent with the vision of the Project. Paula, a seventh grade mathematics teacher, used graphing calculators to help her students learn about pie graphs, box and whisker plots, scatter plots, and histograms. She did so by having pairs of students input data into the calculators and then use them to generate the noted graphs. As a culminating activity for a unit on simple and compound interest, Cathy, a 7-12 instructor, had her seventh and eighth grade students use spreadsheets and their built in programming capabilities to calculate compound interest on an investment.

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Bryan, an assistant superintendent, was able to encourage and support technology use throughout the faculty with whom he worked. His high school teachers taught a school-wide interdisciplinary thematic unit associated with Edgar Allen Poe’s The Pit and the Pendulum. Many teachers made use of TI-Navigators to disseminate information and assignments as well as to collect, analyze, and anonymously display students’ work. The capacity of the technology to display student-generated work allowed teachers and students to engage in rich discussions about that work, while protecting the student-author’s identity. A mathematics teacher used Navigators and Cabri Jr. to explore the relationship between the circumference of a circle and its radius. The tools were also used to relate the topics to both Poe’s tale and gear ratios. Although the following lesson was not observed, Samantha and Megan, secondary mathematics teachers, submitted video clips from classes in which they had their algebra students explore linear regression and use regression lines as predictive functions. The teachers did so through an activity in which pupils made a cradle from rubber bands that would hold a hard-boiled egg in place. Students then attached more rubber bands to their cradles to form makeshift bungee jumping equipment. Students kept records of the number of rubber bands used in their assemblies (cradle and rope) and how far the egg descended when dropped for varying numbers of rubber bands used. The data were entered into graphing calculators, which were then used to generate a linear regression model for the data. Next, students measured the height of some bleachers, and each group used its regression line to predict how many rubber bands should be used to create a bungee assembly that would bring an egg within a foot of the ground without striking it. Samantha reported that every group was able to complete the drop without breaking their egg, and one group came within about seven inches of the ground. Perceived obstacles. When asked “what are the greatest obstacles to your efforts to teach mathematics with technology,” categories into which participants’ responses were assigned and accompanying frequencies were as follows: • lack of or access to resources (8), • knowledge of resources and/or methods (5), • time constraints (3), and • financial constraints (3). Again, the responses only include data for the first course completed by those who took both courses. It is intriguing that despite the reported familiarity with methods and resources for teaching through technology, the second most frequently cited

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obstacle to such instruction was lack of knowledge of resources and methods for teaching by way of technology. It is also interesting that all of the obstacles noted by Project participants were among the barriers to teaching with technology that Forgasz (2006) identified as those most frequently cited by teachers. Moreover, Forgasz reported that teachers’ most frequently cited obstacles to teaching through technology have remained largely unchanged over the past 10 years. Hadley and Sheingold (1993) identified similar constraints, and like Forgasz, found that such constraints were relatively static. It is certainly reasonable to maintain that these obstacles will always be among the most commonly cited barriers to teaching with technology because one’s ability to do so will always be constrained by both one’s access to technology and one’s knowledge of technological methods and resources. However, it is important to note that Forgasz’ data were collected in Australia while the data for the TIME Project and Hadley and Sheingold’s (1993) study were collected in the United States. This coupled with the temporal stability of what teachers perceive as obstacles to their efforts to integrate technology into their instruction suggests that obstacles to teaching with technology are generally pervasive and difficult to overcome. This also suggests that a substantive change in pedagogy takes time and requires extended support for teaching in ways that are compatible with the proposed modifications to instruction. These claims find some support in that despite significant increases in participants’ perceptions of their preparedness to teach with technology and despite the Project’s emphasis on exploring a variety of resources, the most commonly recommended (32%) change to Project courses was to add more practice time with the resources. Moreover, the lengthiness of the process of pedagogical change and the need for extended support to affect such change has often been noted (Hoffman, 1997; Jennings, 1999; Shaw & Jakubowski, 1991). CONCLUSION In light of all of the supporting data, it appears that the TIME Project attained its primary objective of improving participating mathematics teachers’ knowledge of and preparedness to teach by way of technological resources. Further, the methods employed in the TIME Project appear to have been highly effective at enhancing participants’ perceptions of their knowledge of technological resources and methods of using them to teach mathematics. This appears especially true for teaching with graphing calculators, spreadsheets, Geometer’s Sketchpad, PowerPoint or other software as well as for locating and using internet resources.

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These improvements in self-perceptions were supported by significant improvements in participants’ ability to identify specific technological tools for teaching specific mathematical topics. Thus, it appears that a viable method for preparing middle and secondary mathematics teachers to teach through technology is to engage them in activities in which they use a variety of technological resources to explore a variety of problems and topics relevant to the level taught. Additional methods used in the Project that may also have a positive impact are to model the effective use of technology as an instructional tool, to have teachers plan technology-infused lessons, and to have teachers critique technological resources. All of these activities are of practical value to instructors seeking to integrate technology into their pedagogy, and the critiques have the added benefit of requiring consideration of what constitutes an effective technological resource for a given purpose. Another factor contributing to the viability of the methods employed in the TIME Project is that they met participants’ needs at every level of Bailey and Pownell’s (1998) hierarchy of technology-related needs. Similarly, the instructional strategies used were consistent with calls for programs that teach in- and preservice teachers how to teach with technology as well as about technology (CEO Forum, 1999; OTA, 1995; Pope et al., 2002), that is, with calls for programs designed to enhance teachers’ technological pedagogical content knowledge (Mishra & Koehler, 2006). This is significant because as this study demonstrates, contextualized approaches to teaching methods of infusing technology into instruction can enhance in- and preservice teachers’ attitudes about technology use, confidence in using technology, and technological pedagogical content knowledge. Further, such changes can lead to more frequent and more effective use of technology as an instructional tool (Buckenmeyer & Freitas, 2007; Mills & Tincher, 2003; Pope et al., 2002; Snider, 2002). Participants did report using technology more frequently than they did before they participated in the TIME Project, but no quantitative analysis of those reports could be conducted due a confounding factor. However, observations indicated that the observed participants were using technology in manners that were consistent with the vision of the Project. Thus, the results of this study were generally consistent with recent research and literature concerning preparing teachers to incorporate technology into their pedagogy. While the TIME Project’s methods of preparing teachers to teach through technology appear to be highly effective, the sample size was small, so the findings must be interpreted cautiously and replication studies are needed. There is also a need for investigations of the effectiveness

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of the Project’s methods for both inservice teachers of urban schools and preservice teachers. Studies that include more substantial observation and interview components could provide deeper insights into why mathematics teachers find their abilities to infuse technology into instruction are enhanced through development experiences like the TIME Project. Such studies could also yield insights into why lack of time, money, access to resources, confidence, and knowledge of resources, and methods continue to obstruct teachers’ efforts to teach with technology. They may also provide insights into how administrative policies and professional development programs could be structured to better help teachers overcome such obstacles. In closing, there is still much to be done, but based on the findings noted herein, it appears that the TIME Project positively impacted participants’ preparedness to teach through technology. Reference Bailey, G.D., & Pownell, D. (1998). Technology staff-development and support programs: Applying Abraham Maslow’s hierarchy of needs. Learning & Leading With Technology, 26(3), 47-51, 64. Beaver, J. (1990). A profile of undergraduate educational technology (in)competence: Are we preparing today’s education graduates for teaching in the 1990’s? (ERIC Document Reproduction Service No. ED332985) Buckenmeyer, J. A., & Freitas, D. J. (2007, March). Effective technology integration: Essential conditions for success. Proceedings of the 18th Annual Meeting of the Society for Instructional Technology and Teacher Education (pp. 2955-2960), San Antonio, TX. CEO Forum. (1999, February 22). The CEO forum school readiness and technology report: Professional development: A link to better learning. Retrieved June 7, 2007, from http://www.ceoforum.org/downloads/99report.pdf Conference Board of the Mathematical Sciences. (2001). The mathematical education of teachers part I. Washington, DC: Mathematical Association of America in cooperation with the American Mathematical Society. Doering, A., Hughes J., & Huffman, D. (2003). Preservice teachers: Are we thinking with technology? Journal of Research on Technology in Education, 35(3), 342-361. Duhaney, D. C. (2001). Teacher education: Preparing teachers to integrate technology. International Journal of Instructional Media, 28(1), 23-30. Dusick, D. M. (1998). What social cognitive factors influence faculty members’ use of computers for teaching? A literature review. Journal of Research on Computing in Education, 31(2), 123-137. Ehrmann, S. (1995). Flashlight current student inventory. Retrieved January 31, 2008, from the Teaching Learning & Technology Group web site http:// www.tltgroup.org/studentcourseeval/Main.htm

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Forgasz, H. (2006). Factors that encourage or inhibit computer use for secondary mathematics teaching. Journal of Computers in Mathematics and Science Teaching, 25(1), 77-93. Glasersfeld, E., von (1991). An exposition of constructivism: Why some like it radical. Journal for Research in Mathematics Education Monograph 4, 1929. Grabe, M., & Grabe, C. (1998). Integrating technology for meaningful learning (2nd ed.). Boston: Houghton Mifflin. Habermas, J. (1978). Knowledge and human interests (2nd ed., J.J. Shapiro trans.). Boston: Heinemann Educational Books Ltd. (Original work published 1968). Hadley, M., & Sheingold, K. (1993). Commonalities and distinctive patterns in teachers’ integration of computers. American Journal of Education, 101(3), 261-315. Halpin, P., & Kossegi, J. D. (1996). The www, preservice teachers and their mathematics courses. (ERIC Document Reproduction Service No. ED405 819) Hardy, M. (2003, April). It should have been stressed in all education classes: Preparing preservice teachers to teach with technology. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, IL. (ERIC Document Reproduction Service ED478379). Hoffman, B. (1997). Integrating technology in schools. The Education Digest, 62(5), 51-55. International Society for Technology in Education. (2002). National educational technology standards for teachers preparing teachers to use technology. Eugene, OR: Author. Jennings, J. (1999). Invited commentary: Better policies leading to improved teaching. Education Statistics Quarterly, 1(1), 12-14. Lewis, L., Basmat, P., Carey, N., Bartfai, N., Farris, E. & Smerdon, B. (1999). Teacher quality: A report on the preparation and qualifications of public school teachers. Education Statistics Quarterly, 1(1), 7-11. Martin, W., Hupert, N., Amon, N., & Gonzales, C. (2003, April). The RETA professional development model: Real teachers, real changes. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, IL. Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A new framework for teacher knowledge. Teachers College Record, 108(6), 1017-1054. Mills, S. C., & Tincher, R. C. (2003). Be the technology: A developmental model for evaluating technology integration. Journal of Research on Technology in Teacher Education, 35(3), 382-401. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

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National School Board Foundation. (2002). Are we there yet? Research and guidelines on schools’ use of the Internet. Retrieved July 25, 2002, from http://www.nsbf.org/thereyet/fulltext.htm Pope, M., Hare, D., & Howard, E. (2002). Technology integration: Closing the gap between what preservice teachers are taught to do and what they can do. Journal of Technology and Teacher Education, 10(2), 191-203. Roblyer, M.D., & Erlanger, W. (1999). Preparing internet-ready teachers: Which methods work best? Leading & Learning with Technology, 26(4), 58-61. Shaw, K. L., & Jakubowski, E. H. (1991, Fall). Teachers changing for changing times. Focus on Learning Problems in Mathematics, 13, 13-20. Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22. Snider, S. (2002). Exploring technology integration in a field-based teacher education program: Implementation efforts and findings. Journal of Research on Technology in Education, 34(3), 230-249 Topp, N. (1996). Preparation to use technology in the classroom. Journal of Computing in Teacher Education, 12(4), 24-27. U.S. Congress, Office of Technology Assessment. (1995). Teachers and technology: Making the connections. OTA-EHR 616, Washington, DC: U.S. Government Printing Office. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.