Technology beliefs and practices of mathematics education faculty.

Using survey methodology, this study examined the beliefs and practices of mathematics teacher educators (MTEs) regarding the integration of technology in their teacher education programs. In addition, the relationship among MTEs' beliefs about the importance of technology, their comfort with using and teaching with technology, and the degree to which they have implemented technology within their mathematics teacher education programs were also examined.

MTEs were consistent regarding which technologies they believed were important for teachers of mathematics at the elementary, middle, and high school levels. More technologies were found to be important for teachers at each of the higher-grade bands. At the elementary and middle school levels, there was little evidence that technology is being used by MTEs in teacher preparation. The technologies employed by MTEs at these levels are generic, focusing on tools such as e-mail and the Internet. At the high school level, MTEs focused more on mathematics specific technologies, such as graphing calculators and dynamic geometry software, in their preservice programs. However there is room for improvement, as other technologies are not often used.

**********

The pervasiveness of technology in society has highlighted the need for schools to prepare students to take advantage of emergent technology tools. For this to occur, the International Society for Technology in Education (ISTE) (2000) asserts that, "today's classroom teachers must be prepared to provide technology-supported learning opportunities for their students" (p. 2). They also add that "being prepared to use technology and knowing how that technology can support student learning must be integral skills in every teacher's professional repertoire" (p. 2).

ISTE acknowledges that various groups are responsible for helping teachers develop knowledge and skills for supporting students' learning with technology, and asserts that prospective teachers must use technology as part of their teacher education coursework. Further, the National Council for the Accreditation of Teacher Education (NCATE) (2002) developed standards stating that teacher candidates should "facilitate students' learning of subject matter through presentation of the content in clear and meaningful ways though the integration of technology" (p. 15). Considered together, the calls from these documents suggest that teacher preparation programs must provide prospective teachers opportunities to learn important skills and examine pedagogical issues for using technology in classrooms.

In mathematics, many groups have encouraged the use of technology as an important means for learning and teaching mathematics (Conference Board of Mathematics Sciences [CBMS], 2001; Mathematics Association of America [MAA], 1991; Mathematical Sciences Education Board [MSEB], 1991; National Council of Teachers of Mathematics [NCTM], 1991, 2000). These organizations recommend the use of technology as tools for supporting students' mathematical explorations and as a valuable tool for mathematics instruction. The prevailing assumption is that available technology can and should change what mathematics is taught and how it is learned (Heid, 1997), has the potential to engage students more fully in mathematical thinking and learning, and provides students access to more advanced mathematics. In the Principles and Standards for School Mathematics, NCTM (2000) states that "technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances learning" (p. 24). The use of technology is encouraged at levels beginning in kindergarten and extending throughout students' mathematics education.

In order for technology to impact K-12 students' learning of mathematics with technology tools, teachers need to be sufficiently knowledgeable about learning and teaching mathematics with technology. This in turn implies that mathematics teacher educators (MTEs) need to implement technology tools in the preparation of mathematics teachers and thus need to have a strong comfort level with, and consistently implement, technology tools as part of their own repertoire of tools in mathematics teacher education courses. To provide background for this study, a brief review of relevant research about the use of technology at three different levels--students' use, teachers' use, and mathematics teacher educators' use--is included.

Related Research

Students' use of technology. Research has provided evidence that the use of computers (Clements & Battista, 1994; Kulik & Kulik, 1987) and calculators (Merriweather & Tharp, 1999; Ruthven, 1990) can aid in the development of mathematical thinking skills, has the potential for enhancing students' understanding of mathematics concepts (Adams, 1997; Graham & Thomas, 2000; Hollar & Norwood, 1999; Schwartz & Hershkowitz, 1999), and improve achievement (Hembree & Dessart, 1992; Kaput, 1992; Kulik & Kulik, 1987; Quesada & Maxwell, 1994; Wenglinsky, 1998; U.S. Department of Education, 2001). Typically, the results from these studies suggest that using technology enables students to solve problems that were not available to them before (Merriweather & Tharp, 1999; Slavit, 1996) and improves their disposition toward mathematics (Roberts & Stephens, 1999). Further, using technology in mathematics class produces positive changes in classroom dynamics and pedagogy (Doerr & Zangor, 2000; Farrell, 1996; Rochowicz, 1996; Simonson & Dick, 1997; Slavit, 1996). Research also indicates that technology can improve the mathematics achievement of special populations, including females (Smith & Shotsberger, 1997; Bitter & Hatfield, 1993; Ruthven, 1990) and low-ability students (Hembree & Dessart, 1986, 1992).

Teacher's use of technology. Despite the calls for the inclusion of technology in instruction and the evidence that technology enhances students' learning, technology tools are not widely used in K-12 mathematics classrooms. Research indicates that many teachers are not using technology tools for teaching mathematics (Huang & Waxman, 1996; Manoucherhri, 1999; Milou, 1999; Schmidt & Callaghan, 1992). In an observational study of middle grades mathematics classrooms, Huang and Waxman (1996) reported that computers are seldom used and that students use calculators only 25% of the time. Manoucherhri (1999) found that teachers have limited views regarding the use of technology for teaching and learning mathematics. In fact, approximately 20% of the teachers reported that technology has no relevance to their curriculum. Moreover, only 13% of the high school teachers reported ever using computers in their instruction.

Milou (1999) reported that, although the majority of high school mathematics teachers support the use of graphing calculators, particularly at the Algebra 2 level, responses from middle school and Algebra I teachers are far less encouraging. A smaller case study of a high school mathematics department reports similar results that teachers are less likely to use graphing calculators in lower-level mathematics classes (Drier, 1998). The general use of calculators at the middle school is apparently more widespread; nearly half of the eighth-grade teachers reported in NAEP 2000 that they use calculators on a daily basis (U.S. Department of Education, 2001). The NAEP report does not identify the type of calculator that is used. If the calculators are only scientific, teachers are unable to take advantage of graphing calculators' capabilities for tabular and graphical representations.

Aside from the availability of technology tools, the limited use of technology in K-12 mathematics may be related to several factors. One major reason teachers cite for failing to integrate technology is the lack of training on the use of a new technology (Hope, 1997; Schmidt, 1998; Schmidt & Callaghan, 1992). Researchers have also found that inservice teachers often do not feel comfortable engaging students in open-ended uses of technology tools until they are comfortable with exploring mathematics with technology themselves (Zbiek, 1995; Timmerman, 1998). This training and comfort level can be developed through mathematics teacher education courses and professional development experiences.

Mathematics teacher educators' use of technology. Waits and Demana (2000) argued that adoption of technology by mathematics teachers requires professional development that focuses on both conceptual and pedagogical issues, ongoing support and assistance, and a desire to change from within the profession. MTEs are faced with the complex task of preparing teachers (pre- and inservice teachers) to use technology as an appropriate tool for learning and teaching mathematics. There have been a variety of research studies done in the past few years with regard to preservice teachers' use of and beliefs about technology in mathematics teaching (Bowers & Doerr, 2001; Drier, 2001; Fine & Fleener, 1994; Olive & Leatham, 2000; Stohl, 2002; Turner & Chauvot, 1995). In addition, there have been several articles published in which MTEs describe how they engaged preservice and inservice teachers in technology-enabled mathematics explorations (e.g., Abramovich & Nabors, 1998; Drier, 2001; Dugdale, 1998; Oppong & Russell, 1998; Garofalo, Drier, Harper, Timmerman, & Shockey, 2000). For a comprehensive review of how technology is used by and with preservice and inservice teachers, see Zbiek and Hollebrands (in press).

The existence of research and description papers written by MTEs fundamentally implies that technology is being implemented at some level in mathematics teacher education. However, it is not clear how technology tools are being used in mathematics teacher education and whether there is widespread effort to implement technology in mathematics teacher education within the United States. The lack of research studies that details how, when, and why MTEs use technology tools in their preparation of mathematics teachers leaves a missing link in understanding the process of meeting the goals of organizations such as ISTE (2000), NCATE (2002), NCTM (2000), and CBMS (2001).

Research Questions

If mathematics teacher preparation programs seek to produce teachers who are capable of using technology to enhance students' conceptual understanding of mathematics and enhance students' mathematics achievements, then MTEs must take an active role in preparing them for this task. Only through extensive engagement with technology will pre- and inservice teachers of mathematics obtain the understanding, skills, and confidence they need to use technology appropriately for teaching mathematics. This notion piqued the authors' interest in determining the extent to which MTEs embrace the use of technology in their own practice as teacher educators.

In this article, the state of the scene regarding the use of technology in the preparation of mathematics teachers is presented. This study used a survey to examine MTEs' beliefs and practices regarding the integration of technology in their teacher education programs. In particular, the following questions are addressed:

1. What types of technology do MTEs believe are important for teachers of mathematics to be proficient with at the elementary, middle and high school levels?

2. Which technologies do MTEs feel most comfortable using when it comes to helping preservice teachers learn to use technology?

3. To what extent do MTEs integrate technology in their mathematics education courses?

4. What is the relationship among MTEs' beliefs about the importance of technology, their comfort with using and teaching with technology, and the degree to which they have implemented technology within their mathematics teacher education programs?

5. How do MTEs learn to use technology, and what support are they provided in that effort?

6. What factors hinder MTEs from implementing technology in mathematics teacher education courses?

METHODS

The following section describes the procedures used for addressing the research questions previously stated. Since this is an attempt to gain an understanding of the widespread use of technology by MTEs in the United States, the decision was made to employ a survey methodology (Sapsford, 1999) and quantitative analysis to summarize results.

Instrumentation 

This study parallels a study by social studies education faculty. The survey used in this study is an adaptation of a survey developed by Berson, Mason, Heinecke, and Coutts (2001). The survey was revised to deal specifically with technology as it relates to mathematics education. An earlier version of the survey was administered to several mathematics educators in a pilot study. Based on the feedback obtained from the pilot study, the instrument was revised. The final survey included 90 questions, some of which contained multiple components.

The survey consisted of several sections. Part 1 included questions that elicited demographic information. Respondents were asked about their current position, rank, primary appointment, number of years as a mathematics educator and K-12 teacher, and information about their current institution. Part 2 examined the respondents' perceptions regarding the importance of technology for teachers of mathematics. They were asked to rate the level of importance at each of three levels: elementary, middle school, and high school. Part 3 sought information about mathematics teacher educators' comfort level with using particular technology and the degree to which they have integrated the technology in their preservice programs. Additionally, they were asked to indicate how they learned to use the technology that they use. In Part 4, MTEs were asked about any organizational support that they were provided regarding technology use. These questions dealt with access to technology, available resources (e.g., graphing calculator and computer labs), and technical support. Part 5 inquired about barriers to incorporating technology in teacher education programs. Part 6 provided respondents an opportunity to respond to open-ended questions to gain further insights to their responses. For example, they were asked to describe how they incorporate technology in their instruction and how the barriers they identified hinder their ability to incorporate technology.

Sample

The target population for this study was mathematics teacher educators in the United States. With this goal in mind, names and addresses of individuals who identified themselves as mathematics educators from two national organizations, the Association of Mathematics Teacher Educators (AMTE) and the NCTM were obtained. An assumption was made that an active mathematics teacher educator would likely be a member of at least one of these organizations. First, surveys were sent to 663 university-based mathematics teacher educators from AMTE and excluded members with other affiliations (e.g., publishers, private educational consultants). Then, a list was obtained from NCTM of 3,538 members who identified themselves as mathematics teacher educators. After removing the names of individuals who were also members of AMTE, those who could be identified as teachers at the K-12 level, education specialists, consultants, or publishers were removed. In total, 639 names were removed using the above process. Of the 2899 remaining on the list, 375 were clearly identified as mathematics teacher educators because of their university affiliations and were included in the sample. Finally, approximately 25% (631) of the remaining individuals from the United States and the District of Columbia were randomly selected to receive surveys. Thus, a total of 1006 surveys were mailed to the selected members of NCTM.

Of the 1669 surveys that were sent, 342 (20%) were returned. Of these 342, 37 were excluded because the individuals did not clearly identify themselves as university or college-based mathematics teacher educators. Consequently, the results reported here are from 305 mathematics teacher educators who responded to this survey. Of these 305 MTEs, 231 included comments in Part 6, the open-ended items.

Data Analysis

Prior to considering the specific questions, the demographic data from the surveys were analyzed. Then, to address the first three research questions about the importance, comfort, and integration of various technologies, the means, standard deviations, percentages, and frequencies from Parts 2 and 3 of the survey were computed. They were computed in two ways: by considering all of the surveys together and by cross-tabulating according to teacher certification levels (elementary, middle school, and high school) gleaned from Part 1 of the survey. The fourth research question concerned the relationship among importance, comfort, and degree of integration. To address this, correlations among the three possible pairings were completed, again doing this overall and by teacher certification levels. Parts 4 and 5 of the survey were used to address the questions about how MTEs learned the technology and the barriers they face in integrating it within their programs, again computing basic descriptive statistics both overall and by teacher certification levels. Finally, responses to the open-ended items in Part 6 were read, analyzed, and categorized to identify emergent themes.

RESULTS AND DISCUSSION

The results section begins by providing a description of the sample. This is followed by a breakdown of the responses into elementary, middle school, and high school categories. After that, the results are presented by examining trends that were apparent across all levels. Next, a description of how MTEs learned to use technology is provided. This is followed by a discussion of organizational support and barriers to integrating technology reported by MTEs. In the analysis, preservice mathematics teachers are classified into three categories: elementary, middle school, and high school. This is done recognizing that some programs lead to K-8 and 6-12 certifications. Similarly, MTEs are referred to according to the group of preservice teachers that they teach. That is, we use the term "elementary MTEs" to refer to MTEs who teach preservice elementary teachers.

Sample Demographics 

Because of the 20% return rate, the results may not be representative of all MTEs. Those more favorably disposed toward the use of technology may have been more inclined to participate in this study. Consequently, the overall usage of technology in mathematics education may be less than is reported here.

Nevertheless, the results do represent a broad cross-section of MTEs (Table 1). Of the 305 surveys included in the study, surveys were returned from all sections of the country, from both public and private institutions, and from both large and small institutions. Similarly, the respondents are faculty with various levels of experience and rank, and who taught preservice teachers of all three levels--elementary, middle, and high school.

Importance of, Comfort with, and Integration of Technology

The first three research questions concern MTEs' beliefs about the importance of various technologies, their comfort with using them, and the degree to which they integrate them into their programs for preservice teachers. Respondents rated these on a scale of 1 to 4, with 1 indicating the most negative response and 4 the most positive. In constructing the survey, the authors decided not to allow a neutral response: 1 and 2 were negative and 3 and 4 were positive responses. If at least 60% of the respondents provided a positive response (3 or 4), the overall view of the MTEs was considered positive. If at least 60% provided a negative response (1 or 2), the overall view was considered negative. If neither of these occurred, the overall view was considered neutral.

Elementary. The top five technology skills that MTEs believe are important for preservice elementary teachers are accessing information on the Web (89%), communicating with e-mails (86%), using calculators (76%), accessing lessons on the Web (74%), and using spreadsheets (63%) (Table 2). Of these five technologies, only calculators and spreadsheets are considered content-specific mathematical tools, although we do not know whether MTEs consider the use of spreadsheets for classroom management purposes (e.g., grade sheets) or for mathematical instruction. In any case, these two technologies had lower mean scores for being integrated into mathematics teacher education courses than the other three technologies. The mean scores for integrating fraction calculators and spreadsheets were 2.37 and 2.22, respectively. As these are both below the middle score of 2.50, the authors conclude that many elementary preservice teachers are most likely not receiving adequate preparation on technology specifically geared for mathematics instruction.

Significant experiences with geometry are now expected at the elementary and middle school levels as well as at high school (NCTM, 2000). Software such as The Geometer's Sketchpad (Jackiw, 2001) or Cabri (Laborde, 2001) can have a dramatic impact on providing students with valuable experiences, helping them to discover relationships and to formulate and test conjectures. Consequently, it is interesting that only 47% of the respondents indicated that dynamic geometry software is important for elementary preservice teachers. Although the mean comfort score for using this type of software was 3.01, the mean score for integrating it was only 2.10.

A wide variety of mathematical software appropriate for elementary students is available. Consequently, it was expected that the elementary MTEs would consider topic specific mathematics software to be valuable for the elementary preservice teachers. However, the survey results do not confirm this. Only 51% of the respondents gave a positive response to the importance of mathematics software. Despite a positive degree of comfort with this type of software (mean of 3.15), the elementary MTEs overall do not integrate this to a large extent into their preparation of elementary mathematics teachers (mean of 2.24).

A final result that is worthy of note is that data collectors received the lowest overall mean score in terms of importance, with 70% giving a negative response. Though they can be powerful tools for bringing the real world into the classroom and for providing rich sources of information to be studied through graphs and simple statistical analysis, the mean score for their importance for elementary teachers, as rated by the elementary MTEs, was only 1.96. The mean score on their integration was also the lowest of all of the technologies, at 1.53. Though the mean score on the elementary MTEs' comfort with using them was higher, at 2.28, it still received the lowest comfort rating of all the technologies. An inference may be that elementary MTEs themselves have not had adequate experiences that would allow them to see the potential of using data collectors in an elementary classroom.

Correlations were examined: (a) between the elementary MTEs beliefs about the importance of a technology and their comfort level with using and teaching it, (b) between importance and the degree to which they have integrated the technology into their program, and (c) between comfort and integration. As expected, all correlations are positive--those who believe a technology is more important tend to be those who are more comfortable with the technology and those who incorporate it into their teaching. It was surprising, however, that the correlations show only a moderate connection among these, generally in the 0.3 to 0.4 range. A few points of interest were found and are discussed below, although we recognize that due to the large number of correlations we investigated, these might be due to chance.

The correlation between the elementary MTEs' beliefs about the importance of dynamic geometry and their comfort in using it was low (0.18) and nonsignificant (p = 0.08). This may suggest that, despite the relatively low support for its importance for elementary teachers, those who favor it have only a slight tendency to be those who are comfortable with it. The overall comfort level is fairly strong (mean of 3.01), yet the MTEs who valued the importance of dynamic geometry software were often not those who were comfortable with it.

The highest correlations for the elementary MTEs' concerned the use of data collectors. The correlation between importance and comfort was 0.44, between importance and integration 0.64, and between comfort and integration 0.57, all of which are significant at the 0.001 level. Apparently, those who believe that data collectors are important for elementary mathematics teachers are often those who have become comfortable with their use and have integrated them into their programs. Perhaps greater exposure to data collectors might help others recognize their potential and lead to their integration. However, this is the type of relationship was expected with dynamic geometry software, but was not found.

Overall, the elementary MTEs' greatest use of technology is in e-mail for communication and the Internet for locating information. These had the highest mean scores for integration, at 3.43 and 3.08, respectively. The use of subject specific technology for the development of mathematical ideas is not nearly as pervasive. In fact even the highest mean for the integration of a subject specific technology, was only 2.37 for calculators, less than the middle value of 2.5 on the survey.

Middle school. MTEs consider several more technologies as important for middle school mathematics teachers than those considered important for elementary mathematics teachers (Table 3). In addition to the generic technologies of e-mail and the Internet, several technologies used specifically for mathematics instruction are judged worthy. Ninety percent of the respondents consider graphing calculators important (along with 76% who gave a positive response to fraction or scientific calculators). Support is also shown for spreadsheets (88%), dynamic geometry software (86%), data collectors (68%), and topic specific software (64%). Only two technologies receive overall negative ratings in terms of importance, Logo and video conferencing. Although Logo has a long history of use in K-8 mathematics instruction, apparently this tool is not deemed as important by MTEs for middle school mathematics instruction.

No strong patterns were found when the means in comfort with using and teaching with a technology and its importance were compared. It must be noted, however, that the means are very close, as can be seen in Table 3. The mean scores on integration of the technologies were consistently lower than the means on both importance and comfort, with the exception being on use of e-mail. Again the authors infer that the technologies are not as widely used in preservice programs for middle school mathematics teachers, even though middle school MTEs believe they are important and tend to be comfortable with using them. This is especially true for the use of data collectors. Although 68% of the MTEs think these tools are important for middle school teachers, the mean score on integrating them by middle school MTEs was a mere 2.10.

The correlations among the importance, comfort, and degree of integration for the middle school MTEs were also investigated. The relationship between importance and comfort, though always positive, was again less than expected. The lowest correlation was for fraction and scientific calculators, but this may be due to the small range in comfort levels; almost all expressed a high level of comfort with them. The highest correlation, as with the elementary educators, was for data collectors, at 0.52. Those who believe data collectors to be important have a fairly strong tendency to be those who are comfortable with using them. Although an argument cannot be made for cause and effect, it is at least possible that as MTEs have the opportunities to work with data collectors, they see the advantages that they can have in the classroom.

The correlation between importance and degree of integration was again lowest for dynamic geometry software, at 0.06. This may suggest that many middle school MTEs who believe software such as The Geometer's Sketchpad (Jackiw, 2001) or Cabri (Laborde, 2000) is important have not had adequate opportunities to integrate them into their program. Part of this may be due to their lack of comfort, as the correlation between importance and comfort was only 0.22, but the correlation between comfort and integration was 0.62. In fact, for the middle school MTEs, the correlations between comfort and integration were high, generally in the 0.6 and 0.7 range. A question for future research is whether the middle school MTEs integrate the technology because they are comfortable with using it or because they believe it is important. The data suggest that the level of integration may be more reliant on comfort level.

Looking at the big picture for middle school teachers, the results suggest that the middle school MTEs believe that several subject-specific technological tools are important. However, the degree to which these tools are integrated into the programs for preservice mathematics teachers does not match the importance ascribed to them.

High school. Survey results indicate that MTEs believe that more technologies are important for high school mathematics teachers than for the other levels (Table 4). More than 90% think that graphing calculators, dynamic geometry software, and spreadsheets are valuable. For those working directly with preservice high school teachers, the mean scores for importance, again out of 4, for graphing calculators and dynamic geometry software were 3.99 and 3.80, respectively. The comfort level scores the high school MTEs reported for using and teaching with the technologies were, again, lower than the scores on importance. However, for the top five technologies, the comfort levels were high, all with mean scores above 3.2 (Table 4).

Another positive result is the degree to which these important technologies are being integrated. The mean scores for integrating graphing calculators and dynamic geometry, 3.64 and 3.32, respectively, suggest that these subject-specific tools play a significant part in the preparation of high school mathematics teachers. Spreadsheets, which, can be invaluable in developing a myriad of mathematical concepts, are integrated less with a mean of 2.91.

Despite the strong support they receive in terms of importance, data collectors (83%) and Computer Algebra Systems (CAS) (80%) are apparently not being integrated to a large extent into high school mathematics preservice programs. High school MTEs' comfort levels for these are also significantly lower than for the other technologies. The authors can only speculate as to the reasons for this. Perhaps high school MTEs do not have access to data collectors that they can use with their preservice students or have not had sufficient opportunities to learn to use them for themselves. In fact, the correlation between comfort and integration of data collectors is very strong (0.75) indicating that those who have sufficient opportunities to become comfortable with them tend to be those who integrate them. The authors hope that with CAS readily available on some current generations of graphing calculators, becoming comfortable with this technology tool and integrating the tool may become less problematic. Because these are considered important, perhaps within a couple of years, as more educators employ these newer generations of graphing calculators, CAS will receive more attention. The correlation between comfort and integration for CAS was also high (0.69), again suggesting that those high school MTEs comfortable with using CAS tend to be those who integrate it within their programs.

On the whole, there is much stronger support for the inclusion of a variety of technologies for high school preservice mathematics teachers than for the lower grade levels. Not only do high school MTEs support the use of generic technology, such as e-mail and the Internet, but also consider tools to help master specific mathematical content valuable. Integration of the technology, though still not satisfactory, especially in the areas of data collectors and CAS, is higher among the high school MTEs. Although organizations such as the NCTM (2000) suggest that technology should be an integral part of teaching and learning mathematics at all levels, it is only at the high school level that a widespread commitment by MTEs to use the tools in preparation of mathematics teachers is found.

Overall results. There was remarkable consistency among the groups in their beliefs about the importance of the technologies (see Tables 2, 3, & 4). For example, the mean of all MTE respondents for the importance of elementary teachers to be able to access information on the Web for classroom use was 3.49; the mean of the subgroup who teach elementary preservice teachers was 3.47. In other words, those who work with middle and high school preservice teachers have very similar ideas about what is important for elementary teachers as those who work directly with the elementary preservice teachers. The largest difference between the overall mean and a group-specific mean was 0.15 on the 4-point scale. This is a good sign; MTEs appear to have a consistent vision of what technology is important at each of the three levels.

As might be expected, more types of technology are deemed important for teachers of higher-grade levels. For the elementary teachers, five types of technology are considered important, for the middle school teachers the number increases to nine, and for the high school teachers the number increases still further to twelve. Much of the technology considered important, especially at the lower levels, is generic in nature and not technology that may help students learn mathematical concepts. For example, the ability to access information on the Web for classroom use receives the strongest support for both elementary and middle school teachers (89% and 91% favorable responses, respectively); this is also considered important for high school teachers. Being able to communicate with e-mail and finding lesson plans on the Web are also deemed important for all three groups. In terms of subject specific technology, two technologies, calculators and spreadsheets, are considered important for all groups.

Some interesting results are evident from the responses about the MTEs' comfort level using and teaching with some of the technologies. For example, the vast majority of MTEs express comfort with using and teaching with electronic communication; they also report that they integrate the use of the Internet with their preservice teachers. However, when examining subject-specific technology, some discrepancies between what is considered important and what MTEs are comfortable with using were found. For example, CAS and data collectors are deemed important for high school preservice teachers, yet the mean comfort scores for those responsible for preparing high school teachers were barely above the middle score of 2.50. In contrast, 75% of all respondents indicate comfort using dynamic geometry software. This result, which runs counter to the authors' personal experiences with MTEs, is surprising and may be an artifact of those inclined to respond to the survey, and merits further investigation.

Spreadsheets are recognized as important by MTEs at all levels (means greater than 3). In addition to classroom management tools, they can be used extensively for mathematics instruction. For example, they can be effective in helping students master connections among numerical, algebraic, and graphical representations of problems and in making a transition from intuitive, recursive functions to explicit ones. Nevertheless, a significant percent (13%) of the MTEs indicate a lack of comfort using or teaching with them; and within each category, the mean level of integration is reported between 2 and 3.

A contrast occurs among the groups when importance and comfort are examined together. For those working with elementary preservice teachers, without exception the mean rating of the MTEs' comfort with using the various technologies was higher than the mean rating of the technology's importance. For example, the mean comfort level for elementary MTEs using spreadsheets was 3.49, but the mean score on the importance of using spreadsheets was 2.91. For the middle school MTEs, no consistent patterns were found in terms of comparing comfort with importance, but for the high school MTEs, the mean scores for comfort with subject specific technologies were consistently lower than the means for importance. This holds true for graphing calculators, dynamic geometry software, spreadsheets, data collectors, and CAS systems. In other words, the elementary MTEs indicate a greater comfort level in using the technology relative to the technology's importance than do the high school MTEs. This may indicate that high school MTEs do not provide their mathematics preservice teachers with sufficient opportunities to use the technology that they deem as important to use in mathematics teaching.

Another interpretation could be that high school MTEs may have greater expectations regarding the use of mathematics specific technology at the higher-grade levels. That is, high school MTEs may not consider knowing some of the basic features of a technology, such as the tabulation and basic graphing features on a spreadsheet, sufficient. In the preparation of teachers of more advanced mathematics, they may believe that more technical features should be incorporated, such as importing data and some of the more complex data analysis. If high school MTEs are not comfortable with using these more advanced features of graphing calculators or spreadsheets, they may report less integration of these technologies.

When the degree to which technologies are integrated was investigated, the results suggested that MTEs integrate technology least in the preparation of elementary school mathematics teachers and most in the preparation of high school teachers. MTEs integrate scientific and graphing calculators primarily at the middle school and high school levels, and, to a lesser extent, a fraction or scientific calculator at the elementary level. At the middle and high school levels, MTEs report the integration of dynamic geometry software, scientific and graphing calculators and, to a lesser extent, spreadsheet applications. Although MTEs believe that CAS and data collectors are important at the high school level, to a large extent these tools have not been integrated into preservice courses. When asked in the open-ended items how technology is incorporated in courses, the majority of responses provided by MTEs were unrelated to the learning and teaching of mathematics with technology. For example, MTEs reported that they use the technology for their own instructional purposes (e.g., PowerPoint presentation and web pages), to communicate or obtain course assignments from students (e.g., e-mail or discussions boards), and as means for students to collect information (lesson plans or other resources from the Web).

Perhaps most interesting is that, with only one exception (communication with e-mail for middle school MTEs), for all technologies deemed important, the mean rating for integrating the technology is lower than its mean rating for importance. This is true across levels. No matter their comfort with using a technology, MTEs may not be providing preservice teachers with sufficient opportunities to use a technology, even though MTEs believe that a technology is important for them to know.

Learning to Use Technology

In the survey, MTEs were asked to identify how they learned to use technology. For the most part, MTEs learned to use technology through self-exploration (96%) or by obtaining assistance from others (92%). These results raise questions regarding whether these methods are used by MTEs because this is their preferred method for learning technology or whether there is an insuffiecient amount of structured venues available to MTEs for learning to use technology. Fifty-five percent of the MTEs reported that they learned about available technology by attending a conference-based workshop. Although effective for demonstrating the potential of a specific technology, conference workshops may not be sufficient for providing the in-depth knowledge base needed to effectively incorporate technology in courses. One of the open-ended items inquired about technological areas in which MTEs wanted to gain greater expertise. The skill that was mentioned most often was web page development. Other items mentioned in order of highest frequency were data collection technology (e.g., CBR, CBL, EA-100), spreadsheets, graphing calculators, and proper integration of technology.

When asked to identify formats that would be most appropriate for developing technological knowledge, MTEs responses ranged from half-day workshops linked to a conference, 2-3 day sessions, to weeklong sessions. Typically, these sessions were preferred with funding and in a convenient location. Three respondents suggested the use of training similar to P[T.sup.3] (Teachers Teaching with Technology) that has been sponsored by Texas Instruments for many years. Others were interested in professional development that would integrate technology in specific grade bands (e.g., dynamic geometry for middle school).

Organizational Support and Barriers to Using Technology

Overall, respondents believed they receive support from their institutions regarding the use of technology, including the access they have, the value placed upon it, and the training and technical support provided to them (Table 5). However, when asked about barriers to incorporating technology, they identified time as a critical factor, with 60% indicating they do not have sufficient time to change their practice. Responses provided from the open-ended items provide further insight into the barrier of time.

Time to become proficient. Sixty-eight percent of the MTEs reported that personal knowledge is a hurdle to be overcome (see Table 5). One of the respondents captures the sentiment of many of the MTEs stating: "There simply isn't enough time to learn the technology, think how best to use it, and then create materials for class use" [232]. Although reward or incentives for technology is not identified as a barrier, several MTEs report that their institutions may have different priorities, which in turn may impact the amount of time they will use to become proficient with technology. Consider the following:

    "Time needed for scholarship--more important at present. Rewards
    for implementing technology--none." [65]

    "As a faculty member, I have been told to put time, thought, and
    energy into publication before spending time developing well
    thoughtout tech enhancement for courses." [169]

Of all the comments provided, only one respondent stated that faculty are rewarded for technology integration.

Time for integration. Although technology is deemed important, it is not always the highest priority for MTEs. Because of the content that must be included in any one course, MTEs often do not have the instructional time to integrate technology. Consider the following quotes:

    "We have a field-based methods program. At least 10 days out of a
    15-week semester are spent in public school classrooms. I consider
    this a strength of the program; however it does place constraints on
    the time in the classroom--which in turn limits the amount of
    technology that can be introduced and practiced." [37]

    "Finding time within the course structure--the use of tech within
    any methods class eats significantly into the limited time
    available. At the elementary level, I don't feel that tech has the
    same priority as the development of good instructional strategies."
    [61]

    "I don't think technology is as important for teachers to know as
    many other things. There is not time to teach them everything of
    importance." [73]

CONCLUSION

To realize the vision for technology use encouraged by many organizations (CBMS, 2001; ISTE, 2000; NCATE, 2002, NCTM, 2000) the use of technology in mathematics teacher preparation programs must increase. At the elementary and middle school levels, little evidence was found that technology is being used by MTEs in teacher preparation. The technologies employed by MTEs at these levels, though important and useful, are generic, and focus on tools such as e-mail and the Internet. Even at the high school level, where there is strong indication that MTEs integrate technology in their preservice programs, there is room for improvement. For example, data collectors and CAS currently do not play a significant role in the majority of mathematics teacher preparation programs.

Assistance at all levels is needed. If we claim that technology should permeate all levels of mathematics instruction from K- 12, as stated in Principles and Standards for School Mathematics (NCTM, 2000), then it is imperative that MTEs prepare all levels of teachers to incorporate technology. Overall, technology integration is not where it should be, but it falls short particularly in the elementary level. Is the view of what technology is important at each of the levels appropriate, especially in light of the dramatic increases in the power of technology? Should the focus at the elementary level be on calculators only? What can be done to help MTEs, especially elementary MTEs, find sufficient time to learn and integrate more technology?

The barriers identified suggest that the integration of technology in mathematics teacher education is related to MTEs' personal knowledge about technology. This implies that, like teachers, MTEs are in need of professional development. In addition to learning to use the technology, they need access to best practices for incorporating technology in teacher preparation programs. Our results, however, show that learning and planning to incorporate technology may be a daunting task for individual MTEs. MTEs must take the lead in assisting teachers to integrate technology in the classroom, yet they also need help. Quite simply, MTEs may not have had sufficient experiences of their own that would enable them to use various technologies effectively themselves, much less teach it to others. This is similar to the effects shown by Zbiek (1995) and Timmerman (1998) with regards to teachers needing to have a comfort level of learning mathematics with a technology tool before they feel comfortable using that technology with students. The same phenomenon seems to apply for mathematics teacher educators. Perhaps, more forums for sharing ideas and learning to use technologies are needed.

Our findings suggest that technology, especially at the elementary level, is used primarily for communicating or accessing information. To a large extent, MTEs have adopted technology for tasks such as submitting assignments, showcasing websites, making multimedia presentations, conducting software evaluations, and searching for resources. However this is insufficient; we must also help future teachers understand how they might use technology to enhance their students' understanding of mathematics. MTEs have made strides, but significant improvement is necessary.

Table 1 MTE Demographic Information

Mathematics Teacher Educators Survey Respondents

Description                         Location of Appointment
Mathematics Educator        72%     Mathematics Department           50%
Mathematicians/Mathematics  28%     College of Education             39%
Educator                            Joint Appointment                 6%
                                    Other                             5%
Rank                                Status
Full Professor              36%     Tenured                          67%
Associate Professor         36%     Tenure-track                     21%
Assistant Professor         19%     Other                            12%
Other                        9%
                                    Courses Taught*
Years of Experience as MTE          Secondary Methods (middle/high)  38%
more than 16                48%     High School Methods only         23%
11-15 years                 19%     Elementary Methods               28%
6-10 years                  17%     Technology Course                21%
less than 5                 14%     Mathematics Content Course       61%

Institutions

Type                                Student Population
Public                      76%     Less than 10,000                 43%
Private                     24%     10,000-19,999                    30%
                                    20,000-29,999                    17%
                                    Greater than 30,000              10%
Undergraduate Programs Offered      Graduate Programs Offered
Secondary Mathematics       93%     Master's degree only             38%
Middle Grades Mathematics   41%     Master's & Doctorate             42%
Elementary Education        95%     Other                            20%

*Note: MTEs may teach several courses listed in this section.

Table 2 Selected Technology Indicators by Elementary Mathematics Teacher
Educators

                                     Elementary MTEs Only
Technology             %MTEs Saying     Importance
                       Important
                       n     %       n    [bar.x]  SD

Access Info on Web     278   89%     141  3.47     0.81
Communicate w/e-mails  280   86%     143  3.43     0.81
Calculators            275   76%     141  3.25     0.82
Access Lessons on Web  278   74%     142  3.18     0.90
Spreadsheets           277   63%     142  2.91     0.89
Math Software          264   51%     136  2.58     0.90
Dynamic Geometry
Software               259   47%     135  2.45     0.92
Data Collectors        263   30%     140  2.17     2.45

                                 Elementary MTEs Only
Technology                  Comfort             Integration
                       n    [bar.x]  SD    [n.bar]  [bar.x]  SD

Access Info on Web     138  3.59     0.77  127      3.08     1.00
Communicate w/e-mails  136  3.86     0.55  129      3.43     0.95
Calculators            135  3.45     0.86  126      2.37     1.21
Access Lessons on Web  136  3.58     0.81  128      3.01     1.08
Spreadsheets           136  3.49     0.78  124      2.22     1.12
Math Software          131  3.15     0.9   125      2.24     1.08
Dynamic Geometry
Software               138  3.01     0.89  125      2.1      1.09
Data Collectors        131  2.28     1.02  121      1.53     0.87

Table 3 Technology Indicators by Middle School Mathematics Teacher
Educators
                                                Middle School MTEs Only
Technology                       % MTEs Saying     Importance
                                 Important
                                 n    %         n   [bar.x]  SD

Access Info on Web               249  91%       82  3.46     0.76
Graphing Calculators             251  90%       81  3.40     0.85
Spreadsheets                     251  88%       82  3.38     0.81
Communicate w/e-mail             248  87%       80  3.39     0.92
Dynamic Geometry Software        250  86%       81  3.33     0.82
Access Lesson on Web             253  77%       82  3.20     0.84
Fraction/Scientific Calculators  249  76%       80  3.20     0.97
Data Collectors                  241  68%       80  2.78     1.06
Topic-specific Math Software     243  64%       80  2.84     0.92

                                        Middle School MTEs Only
Technology                            Comfort         Integration
                                 n   [bar.x]  SD    n  [bar.x]  SD

Access Info on Web               83  3.41     0.92  66  2.98    1.03
Graphing Calculators             80  3.13     0.99  66  2.98    1.03
Spreadsheets                     82  3.33     0.96  65  2.55    1.09
Communicate w/e-mail             82  3.77     0.73  67  3.49    0.91
Dynamic Geometry Software        83  3.00     0.94  65  2.85    0.97
Access Lesson on Web             82  3.44     0.92  67  2.99    1.11
Fraction/Scientific Calculators  81  3.43     0.92  66  3.00    0.98
Data Collectors                  81  2.32     1.03  63  2.10    0.98
Topic-specific Math Software     78  2.99     0.96  64  2.40    0.99

Table 4 Technology Indicators by High School Mathematics Teacher
Educator

                                             High School MTEs Only
Technology                    % MTEs Saying     Importance
                              Important
                              n    %         n   [bar.x]  SD

Graphing Calculator           282  98%       70  3.99     0.12
Dynamic Geometry Software     281  94%       70  3.80     0.50
Spreadsheets                  279  94%       69  3.70     0.62
Access Info on Web            279  91%       69  3.67     0.56
Communicate w/e-mail          278  86%       68  3.49     0.83
Data Collectors               267  83%       69  3.29     0.85
Computer Algebra Systems      270  80%       69  3.30     0.86
Access Lesson on Internet     281  75%       69  3.35     0.78
Topic-Specific Math Software  269  68%       69  3.10     0.94
Multimedia Software           278  65%       70  2.91     0.86
Databases                     278  64%       70  2.87     0.93
Videos                        277  61%       67  2.79     0.86

                                     High School MTEs Only
Technology                        Comfort          Integration
                              n   [bar.x]  SD    n   [bar.x]  SD

Graphing Calculator           67  3.52     0.68  61  3.64     0.68
Dynamic Geometry Software     69  3.23     0.75  62  3.32     0.83
Spreadsheets                  68  3.60     0.69  62  2.91     1.08
Access Info on Web            67  3.52     0.68  61  3.16     0.99
Communicate w/e-mail          69  3.96     0.27  63  3.44     0.96
Data Collectors               66  2.64     0.95  57  2.47     1.00
Computer Algebra Systems      67  2.51     1.15  59  2.20     1.01
Access Lesson on Internet     69  3.54     0.76  61  3.03     1.03
Topic-Specific Math Software  67  3.21     0.90  58  2.44     1.01
Multimedia Software           67  3.09     0.97  59  2.41     1.08
Databases                     66  3.03     1.07  59  2.03     1.13
Videos                        67  3.04     0.94  59  2.22     1.01

Table 5 Organizational Support and Barriers to Using Technology

Organizational Support for Technology, Listed by Percent Positive

Item                                     %         n    [-.[chi]]  SD
                                         Positive

I can easily access technology
  (graphing calculators, etc,) for
  instructional use.                     85%       299  3.39        .85
Students can easily access the
  technology they need.                  84%       295  3.16        .78
I have access to software that
  I want to use in my instruction.       82%       298  3.20        .80
Using technology for instruction
  is important to administrators
  in my institution.                     82%       293  3.09        .82
I can easily access a computer
  lab for instructional use.             81%       281  3.25        .87
My institution provides sufficient
  training on technology for
  instructional use                      68%       296  2.88        .88
My institution provides technical
  support for integrating technology
  in my instruction.                     66%       299  2.83        .90
I am satisfied with the technical
  support that I receive from my
  department/college.                    63%       295  2.69        .90
I collaborate with colleagues in
  planning technology-based activities.  55%       299  2.55        .84
I have adequate funds and support
  for obtaining needed equipment or
  software.                              49%       295  2.42        .89
I have time to plan for technology
  in my instruction.                     40%       296  2.26        .90

Barriers to Incorporating Technology

Personal knowledge about technology
  used for teaching mathematics.         68%       294  2.99        .98
Time to change practice                  64%       293  2.80       1.01
Funds to purchase new equipment or
  software when needed.                  52%       291  2.44        .98
Reward system associated with
  technology usage                       48%       289  2.44       1.03
Access to existing technology
  resources (labs, other examples)       27%       293  1.97        .94
Importance to college or institutional
  administrators                         16%       293  1.70        .82

References

Abramovich, S., & Nabors, W. (1998). Enactive approach to word problems in a computer environment enhances mathematical learning for teachers. Journal of Computers in Mathematics and Science Teaching, 17(2/3), 161-180.

Adams, T.L. (1997). Addressing students' difficulties with the concept of function: Applying graphing calculators and models of conceptual change. Focus on the Learning Problems in Mathematics, 19, 43-57.

Berson, M.J., Mason, C.L., Heinecke, W.F., & Coutts, C.B. (2000, November). Technology innovation: An examination of beliefs and practices of social studies methods faculty. A paper presented at the College and University Assembly of the National Council of Social Studies annual conference. San Antonio, Texas.

Bitter, G.G., & Hatfield, M.M. (1993). Integration of the math explorer calculator into mathematics curriculum: The calculator project report. Journal of Computers in Mathematics and Science Teaching, 12, 59-81.

Bowers, J., & Doerr, H.M. (2001). An analysis of prospective teachers' dual roles in understanding the mathematics of change: Eliciting growth with technology. Journal of Mathematics Teacher Education, 4, 115-137.

Clements, D., & Battista, M. (1994). Computer environments for learning geometry. Journal of Educational Computing Research, 10(2), 173-197.

Conference Board of Mathematical Sciences (2001). The Mathematics Education of Teachers. Washington, DC: American Mathematical Society & Mathematics Association of America.

Doerr, H.M., & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41, 143-163.

Drier, H.S. (1998). How are graphing calculators used in mathematics classrooms? Teachers' beliefs and practices. Curry Journal of Education 1, 39-50.

Drier, H.S. (2001). Beliefs, experiences, and reflections that affect the development of techno-mathematical knowledge. In J. Price, D. Willis, N. Davis, & J. Willis (Eds.), Proceedings from the Twelfth International Meeting of the Society for Informational Technology and Teacher Education (pp. 1353-1358). Charlottesville, VA: Association for the Advancement of Computing in Education.

Dugdale, S. (1998). A spreadsheet investigation of sequences and series for middle grades through precalculus. Journal of Computers in Mathematics and Science Teaching, 17(2/3), 203-222.

Farrell, A.M. (1996). Roles and behaviors in technology integrated precalculus classrooms. Journal of Mathematics Behavior, 15, 35-53.

Fine, A.E., & Fleener, M.J. (1994). Calculators as instructional tools: Perceptions of three preservice teachers. Journal of Computers in Mathematics and Science Teaching, 14(4), 481-498.

Garofalo, J., Drier, H.S., Harper, S.R., Timmerman, M.A., & Shockey, T. (2000). Promoting appropriate uses of technology in mathematics teacher preparation. Contemporary Issues in Technology and Teacher Education, 1(1), 66-88. [Online]. Available: http://www.citejournal.org.

Graham, A.T., & Thomas, M.O. (2000). Building a versatile understanding of algebraic variables with a graphic calculator. Educational Studies in Mathematics, 41(3), 265-282.

Heid, M.K. (1997). The technological revolution and the reform of school mathematics. American Journal of Education, 106, 5-61.

Hembree, R., & Dessart, D. (1986) Effects of handheld calculator in precollege education: A meta analysis. Journal for Research in Mathematics Education, 17, 83-99.

Hembree, R., & Dessart, D. (1992). Research on calculator in mathematics education. In J. T. Fey & C. R. Hirsch (Eds.), Calculators in mathematics education: 1992 yearbook (pp. 23-32). Reston, VA: National Council of Teachers of Mathematics

Hollar, J. C., & Norwood, K. (1999). The effects of a graphing-approach intermediate algebra curriculum on students' understanding of function. Journal for Research in Mathematics Education, 30(2), 220-226

Hope, W.C. (1997). Why technology has not realized its potential in schools: A perspective. American Secondary Education, 25, 2-9.

Huang, S. Y., & Waxman, H.C. (1996). Classroom observations of middle school students' technology use in mathematics. School Science and Mathematics, 96(10), 28-34

International Society for Technology in Education (2000). National Educational Standards for Teachers. Eugene, OR: Author.

Jackiw, N. (2001). The Geometer's Sketchpad (Version 4.0). [Computer Software]. Emeryville, CA: Key Curriculum Press.

Kaput, J. (1992). Technology and mathematics education. In D. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 525-556). New York: MacMillan.

Kulik, J.A., & Kulik, C.L.C. (1987). Reviews of recent research literature on computer based instruction. Contemporary Educational Psychology, 12, 222-230.

Laborde, J.M. (2000). Cabri. [Computer Software]. Dallas, TX: Texas Instruments Incorporated.

Manoucherhri, A. (1999). Computers and school mathematics reform: Implications for mathematics teacher education. Journal of Computers in Mathematics and Science Teaching, 18(1), 31-48.

Mathematics Association of America (1991). A call for change: Recommendations for the preparation of teachers of mathematics. Washington, DC: Author.

Mathematics Sciences Education Board (1991). Counting on you: Actions supporting mathematics teaching standards. Washington, DC: Author.

Merriweather, M., & Tharp, M.L. (1999). The effects of instruction with graphing calculators on how general mathematics students naturalistically solve algebraic problems. Journal of Computers in Mathematics and Science Teaching, 18(1), 7-22.

Milou, E. (1999). The graphing calculator: A survey of classroom usage. School Science and Mathematics, 99, 133-140.

National Council for the Accreditation of Teacher Education (2002). Professional standards for the accreditation of schools, colleges, and department of education. Washington, DC: Author. Retrieved on August 12, 2002 from: http://www.ncate.org/standard/m_stds.htm

National Council of Teachers of Mathematics (1991). Professional standards for teaching mathematics. Reston, VA: Author.

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

Olive, J., & Leatham, K. (2000). Using technology as a learning tool is not enough. Paper presented at the international conference on Technology in Mathematics Education, Auckland, New Zealand.

Oppong, N.K., & Russell, A. (1998). Using combinations of software to enhance preservice teachers' critical thinking skills. Mathematics and Computer Education 32(1), 37-44.

Quesada, A.R., & Maxwell, M.E. (1994). The effects of using graphing calculators to enhance college students' performance in precalculus. Educational Studies in Mathematics, 27(2), 205-215.

Roberts, D.L., & Stephens, L.J. (1999). The effects of the frequency of usage of computer software in high school geometry. Journal of Computers in Mathematics and Science Teaching, 18(1), 23-80.

Rochowicz Jr., J.A. (1996). The impact of using computers and calculators on calculus instruction. Journal of Computers in Mathematics and Science Teaching, 15, 423-435.

Ruthven, K. (1990). The influence of graphic calculator use on translation from graphic to symbolic form. Educational Studies in Mathematics, 21, 431-50.

Sapsford, R. (1999). Survey research. Thousand Oaks: Sage.

Schmidt, M.E. (1998). Research on middle grades teachers' belief about calculators. Action in Teacher Education, 20(2), 11-23.

Schmidt, M.E., & Callaghan, L.G. (1992). Teachers and principals' beliefs regarding calculator in elementary mathematics. Focus on Learning Problems in Mathematics, 14(4), 17-29.

Schwarz, B.B., & Hershkowitz, R. (1999). Prototypes: Brakes or levers in learning the function concepts? The role of computer tools. Journal for Research in Mathematic Education, 30(4), 362-389.

Simonson, L.M., & Dick, T.P. (1997). Teachers' perceptions of the impact of graphing calculators in the mathematics classroom. Journal of Computers in Mathematics and Science Teaching, 16(2), 239-268.

Slavit, J. (1996). Graphing calculators in a "hybrid" algebra II classroom. For the Learning of Mathematics, 15(1), 9-14.

Smith, K.B., & Shotsberger, P.G. (1997). Assessing the use of graphing calculator in college algebra: Reflecting on dimensions of teaching and learning. School Science and Mathematics, 97, 368-376.

Stohl, H. (2002). Prospective teachers learning to facilitate social interaction and mathematical problem solving with technology tools. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.

Timmerman, M.A. (1998). Learning in the context of a technology-enriched mathematics teacher education course: Two case studies of elementary teachers' conceptions of mathematics, mathematics teaching and learning, and the teaching of mathematics. Unpublished doctoral dissertation. The Pennsylvania State University, State College, PA.

Turner, P., & Chauvot, J. (1995). Teaching with technology: Two preservice teachers' beliefs. In D. Owens, M. Reed, & G. Millsaps (Eds.) Proceedings of the Seventeenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 115-121). Columbus: ERIC.

U.S. Department of Education (2001). The nation's report card: Mathematics 2000 (NCES 2001-517). Washington, D.C.

Waits, B.K., & Demana, F. (2000). Calculators in mathematics teaching and learning: Past, present, and future. In M.J. Burke & F.R. Curcio (Eds.), Learning mathematics for a new century: NCTM 2000 yearbook (pp. 51-66). Reston, VA: National Council of Teachers of Mathematics.

Wenglinsky, H. (1998). Does it compute? The relationship between educational technology and student achievement in mathematics. Princeton, NJ: ETS 

Zbiek, R.M. (1995). Her math, their math: An inservice teacher's growing understanding of mathematics and technology and her secondary school students' algebra experience. In D. Owens, M.K. Reed, & G.M. Millsaps (Eds.), Proceedings of the Seventeenth Annual Meeting, North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 214-220). Columbus, OH: ERIC Clearing-house for Science, Mathematics, and Environmental Education. (ERIC Document Reproduction Service No. ED 389 610)

Zbiek, R., & Hollebrands, K. (in press). A research-informed view of the process of incorporating mathematics technology into classroom practice by inservice and prospective teachers. In M.K. Heid & G. Blume (Eds.), Handbook of research on technology in the learning and teaching of mathematics: Syntheses and perspectives. Greenwich, CT: Information Age Publishing.

GLADIS KERSAINT

University of South Florida 

USA

[e-mail]

BOB HORTON

Clemson University 

USA

HOLLYLYNNE STOHL

North Carolina State University 

USA

JOE GAROFALO

University of Virginia 

USA