The effectiveness of long term vs. short term training in selected computing technologies on middle and high school mathematics teachers' attitudes and beliefs.

This article describes two professional development experiences for middle and high school mathematics teachers: one long-term, the other short-term. The training of the long-term group (n=12) took place over an entire semester, in a 15-week, 45-hour graduate course, at an urban institution in New York City, that accented the use of computing technologies, especially the "TI83 Plus" graphing calculator and the "Geometer's Sketchpad," to enhance the teaching of mathematics in secondary schools. The training of the short-term group (n=11) took place in a series of three workshops totaling 7 hours, with teachers from the institution's Professional Development School, using essentially the same types of technology tools. Attitude changes about the use of technology, obtained through a 16-item pre-and post-survey given to both groups, are presented. Comments from teachers' written reports and reflections about their beliefs in the effectiveness of using technology in the mathematics classroom are included as well. Professional development in computing technologies can be effective in changing teachers' attitudes and beliefs if implemented through a long-term, sustained, and coherent form of training that provides teachers with opportunities for active learning in the use of relevant technology tools in general.

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Microcomputers and calculators are entering classrooms in substantial numbers, with attractive software applications, advanced multimedia capabilities and, above all, the World Wide Web. Research interest in the use of calculators and computing technologies in education has increased dramatically over the past decade because of this technology-enriched environment. In such settings, technology impacts not only what is taught and how it is taught but also what students learn and how they learn it (Beckmann, Thompson, & Senk, 1999). This has posed a challenge and an opportunity for teachers to learn more about computers and software, and how to integrate technology to teach or to enhance their curricula. Research has shown, however, that providing support for the use of technology in the schools is only half the issue; the other half involves changing attitudes and mental structures (Thatcher, 1996). Positive teacher attitudes toward technology are necessary for its effective use in the classroom (Lawton & Gerschner, 1982; Woodrow, 1992; Christensen, 2002). The question is to know what type of professional development can best change teachers' attitudes and beliefs toward the use of computing technologies in the mathematics classroom. Is it best to learn slowly over a period of time (as in a course), or does a small number of concentrated workshops suffice to train teachers?

This article presents findings from a study that involved two groups of mathematics teachers who were trained to use selected computing technologies through two different professional development experiences: one long-term, the other short-term. The training of the long-term group took place over an entire semester, in a 15-week, 45-hour graduate course. The training of the short-term group took place in a series of three workshops totaling 7 hours. Changes in teacher attitudes and beliefs due to the technology training are presented.

Role of Technology in Mathematics Instruction

Computing-technologies have the potential for wide-ranging and long-lasting impact in the mathematics classroom (Heid & Baylor, 1993). They facilitate in-depth exploration of mathematical topics previously too complex for typical classrooms, especially when such topics involve real-world, "messy" data. They also give all students, whether functioning at Piaget's concrete or formal operational level, the technology tools that enable them to visually examine "concrete" representations of mathematics concepts (Shoaf-Grubbs, 1992; Hollylynne, Dawson, & Garofalo, 1999). For example, in using the graphing calculator, "the analysis of the calculator images would provide the student with a concrete learning opportunity to recognize her (or his) thinking processes, procedures, and structures, therefore enabling her (or him) to move towards a higher, more formalized level of understanding" (Shoaf-Grubbs, 1992, p.30). The National Council of Teachers of Mathematics (NCTM) has argued even more persuasively in support of the use of computing technologies in the classroom.

    Electronic technologies-calculators and computers- are essential
    tools for teaching, learning, and doing mathematics. They furnish
    visual images of mathematical ideas, they facilitate organizing and
    analyzing data, and they compute efficiently and accurately. They
    can support investigation by students in every area of mathematics,
    including geometry, statistics, algebra, measurement, and number.
    When technological tools are available, students can focus on
    decision-making, reflection, reasoning and problem solving (NCTM,
    2000, p.24).

Mathematics Teachers' Attitudes and Beliefs Toward Technology

Even though NCTM's conclusions value the use of technology in the mathematics classroom, research on mathematics teachers' beliefs and attitudes toward such use indicates that firmly held tenets are resistant to change. Teachers have continued not to want to face the uncertainties related to the use of computing technologies in the classroom, and often question whether students will do as well with technology as with traditional methods. In 1988, Dick and Shaughnessy studied the effects of providing classroom sets of symbolic-manipulation calculators for volunteer high school mathematics teachers. Despite the change in attitudes for both their male and female students, "teachers felt that the use of the calculators brought only minor changes in the dynamic of classroom interaction" (p.333). Tharp, James, Fitzsimmons, and Ayers (1997) examined the perceptions of teachers as they engaged in initial instruction using graphing calculators. Participants' views changed significantly (p <.001) in favor of viewing the graphing calculator as a "thinking tool" to enhance conceptual understanding. However, data from questionnaires administered revealed a significant correlation between holding a more rule-based viewpoint about learning mathematics and the view that graphing calculators do not enhance instruction and may even hinder it. Tharp et al. concluded that rule-based teachers are most likely to quickly return to lecture mode after engaging in initial instructional experiences with graphing calculators.

Models of Professional Development

Short-term forms of professional development, most often in the guise of one or two-shot workshops, continue to be most commonly used in the United States to support teachers in implementing innovative programs in to classroom. As such, school districts are able to avoid the expenses--in personnel and resources--entailed in long term professional development that might extend to a full academic semester or full-year commitment.

Such forms of training have no continuity, and no follow-up, and leave teachers with the decision to continue on their own (Zigarmi, Betz, & Jensen, 1977; Clarke, 1994). The danger is that teachers are usually not motivated to implement any new program if they are not convinced of its effectiveness, therefore annihilating any potential for change and improvement. Today, such form of training has not changed much across the US. A recent CEO forum (1999) reports that districts spend only about 1% of their technology budget on teacher training, far less than the U.S. Department of Education recommended amount of 30%. If the goal for schools and educators is to improve student achievement, this situation needs to change. The role of technology in education and in society will only increase, and research has shown that not only does effective technology training of teachers change their attitudes, but also it positively affects student achievement (Christensen, 2002).

It is clear from a review of the research that a model of professional development that provides teachers with time to design a plan for using suggested materials and methods in their classrooms resulting in greater educational gains for students, will be the catalyst to initiate a shift in teachers' attitudes. For instance, a study within the Apple Classrooms of Tomorrow (ACOT), a multi-year project that provides support for technology integration in the classroom, showed that significant changes in attitudes among participant teachers happened only during the second year of the project. Teachers felt comfortable using technology in their classrooms only after personal appropriation of the technology tools had taken place (Dwyer, Ringstaff, & Sandholtz, 1991). In a study conducted through a professional development project that helps elementary school teachers create learner-centered, technology rich environments in their schools, Burns (2002) also found that valuing comfort over proficiency and providing time for sharing ideas are key elements in the training of teachers that would foster significant and lasting change on their attitude toward the use of technology in the classroom. Porter, Garet, Desimone, Yoon, and Birman (2000), found in their longitudinal large-scale study that examined the effectiveness of professional development on improving classroom teaching practice for mathematics and science teachers that a high quality professional development depends in large measure on six features: form, duration, collective participation, content, active learning, and coherence. Activities of longer duration (long-term training) and activities that encourage collective participation of teachers tend to place more emphasis on content than other activities, provide more opportunities for active learning, provide a more coherent professional development, and lead to teachers reporting enhanced knowledge and skill and change in teaching practices (Porter et al., 2000).

This article describes the results of a study of two groups of mathematics teachers who were trained to use graphing calculators and specialized software in two different professional development models. The first group included middle and high school mathematics teachers enrolled in a 15-week, 45-hour graduate course needed to complete requirements for their advanced degree in mathematics education. The second group was comprised of middle school mathematics teachers from the college's Professional Development School (PDS). They received a short-term training of a series of three workshops. The researcher sought to determine whether teachers' beliefs and attitudes about the use of technology in the mathematics classroom changed as a result of long-term vs. short-term professional development.

METHOD

Context

The course and its participants. Participants in the Spring 2001 semester graduate course (n = 12) included four female and eight male teachers, eleven of whom were matriculated students in the Master's of Mathematics Education program. Of the 12 teachers, six taught in middle school, and six taught in high school. They used the TI83-Plus (Texas Instrument, 2001) for most of each of 10 sessions, and the Geometer's Sketchpad (Key Curriculum Press, 2001) for most of each of 3 sessions. Not a single teacher had ever used the TI83 Plus graphing calculator in teaching mathematics concepts, nor had known about the Geometer's Sketchpad prior to taking the course.

The investigator chose this course for the study because it was redesigned to meet the request of students in the Master's program. They had indicated through the annual evaluation survey given by the Division of Education of the college that they would like to see more technology integrated in mathematics education courses. Responding to teachers' requests in a manner consistent with their expectations is a key element of a successful professional development experience (Clarke, 1994). In redesigning the course however, the path recommended by Stein, Smith, and Silver (1999) was followed. That is, the teaching of teachers for the 21st century should be done in a new way. The topics in this course offered the opportunity to introduce these teachers to technology in mathematics teaching that support and facilitate conceptual development of mathematics content in the context of the curriculum they are teaching.

Teacher's participation to the study was voluntary. They were informed that lack of participation would have no influence on the course grade. All teachers' names in this article are pseudonyms.

The workshops and its participants. This group of participants (n=11), which included six female and five male teachers, attended three workshops during the 2001 Fall Semester. They were first exposed to an algebra computer-based manipulative called Virtual Tiles (Bradford, 1996) in one three-hour session, then introduced to Geometer's Sketchpad activities in one two-hour session, before they studied and discovered some key concepts in pre-algebra, algebra, and statistical analysis with the TI83-Plus graphing calculator, also in one two-hour session. Prior to these workshops, none of these teachers had used some kinds of technology to teach mathematics concepts.

The researcher spends each semester one day a week at the PDS as the college's liaison to the site, supervising student teachers, and working with practicing teachers towards yearly PDS goals identified by the two partners as in a model suggested by Teitel (2001). The technology training of PDS teachers took place because one of the year's main PDS goals was to increase mathematics teachers' awareness of technology-based curricula. The two partners made the decision to use the only two citywide Professional Development Days available that year, to conduct three workshops to train them on how to use computing technologies to enhance the curriculum. Time constraints and lack of materials were the barriers that made it impossible for the researcher to work with teachers at any other time during the year. At the time of the training, not much computing technologies was available at the PDS site, other than scattered sets of four computers in each classroom. Teachers had no uses for those computers. They often question their ability to use them with 30 students or more in a classroom. The two partners however, have developed plans to create computer labs, and have designed a course that would be co-taught at the site by faculty from both institutions who would train mathematics and science teachers on developing curriculum materials that use technology.

Procedures

To determine the changes in teachers' beliefs and attitudes about the use of technology in the mathematics classroom, the same survey (see Appendix A) was given to both groups of teachers at the beginning and at the end of the training. Additionally, course participants submitted reflections about the training, and gave their insights regarding the role of technology in the mathematics classroom at the end of the course. Insights from workshop participants were obtained through the evaluation form given at the end of the second professional development day.

Instrument

The researcher did a quantitative analysis of the data that was based on the pre- and post-survey results of all teacher participants. The survey, designed by Tharp et al. (1997), included 16 background questions as well as Likert-scale statements (with responses ranging from 0 = Strongly Disagree to 4 = Strongly Agree) dealing with teaching mathematics and using calculators in the classroom such as: (a) teacher view of calculator use, (b) teacher view of mathematics learning, (c) access to calculators, (d) teacher efficacy, (e) student efficacy, and (f) administrative support. The attitude-based survey was used to measure a perspective on mathematics learning: "the view of learning math as a rule-based subject" (VLMRBS). Tharp (1992) designed "the VLMRBS measure of perspective on mathematics learning to assess the degree to which a person adheres to the view that mathematics learning is mostly oriented toward processes which involves the manipulation of symbols and memorization of facts as opposed to the view that mathematics learning is based on reasoning about relationships and patterns (Tharp et al., 1997). The measure is fairly new and has therefore no reliability and validity information available. However, this measure has concurrent validity with a Perry Measure of r = -0.43 with p < 0.05 (Tharp & Lovell, 1995).

In this study however, the questionnaire was mainly intended to determine whether attitudes and beliefs about technology could change between the beginning and the end of a training program that integrates the use of technology in the mathematics classroom. Consequently, only the responses to the six statements 1, 2, 3, 4, 14, and 15, could be considered to determine if a view was favorable or not favorable to the use of graphing calculators. For instance, for questions 1, 4, 14, and 15, if one disagreed or strongly disagreed, his/her position was considered favorable to the use of graphing calculators or technology. For questions 2 and 3, if one agreed or strongly agreed, his/her position was also deemed favorable. Otherwise, the position was classified undecided--a response of 2--or unfavorable.

The methods employed were also interpretive, in that they involved an analysis of teachers' comments and reflections about the use of the graphing calculators and computing technologies in the mathematics classroom. Course participants submitted reflections about the ways the course has contributed to their belief--or disbelief--about the effectiveness of computing technologies. Workshop participants gave their insights through an evaluation form given at the end of the last professional development day.

Data Treatment

To analyze the differences between the two groups, a 2X2 analysis of variance with repeated measures was performed. The first factor was Group (Course vs. PDS), and the second factor, the repeated measure, was Test (Pre-survey, Post-survey). For each item of the survey, such measure allowed the researcher to determine if the interactions between the two groups were significant, and if the differences between the pre- and post- survey responses of all participants were also significant. Additionally, within each group, each question item was analyzed by using a paired-sample t-test showing the mean difference between the pre and post-survey responses.

RESULTS

Table 1 shows a pre-survey average response of 2.25 for the course, which appears to indicate that the course participants were undecided since a rank of 2 is midway between the most favorable (0) and the least favorable answer (4). For the post-survey, the mean average of .67 shows that course participants' attitudes changed significantly (p<.05) as they disagreed with the statement "Calculators should 'only' be used to check work."

The PDS (Workshop) group results showed no significant differences between the pre- and post-survey average responses of 1.45 and 1.36. It appears however, that these participants did have a favorable attitude toward the use of calculator before and after the training, since both pre- and post-survey scores were close to the second most favorable response, 1, which was also the most selected response (the mode) by 8 teachers. The results also show that when combined, all participants (N=23) significantly (p<.05) changed their attitudes on Item 1.

Table 2 shows that, on Item 2, no significant changes between pre-and post-survey responses were recorded for the course, workshop participants, and altogether. The pre- and post-survey mean responses were all close to 2, which may lead to believe that all teachers were somewhat "undecided" since a rank of 2 is midway between the most favorable (4) and the least favorable answer (0). However, the post-survey responses which were most selected by 16 of 23 teachers responding to this item was 3 or 4. Demonstrating that, perhaps, there was a small shift in favor of the statement "A graphing calculator can be used as a tool to solve problems I could not solve before," despite the non-significant mean difference of -.30 (p>.1).

An analysis of Table 3 and Table 4 shows that course and workshop participants had a favorable view about the use of graphing calculators on Item 3 and Item 4. Most teachers agreed with the statement (3) "Using a graphing calculator to teach mathematics or science allows me to emphasize the experimental nature of the subject," and disagreed with (4) "Using a graphing calculator to teach math or science does not enhance student learning or understanding of concepts" before and after the training. The pre- and post-survey mean responses recorded on these two items show a favorable belief that graphing calculator can enhance student learning.

For Item 14 shown in Table 5, there was a significant change of attitude for course participants. The pre-survey mean response of 2.58, shows that prior to the course, participants were favorable (agreed with) to the statement "Students lack the ability to work with a calculator as complex as graphing calculator." Six (6) of 12 teachers chose the response 3 (agree) or 4 (strongly agree). However, the post-survey mean response of 1.25 was a clear indication that a shift has taken place, since most teachers (7) choose a response of a rank of 1 (agree) or 0 (strongly disagree). The mean difference of 1.50 was significant (p<.05). The attitudes for all participants also changed significantly (P < .05). In contrast, pre- and post-survey average responses of 2.27 and 2.36 show that PDS teachers were undecided prior to and after the workshops.

Finally, Table 6 shows that both groups seem to have shifted from an undecided position to a "somewhat" favorable position with Item 15, "If students are taught to use technology, they will come to rely on it and lose their ability to think." The course recorded pre- and post-survey average responses of 1.92, and 1.25, whereas the workshop recorded pre- and post-survey average responses of 1.73 and 1.45. Even though in both groups the mean differences were not significant (p > .05), the post-survey average responses were close to 1, the second most favorable position. The overall change for the two groups combined was also not significant.

DISCUSSION

For the course participants, a favorable shift significantly took place on only two items, 1 "Calculators should 'only' be used to check work," and 14 "Students lack the ability to work with a calculator as complex as graphing calculator." On each of the other four items (2, 3, 4, and 15), however, the post-survey average response (2.75, 3.17, .50, and 1.25) was closer to the response that was considered to be the second most favorable to the use of graphing calculators in the classroom, demonstrating that teachers did improve attitude in favor of the use of technology in the mathematics classroom. Moreover, the significant difference on Item 14 seems to indicate that teachers' view and perception about students' ability to work with the graphing calculator grew more favorably as did their own ability and confidence to use this particular technology tool.

What may explain the course's positive outcomes may be the length and extent to which concepts were studied. It took teachers 15 consecutive weeks to learn, practice, reflect, and be tested on the different activities involving the "TI83 Plus" graphing calculator and the Geometer's Sketchpad. During these class sessions, teachers were exposed in depth to a variety of mathematics topics with the opportunity to design one or more activities involving the use of these technology tools. They not only discussed issues that were related to the use of technology in the mathematics classroom, but also submitted reflections as answers to specific questions about their pre- and post-training beliefs and attitudes. At the end, most wrote that their pre-training beliefs and attitudes were the consequence of their lack of opportunity to experience the use of technology in a way similar to what they did in the course, and of their lack of confidence in their ability to design activities to enhance the mathematics curriculum. In general, a shift in their attitudes was however apparent, way before the end of the course, as teachers got exposed to how different concepts can be introduced through simple discovery using technology, whether with the graphing calculator or with the Geometer's Sketchpad. Many teachers decided to experiment teaching mathematics concepts using the TI-83 graphing calculators in their classes, and reported on students' reactions and on the success of the experiments (Such reports will be the subject of a second study involving middle and high school students).

For the workshop group, the training seemed to have had no effects on its participants' views about the use of technology in the mathematics classroom. The differences between the pre- and post-survey mean responses were very small and were not significant on any of the six items. Such results were not surprising since the length and the extent to which the concepts presented to PDS teachers were very short, and their experiences with technology limited because of time constraints. They attended only one three-hour session and two two-hour sessions more than a month later. They were not tested, nor were they asked to design and implement technology-oriented activities. There was no continuity or follow-ups in the concepts studied. They just had a glimpse of some of the possibilities that could be used and may not have had enough time and training for a better appreciation of the effectiveness of the technology tools presented to them.

What was unexpected however, was PDS teachers' initial view about the use of technology in the classroom. Pre-survey average responses show that they had a "somewhat favorable" position on five out of the six items prior to beginning the workshops, perhaps explaining the no-effects of the workshops. It is also possible that PDS teachers had had previous technology training that was positive and/or had experienced positive outcomes for themselves or their students.

CONCLUSIONS

An analysis of course participants' comments and reflections show that all agreed on the nature of technology as a great motivational tool as demonstrated by what one student said at the sound of the bell after being introduced for the first time to the graphing calculator, "I finally learned something today." The teacher, Robert, thinks that such reactions can perhaps be explained by the technology-rich oriented society we live in today.

    Many students, because they play with more complicated devices such
    as Nintendo 64 or Play Station 2, are more than motivated to learn
    mathematics concepts using the TI83 graphing calculator.

A point reinforced by Maria:

    Students are so accustomed to playing with computer arcade games
    that the technology tools become like toys. The solution resides in
    an effective training of teachers toward the use of technology to
    enhance mathematics learning.... It is almost a sin not to make use
    of technology in the preparation of tomorrow's teachers and in the
    classroom. It is regrettable that my district or school does not
    provide graphing calculators, nor offers the training (Maria).

In addition, almost all teachers in both the course and workshops expressed this lack of administrative support. Most schools did not have a sufficient number of graphing calculators for all teachers to use at will. In some instances, teachers were not even aware that graphing calculators were available at their school. At the end of the last workshop, some PDS teachers, expressed their frustration not only about the lack of materials, but also about the lack of effective guidance on how to implement technology activities in the mathematics classroom.

    This is fine information, but I wonder why are we spending time on
    stuff we don't have, and I can't see when we'll have this stuff. We
    need to focus on attainable goals and situations I suggest we get
    trained on how to do things with little or no technology, because
    that's where we are (John, from the workshops). Good crash course,
    but the material relevant to 6th grade curriculum was not reviewed
    (Christine, from the workshops).

Indeed, the workshops did not provide PDS teachers with time to design a plan for using suggested materials and methods in their classrooms. A long, sustained, and more coherent form of training would have provided more opportunities for active learning, and could have lead PDS teachers to report more favorably about their experience with technology. In contrast, because course participants were provided with more opportunities for active learning, they all reported a change in beliefs and attitudes toward the use of technology in the classroom, as evidenced by the comments.

    In the past, I believed that using calculators was basically
    cheating, because students didn't need to know how to find the
    answer. They would just put the numbers in. I now believe this is a
    good tool for students to see a lot of concepts. For example, a
    class may only have time to graph 2 or 3 functions by hand, but if
    a teacher wanted to show the effects that adding a constant to the
    function or multiplying the function by a number might have, he/she
    would want students to see more than just one or two examples.
    Calculators can allow you to do that and help eliminate the time
    factor (Judy from the course).

    The technology tools used in this course have reinforced my belief
    in the use of technology in the teaching of some mathematics
    concepts. Because of the fact that most of our students are visual
    learners and that the use of technology reduces the emphasis on
    basic skills, the learner at this level can concentrate on the
    concepts being developed. The graphing calculator provides a
    laboratory approach to mathematics where students are given an
    opportunity to take an active role in the development of their
    knowledge base (Jean, from the course).

Teachers in the course, however, raised some additional concerns about the use of technology tools to teach mathematics. They called for prudence in designing curricular materials that use technology, by expressing concerns in the ability of the teacher to design effective lessons so that, when students are allowed to use calculators, they will not come to basically rely on them and lose the ability to think.

The TI83 can certainly be a 'dangerous weapon' if one does not understand the mathematics (Robert).

That is, teachers need to have the content background, and need to be trained effectively so to enable them to develop well-designed activities that are appropriate to students' levels of learning.

APPENDIX A

Attitude Questionnaire

Circle the number that best reflects your present attitude

0 Strongly Disagree  1 Disagree  2 Undecided  3 Agree  4 Strongly Agree

 1. Calculators should "only" be used to check work.       0  1  2  3  4
 2. A graphing calculator can be used as a tool to solve
    problems I could not solve before.                     0  1  2  3  4
 3. Using a graphing calculator to teach mathematics or
    science allows me to emphasize the experimental
    nature of the subject.                                 0  1  2  3  4
 4. Using a graphing calculator to teach math or science
    does not enhance student learning or understanding of
    concepts.                                              0  1  2  3  4
 5. Learning mathematics is mostly memorizing a set of
    facts and rules.                                       0  1  2  3  4
 6. When doing mathematics, it is only important to know
    how to do a process and not why it works.              0  1  2  3  4
 7. Learning mathematics means exploring problems to
    discover patterns and make generalizations.            0  1  2  3  4
 8. I have difficulties gaining access to graphing
    calculators for use in my classroom.                   0  1  2  3  4
 9. I have enough calculators for individual student use.  0  1  2  3  4
10. It is difficult to get funds to buy graphing
    calculators.                                           0  1  2  3  4
11. My administration encourages use of graphing
    calculators.                                           0  1  2  3  4
12. I lack confidence and skill with graphing
    calculators.                                           0  1  2  3  4
13. Teaching with a graphing calculator is a high
    priority in my department.                             0  1  2  3  4
14. Students lack the ability to work with a calculator
    as complex as a graphing calculator.                   0  1  2  3  4
15. If students are taught to use technology, they will
    come to rely on it and lose their ability to think.    0  1  2  3  4

Table 1 Comparison of the Pre- and Post-Survey Responses for Item 1

Item 1. Calculators should "only" be used to check work.

                          Rank         Mean    Standard     Mean
                     0   1  2  3  4  Response  Deviation  Difference

Course  Pre-Survey   1   3  2  4  2   2.25       1.29
(N=12)  Post-Survey  6   5  0  1  0    .67        .89      1.58
PDS     Pre-Survey   3   3  2  3  0   1.45       1.21
(N=11)  Post-Survey  1   8  0  1  1   1.36       1.12       .1
Total   Pre-Survey   4   6  4  7  2   1.87       1.29
(N=23)  Post-Survey  7  13  0  2  1   1.00       1.04       .87

                       t      p

Course  Pre-Survey
(N=12)  Post-Survey    3.50   .027*
PDS     Pre-Survey
(N=11)  Post-Survey     .166  .871
Total   Pre-Survey
(N=23)  Post-Survey    2.30   .032*

* p<.05 significant

Table 2 Comparison of the Pre- and Post-Survey Responses for Item 2

Item 2. A graphing calculator can be used as a tool to solve problems
that I could not solve before.

                        Rank          Mean    Standard     Mean
                     0  1  2  3  4  Response  Deviation  Difference

Course  Pre-Survey   2  2  2  4  2  2.17      1.40
(N=12)  Post-Survey  0  3  0  6  3  2.75      1.14       -.58
PDS     Pre-Survey   1  0  3  4  3  2.73      1.19
(N=11)  Post-Survey  1  1  2  3  4  2.73      1.35       0
Total   Pre-Survey   3  2  5  8  5  2.43      1.31
(N=23)  Post-Survey  1  4  2  9  7  2.74      1.21       -.30

                      t       p

Course  Pre-Survey
(N=12)  Post-Survey  -1.168   .267
PDS     Pre-Survey
(N=11)  Post-Survey   0      1.00
Total   Pre-Survey
(N=23)  Post-Survey   -.850   .404

Table 3 Comparison of the Pre- and Post-Survey Responses for Item 3

Item 3. Using a graphing calculator to teach mathematics or science
allows me to emphasize the experimental nature of the subject.

                        Rank           Mean    Standard     Mean
                     0  1  2   3  4  Response  Deviation  Difference

Course  Pre-Survey   1  0  1   8  2  2.83      1.03
(N=12)  Post-Survey  0  1  1   5  5  3.17       .94        .17
PDS     Pre-Survey   0  0  5   4  2  2.73       .79
(N=11)  Post-Survey  0  1  0   8  2  3.00       .77       -.27
Total   Pre-Survey   1  0  6  12  4  2.78       .90
(N=23)  Post-Survey  0  2  1  13  7  3.09       .85        .22

                      t       p

Course  Pre-Survey
(N=12)  Post-Survey   -.804  .438
PDS     Pre-Survey
(N=11)  Post-Survey   -.896  .391
Total   Pre-Survey
(N=23)  Post-Survey  -1.32   .200

Table 4 Comparison of the Pre- and Post-Survey Responses for Item 4

Item 4. Using a graphing calculator to teach math or science does not
enhance student learning or understanding of concepts.

                        Rank           Mean    Standard     Mean
                      0  1  2  3  4  Response  Deviation  Difference

Course  Pre-Survey    4  5  2  1  0  1.00       .95
(N=12)  Post-Survey   6  6  0  0  0   .50       .52        .50
PDS     Pre-Survey    6  2  1  1  0   .82      1.08
(N=11)  Post-Survey   4  3  1  3  0  1.27      1.27       -.45
Total   Pre-Survey   10  7  3  2  0   .91      1.00
(N=23)  Post-Survey  10  9  1  3  0   .87      1.01        .04

                      t      p

Course  Pre-Survey
(N=12)  Post-Survey  1.732  .111
PDS     Pre-Survey
(N=11)  Post-Survey  -.922  .378
Total   Pre-Survey
(N=23)  Post-Survey   .149  .883

Table 5 Comparison of the Pre- and Post-Survey Responses for Item 14

Item 14. Students lack the ability to work with a calculator as complex
as graphing calculator.

                         Rank        Mean     Standard     Mean
                     0  1  2  3  4  Response  Deviation  Difference

Course  Pre-Survey   0  3  2  4  3    2.58      1.16
(N=12)  Post-Survey  7  0  3  1  1    1.08      1.44        1.50
PDS     Pre-Survey   1  1  5  2  2    2.27      1.19
(N=11)  Post-Survey  0  3  3  3  2    2.36      1.12         .1
Total   Pre-Survey   1  4  7  6  5    2.43      1.16
(N=23)  Post-Survey  7  3  6  4  3    1.70      1.43         .73

                       t      p

Course  Pre-Survey
(N=12)  Post-Survey   2.292  .043*
PDS     Pre-Survey
(N=11)  Post-Survey   -.219  .831
Total   Pre-Survey
(N=23)  Post-Survey   2.071  .05*

* p<.05 significant

Table 6 Comparison of the Pre- and Post-Survey Responses for Item 15

Item 15. If students are taught to use technology, they will come to
rely on it and lose their ability to think.

                           Rank       Mean     Standard     Mean
                     0   1  2  3  4  Response  Deviation  Difference

Course  Pre-Survey   1   6  1  1  3    1.92      1.44
(N=12)  Post-Survey  3   6  1  1  1    1.25      1.01         .67
PDS     Pre-Survey   1   4  3  3  0    1.73      1.01
(N=11)  Post-Survey  3   3  3  1  1    1.45      1.29         .28
Total   Pre-Survey   2  10  4  4  3    1.83      1.23
(N=23)  Post-Survey  6   9  4  2  2    1.35      1.23         .48

                       t     p

Course   Pre-Survey
(N=12)   Post-Survey  .804  .438
PDS      Pre-Survey
(N=11)   Post-Survey  .559  .588
Total    Pre-Survey
(N=23)   Post-Survey  .369  .185

Acknowledgements

I would like to thank Stan Taback, David Fletcher, Anne Rothstein, and the anonymous reviewers for their valuable and constructive comments on the earlier drafts. Also, thanks to all teachers who participated in the study.

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SERIGNE MBAYE GNINGUE

Lehman College, City University of New York

USA

[e-mail]