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Article Excerpt
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...
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