Monday, October 13, 2008

READINGS...

Learning to teach mathematics at the middle and secondary levels should include many opportunities for teachers to learn how to use technology to better understand mathematics themselves and promote students' learning of mathematical concepts with technology-enabled pedagogy. This article highlights work done in a variety of pre-service and in-service mathematics teacher education courses to help teachers use commonly available spreadsheets as an interactive exploratory learning tool. Several examples of teachers' subsequent use of spreadsheets in their own teaching are also discussed.

"Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning" (National Council of Teachers of Mathematics ([NCTM], 2000, p. 11). This statement is one of six principles described in the NCTM's document, Principles and Standards for School Mathematics. The use of the word essential in the statement has many implications for school mathematics, as well as preservice and in-service mathematics teacher education. Not only are teachers charged with a vision of transforming their teaching and students' learning of mathematics, but teacher educators are challenged with the task of preparing teachers who can utilize technology as an essential tool in developing a deep understanding of mathematics, for themselves and for their students. Recent trends in teacher education have emphasized the importance of learning with technology rather than learning about technology. This implies that teachers should learn to use a computer as a cognitive tool to enhance student learning of content material (e.g., mathematics, social studies, or science) rather than acquiring isolated skills in basic computing applications (e.g., word processing, database, spreadsheets, or hypermedia) or merely learning a specific programming language (Abramovich & Drier, 1999). Thus, to promote the use of technology for students' conceptual development, mathematics teachers should learn how to use widely available software, such as spreadsheets, as a conceptual teaching and learning tool (Abramovich, et al., 1999). During the past decade, spreadsheets have been used in teacher education and K-12 classrooms to explore a variety of mathematical concepts and to help students use numerical and graphical methods to solve problems (Abramovich, 1995; Abramovich & Nabors, 1998; Clements & Samara, 1997; Dugdale, 1998; Neuwirth, 1995). These uses of spreadsheets allow students to explore alternative solution processes that go beyond symbolic manipulation and can provide students with a deeper understanding of concepts embedded in a problem. One unique use of spreadsheets is the ability to interactively model and simulate mathematical situations. In much the same way scientists use a laboratory to discover and test scientific laws, mathematics teachers can use spreadsheets to create dynamic experiential environments for discovering mathematical relationships. Such activities can facilitate students' engagement with mathematical concepts and their conceptualization of relationships among numerical, graphical, and algebraic representations. The flexibility and power of the Microsoft Excel (1997) spreadsheet software allows teachers to be engaged in meaningful mathematical activities that, in turn, empower them to use spreadsheets as interactive environments in their own teaching.
Teaching with the use of spreadsheets help them to explore more on the development of the skills of the skills especially on how they will deal on problems that uses spreadsheets. However, today’s students are engaging more on the use of computer.
On the other hand, calculators and other technological tools, such as computer algebra systems, interactive geometry software, applets, spreadsheets, and interactive presentation devices, are vital components of a high-quality mathematics education. With guidance from effective mathematics teachers, students at different levels can use these tools to support and extend mathematical reasoning and sense making, gain access to mathematical content and problem-solving contexts, and enhance computational fluency. In a well-articulated mathematics program, students can use these tools for computation, construction, and representation as they explore problems. The use of technology also contributes to mathematical reflection, problem identification, and decision making.
However, there are some arguments that the use of technology cannot replace conceptual understanding, computational fluency, or problem-solving skills. In a balanced mathematics program, the strategic use of technology enhances mathematics teaching and learning. Teachers must be knowledgeable decision makers in determining when and how their students can use technology most effectively. All schools and mathematics programs should provide students and teachers with access to instructional technology, including appropriate calculators, computers with mathematical software, Internet connectivity, handheld data-collection devices, and sensing probes. Curricula and courses of study should incorporate instructional technology in learning outcomes, lesson plans, and assessments of students’ progress.

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