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>The thought processes of ninth grade students from the University of Puerto Rico's secondary school when using TI -73 graphic calculators to solve single variable linear inequalities in elementary algebra.
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The thought processes of ninth grade students from the University of Puerto Rico's secondary school when using TI -73 graphic calculators to solve single variable linear inequalities in elementary algebra.
The purpose of this investigation was to discover the thought processes of two ninth grade students who used TI-73 graphic calculators to solve single variable linear inequalities in their elementary algebra class. Specifically, this study considered: (1) the relationship between the concrete and abstract phases of problem-solving; (2) the time needed for students who are in either the concrete or abstract phases of learning to construct their own knowledge, according to the constructivist learning theory; (3) the cognitive obstacles that students encounter when solving these types of problems; (4) how the TI-73 graphic calculator was able to help these ninth grade students in the transition from the concrete to the abstract phases of learning and to analyze whether it is appropriate, regardless of the students' cognitive developmental stages, to use the TI-73 calculator; (5) generate pedagogical understanding of the mathematical content within this type of teaching-learning setting.;The Longeot Test was administered to thirty students. Two students were selected: one who was at the formal stage and another who was at the concrete stage of cognitive development, according to the results of the test. The information-gathering techniques that were used included interviews, "thinking out loud," retrospective exploration, observation and the analysis of the students' written work during the problem-solving exercises.;The findings of the investigation revealed: (1) that both students, regardless of their stage of cognitive development, followed a similar algorithm to solve single variable linear inequalities, and that the TI-73 graphic calculator was helpful to both students in their transition to the abstract phase of problem-solving; (2) the mental representation was related to the information provided by the TI-73 graphic calculator, and (3) the mental representation that each of the two participating students formed of the set of solutions for the inequalities proved to be different. This finding agrees with Piaget's hypothesis which was the framework behind this investigation.;This study offers evidence leading to the following conclusions related to the use of the TI-73 graphic calculator in teaching single variable linear inequalities: (1) the calculator promotes the capacity to create mental representations that reinforce the concepts that are being taught; (2) the calculator proved to be equally useful to students who are either at the concrete stage or formal stage of their cognitive development, and finally, (3) it is important to provide students the time necessary to construct their own knowledge when using the TI-73 graphic calculator.
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