HOW DO STUDENTS USE GRAPHICAL CALCULATORS TO MODEL AND SOLVE SPEED PROBLEMS
Rodolfo Oliveros
Universidad Autónoma Chapingo
This work focuses on how students in an introductory calculus course modeled problems of distance vs time relationships, using calculators with curve fitters to infer speeds with the model they found. The research questions that guided the study were: What specific difficulties in representation did students deal with when they used the calculators? How did they select a model among the various functions of the calculator to relate distance and time? The study was conducted with a 12th grade high school group during a semester-long introductory calculus course. Teams of cooperative learning groups of 3 or 4 students were formed. Each team had one TI-82 calculator, which they were taught to use while they solved. Observing students using calculators revealed that some of the difficulties they have do not necessarily concern dealing with new representations, but sometimes old, well-identified problems emerged, for example, it is assumed that there was a lack of understanding of letters as representations of numbers and of multiplication of signs or by zero.
With the introduction of technology, the manner of representing mathematical concepts increases. Could this increase the risk of problems in communication? This may well be, as long as some students seem to see calculator notation as if it were formal algebraic notation, in spite of warning them that each software or calculator has a different way of expressing mathematical concepts. This is the same warning contained in Principles (NCTM, 1998). It would help if the notations used by technology would adjust more to those most frequently used in algebra. In modeling, some students had problems in identifying the variables of the model. In spite of the fact that some students encountered many difficulties, others were able to model and infer the speed of that model using a variety of strategies.
Reference
NCTM. (1998). Principles and Standards for School Mathematics: Discussion Draft. Reston, VA: Author.