engleski

Redesigning a contextual textbook task with an exponential-type function using a posteriori analysis of the prospective mathematics teachers’ work

An exponential function is one of the elementary functions in mathematical modelling and a common part of the upper secondary mathematics curriculum. A horizontal asymptote is a prominent feature of an exponential function graph. We have performed a comprehensive study within the Anthropological theory of the didactics on asymptotes and asymptotic behaviour in the context of upper secondary mathematics education in Croatia. Therein, we administered three questionnaires with prospective mathematics teachers. One of the tasks from the questionnaires was a priori designed to explore the role of an asymptote in graphing and describing an exponential function. In this paper, we present results of an a posteriori analysis of students' work on the modified contextual textbook task with an exponential-type function. We discuss the affordances of the textbook versus redesigned task and provide suggestions for task selection and design to promote coherency and discourse in students' available mathematical knowledge.

Anthropological theory of the didactics ; a posteriori analysis ; contextual task ; exponential function ; function graph ; task design

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