JUNIOR CYCLE STUDENTS’ UNDERSTANDING OF GRAPHING AND FUNCTIONS: A CASE STUDY

Date

2023-9-11

Author

Şen, Ümmü Gülsüm

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The present study aims to investigate the effects of an instructional design that introduces functions through graphs on learning graphing and functions by first-year Junior Cycle students in Ireland. To this end, an instructional design based on APOS Theory was developed and tested through a case study involving two cycles. The first cycle was conducted with one student, and the second cycle with three other students chosen conveniently via the personal connections of the researcher. Data were collected from December 2019 to May 2020 from four students in their first year of the Junior Cycle. Four sources were utilized in the data collection process: written responses to activities, video recordings of lessons, posttests, and in-depth interviews. The data were analyzed using APOS Theory. The findings suggest that the proposed genetic decomposition allows students to learn how to solve real-world problems involving functions and create graphs of functions, including qualitative ones, without requiring knowledge of the formal definition of functions or reliance on algebraic representations. This study is the first to suggest a genetic decomposition of graphing functions prior to the pre-algebra level. The genetic decomposition developed in this study can serve as a guide for curriculum developers, instructional designers, and textbook writers, offering a dependency map for the concepts and processes involved in graphing functions. The study also provides examples of instructional materials and student responses to them, which may be useful in the development of instructional materials.

Subject Keywords

APOS Theory, Graphing and Functions, Instruction Design, Patterns, Representations of Functions

URI

https://hdl.handle.net/11511/105619

Collections

Graduate School of Natural and Applied Sciences, Thesis