Education technology -training course
R. Afkhami; N. Asghary; alireza medghalchi; F. Pashaie
Abstract
Background and Objectives: The principles and standards of school mathematics (NCTM) in the branch of algebra propose standards that consider the development of students' understanding of algebraic symbolization and especially the understanding of the variable concept as one of the basic needs of students. ...
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Background and Objectives: The principles and standards of school mathematics (NCTM) in the branch of algebra propose standards that consider the development of students' understanding of algebraic symbolization and especially the understanding of the variable concept as one of the basic needs of students. Functional thinking is also the highway of algebraic thinking and teachers should consider it as the heart and soul of math education. Figural patterns have characteristics that are favorable for starting the generalization and development of functional thinking and can be used in school mathematics. Also, attention to mathematical structure should be an important part of the teaching and learning mathematics. The structure of a mathematical pattern is the way a pattern is organized and is often expressed as a generalization. The purpose of this research was to investigate the performance of students in building the concept of figural pattern generalization based on APOS theory (action-process-object and schema) and to improve the stages using the states of awareness of the structure, and will help teachers and students to have a more accurate evaluation of the figural pattern generalization and better identify the problems and improve their stages of understanding.Methods: The data collection method was quantitative-qualitative. The data collection tool included a researcher-designed test and a semi-structured interview. The statistical population included 493 seventh grade students of public schools in Malekan city (Azerbaijan-e-sharghi). According to Cochran's sample size formula, 220 male and female seventh-grade students were selected and participated in the researcher-designed test. The validity of the test was checked and confirmed by three mathematics teachers and four experienced teachers. The reliability and internal consistency of the questions were confirmed by finding Cronbach's alpha coefficient and alpha as 0.69.Findings: Students' mental structures were identified according to APOS theory in the figural pattern generalization. The highest percentage of correct response was at the action stage and the lowest percentage was at the object stage. The stages of APOS were hierarchical and from simple to complex, and the results of this research confirmed the characteristics of this theory. At the action stage, about 18% of the students were unsuccessful, and according to the first attentional state (holing wholes) looking at the figural pattern was introduced as a tool to improve the understanding of these students. About 60% were unsuccessful at the process stage, which the discerning details and recognizing relationships as second and third attentional states helped students to reach the process stage. About 88% of the students failed to reach the object that the fourth attentional state (perceiving properties) as auxiliary tool was introduced. Reasoning on the basis of identified properties as the fifth attentional state was used to upgrade students to the schema stage in APOS theory.Conclusion: This research provided a framework for measuring and evaluating students in the figural pattern generalization that teachers can use in better teaching of this concept. At each stage, solutions can be provided according to the student s' stage to improve their understanding of generalization to higher stage. This research showed the power of APOS theory in compatibility with other constructionist theories. Adapting the APOS theory with the theory of structural awareness and benefiting from this adaptation in order to improve the stage of understanding of the seventh-grade students in figural pattern generalization was considered as one of the innovative aspects of this research.
