Elementary students’ functional thinking: From recursive to correspondence

Abstract

This study aims to identify elementary students' functional thinking processes in solving pattern problems. Previous studies showed that elementary students' functional thinking still often experience errors in solving pattern problems. The study of the functional thinking process in solving pattern problems is a fundamental key as a solution to find out the strengths and weaknesses of elementary school students, so that they are better prepared in generalizing relationships, representing and analyzing function behavior in advanced algebra classes. This study used a descriptive qualitative approach with a case study method. Participants of study was sixty-five elementary students who had not yet received generalization patterns material. The instruments were tasks and interview guidelines. Based on the task results, students who had correct answers were chosen using purposive sampling to be given an in-depth interview. The finding indicated that elementary students are able to think functionally in different ways. Students' functional thinking begins with recursive thinking in the pre-finding formula in the entry stage. Students find the formula by corresponding thinking in the attack stage. Finally, students use the formula to get inverse in the review stage.

An Approach to the State of the art of Variational Thought in First Grades of Schooling

“…Subsequently, there are some studies that also work with the category of functional thinking and whose objective is to determine the appropriate type of instruction, specifically in working with patterns, so that students in the first grades of schooling manage to move from recursive thinking or recursive relations to covariational or correspondence relations (Blanton et al, 2011;Blanton et al, 2015;Cañadas & Fuentes, 2015;Cañadas et. al., 2016;Morales et al, 2018;Pinto et al, 2016;Stephens et al, 2012;Stephens et al, 2017;Syawahid et al, 2020). For works such as those of Torres et al, (2019;, the interest is to identify the nature of the functional structure that early grade school students can establish when working with linear and affine functions to model the solution of the proposed tasks.…”

Kemampuan Guru Junior dalam Mengajarkan Proses Berpikir untuk Menyelesaikan Soal Cerita Sederhana: Studi pada Guru Matematika Sekolah Dasar

“…Bentuk ujian nasional yang hampir sepanjang tahun menggunakan pilihan ganda juga tidak mendorong guru matematika untuk mendorong siswanya menunjukkan pemikiran matematisnya. Syawahid et al (2020) mengidentifikasi tiga faktor penting yang mempengaruhi kesiapan guru dalam menerapkan inovasi. Faktor-faktor tersebut adalah sense-making, kepemilikan, dan agensi.…”