Cognitive flexibility: exploring students’ problem-solving in elementary school mathematics learning

Abstract

In classroom learning, students need mathematical cognitive flexibility to be able to solve mathematical problems with the various ideas they express. To solve the problems, they must be able to grasp the problem, see it from various points of view, and should not be rigid thinking with one solving method. In fact, the students still lack the ability to think flexibly in solving math problems. This exploration is necessary to determine how to encourage the students’ creative problem-solving. The purposive sampling technique is used to select two out of 150 of 4th Grade students who have taken an initial test to measure their creative abilities. Problem-solving worksheet, think-aloud records, and interviews are used as data collection instruments. Then, the data were analyzed using a qualitative descriptive approach. The research instrument is validated by two professors of mathematics. Through a series of revisions based on expert advice, the validity results are said to be feasible for use. To check for reliability, field tests are tested on 10 students who meet the criteria as research subjects. Analysis results indicate that cognitive abilities involve cognitive processes in the form of the ability to assess process by looking for patterns of numbers, mentally compute, estimate, and assess the rationality or reasonableness of calculation results. Other findings on students' cognitive processes in solving math problems include looking for number patterns, carrying out trial-and-error (also called guess-and-check), and drawing diagrams. Students with cognitive flexibility tend to use trial-and-error when solving mathematical problems.

The Characteristics of Mathematical Literacy Based on Students’ Executive Function

“…According to research by Purpura et al (2017), working memory played a role in mathematical abilities such as counting, comparisons, and formulating mathematical problems. In contrast, the cognitive flexibility aspect was related to the conceptual element of mathematical ability (Purpura et al, 2017;Rahayuningsih et al, 2020). The findings in students' mathematical literacy skills showed that the PISA indicators could not appear in achieving mathematical literacy skills when solving PISA questions.…”

Analisis Kemampuan Literasi Matematis Siswa Dalam Menyelesaikan Soal Berorientasi Pisa Konten Uncertainty and Data

“…Matematika merupakan perantara berpikir ilmiah dalam mengembangkan kemampuan dan keterampilan intelektial siswa, dengan demikian siswa mampu menyelesaikan masalah yang berkaitan dengan matematika maupun ilmu lain (Holis et al, 2016). Menurut (Rahayuningsih et al, 2020), pemecahan masalah adalah salah satu aspek utama dari kurikulum matematika yang tidak hanya berlaku di Indonesia tetapi juga di seluruh dunia. Sehingga saat ini siswa di tuntut untuk dapat berpikir secara logis dan kritis dalam menyelesaikan berbagai permasalahan matemaika.…”

Mathematical Creative Thinking Ability and Self-Efficacy: A Mixed-Methods Study involving Indonesian Students

“…The Mathematics Creative Thinking Ability Scale was developed based on the research instrument of Rahayuningsih et al (2020). It contains an indicator of creative thinking ability that is cognitive flexibility (Singer et al, 2017& Rahayuningsih et al 2020).…”

“…The Mathematics Creative Thinking Ability Scale was developed based on the research instrument of Rahayuningsih et al (2020). It contains an indicator of creative thinking ability that is cognitive flexibility (Singer et al, 2017& Rahayuningsih et al 2020). According to Singer et al, (2017), the context used to examine students' creativity in mathematics involves mathematics tasks, like problem-solving sheets, that can be used as an instrument to measure students' mathematical creative thinking ability.…”