Abstract
Abstract This study aimed to describe teacher interventions in students’ problem-solving. The subjects were three upper-class students at an elementary school in Indonesia who used system 2 when solving problems. This study used a qualitative case study approach. Data were obtained from students’ written answers and audio-visual recordings of teacher interventions to students. The results showed that the subjects needed teacher interventions to induce their awareness when involving system 2. Each subject needed intervention different stages. Subject 1 required intervention stage 3, subject 2 required intervention stage 2, and subject 3 only required intervention at stage 1. From the research results, it was known that the active moment of system 2 in all three subjects was the same, that is after the core problem was known. The core of the problem was ascertained after a doubtful feeling arose on the truth of the resulting answers. This feeling arose because the teacher intervened in the form of questions conducted dialogically.
Highlights
Problem-solving is an essential topic in Mathematics instruction (BALTACI; YILDIZ; GUVEN, 2014; CUNHA; LAUDARES, 2017; GUVEN: OZUM, 2013; JACINTO; CARREIRA, 2017; SPINILLO et al, 2017; CĂPRIOARĂ, 2015), taught since the elementary school level (AMARAL; CARREIRA, 2017; SOUSA; MENDES, 2017)
The most significant activity for students in mathematics classroom is working on tasks, problem-solving (AMARAL; CARREIRA, 2017; CUNHA; LAUDARES, 2017; JACINTO; CARREIRA, 2017)
In the view of dual-process theory, the most common source of error in reasoning is the inactivity of system 2 to control the response of system 1 (BAGO; DE NEYS, 2017; LERON; HAZZAN, 2009)
Summary
Problem-solving is an essential topic in Mathematics instruction (BALTACI; YILDIZ; GUVEN, 2014; CUNHA; LAUDARES, 2017; GUVEN: OZUM, 2013; JACINTO; CARREIRA, 2017; SPINILLO et al, 2017; CĂPRIOARĂ, 2015), taught since the elementary school level (AMARAL; CARREIRA, 2017; SOUSA; MENDES, 2017). Inadequate reasoning may cause difficulties and failures in problem-solving (BABAI; SHALEV; STAVY, 2015; MULLIS et al, 2012; OECD, 2018). Inadequate reasoning generally occurs because students do not have conceptual and procedural knowledge (BORODIN, 2016; DARMAWAN et al, 2020; LERON; HAZZAN, 2009). Even when students have conceptual and procedural knowledge, difficulties can still occur. When students do not know the core of the problem, their attention is not directed to information, giving solutions to the problem. Directing attention to information that supports solutions to problems is the most necessary cognitive ability that students can have. This ability is the initial step in students’ success because it underpins the steps
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