This study aims to investigate the problem-solving behaviors of a teacher and his students based on a cognitive – metacognitive framework. The problem-solving behaviors of 6-8th-grade students and a mathematics teacher were recorded and encoded during task-based interview sessions about solving problems, and semi-structured interviews were used to obtain information regarding the mathematics teacher's perceptions of mathematical problem-solving processes. They solved the problems in a learning environment, and their problem-solving processes were investigated using the think-aloud method. The results indicated that the students and the teacher followed a similar path involving reading, understanding, exploring, planning, and implementing. Furthermore, not all episodes occurred in each problem-solving task and the behaviors that represented given episodes changed according to the participants. Students with different problem-solving skill levels were found to exhibit different frequencies of cognitive and metacognitive behaviors while solving problems. The problemsolving behaviors of the teacher and the students revealed information related to metacognitive behaviors that are to be developed in further studies.
Karl Popper lamented the prevalence of dogmatic argument in philosophy and commended the kind of critical argument that is found in the sciences. David Miller criticises the uncritical nature of so-called critical thinking because of its attachment to dogmatic arguments. I expound and clarify Popper’s distinction between critical and dogmatic arguments and the background to it. I criticise some errors in Miller’s discussion. I reaffirm the need for philosophers to eschew dogmatic arguments in favour of critical ones., Karl Popper naříkal nad převahou dogmatického argumentu ve filozofii a pochválil druh kritického argumentu, který se nachází ve vědách. David Miller kritizuje nekritickou povahu takzvaného kritického myšlení z důvodu jeho vazby na dogmatické argumenty. Vysvětluji a objasňuji Popperův rozdíl mezi kritickými a dogmatickými argumenty a pozadím. Kritizuji některé chyby v Millerově diskusi. Znovu potvrzuji, že je třeba, aby se filozofové vyhýbali dogmatickým argumentům ve prospěch kritických argumentů., and Danny Frederick