Problem solving as a methodology for teaching mathematics in basic education: a systematic literature review

Abstract

Problem solving, according to Polya, became visible in 1945. However, the variety of concepts and the reduction in the impact of research in the mathematics curriculum area has created difficulties in its use in the practice of the mathematics teaching process. This study systematically reviewed how problem solving in mathematics teaching in elementary and secondary (K-12) education is approached. 16 articles on the subject were reviewed in detail, taking into account aspects such as (a) use of Digital Information Communication and Technology (DICT) associated with teaching proposals with a problem-solving perspective; (b) comparison between traditional teaching proposals and teaching proposals based on the problem-solving strategy; (c) comparison between traditional teaching proposals with teaching proposals based on problem solving as a teaching methodology; and (d) problem solving as a methodology approach and its implications for the teaching-learning process. The results show that (a) DICTs favor collaborative educational practices; (b) teaching based on problem solving can be an alternative to the teaching-learning process of mathematics; (c) computer games and the use of systems are favorable for problem solving and (d) the teaching of mathematics through problem solving can provide educational experiences that transcend the teaching of mathematics, promoting discussion, reflection, questioning, dialogue, cooperation, collaboration, written production and engagement. Furthermore, the results indicate that 62.5% of the selected works make use of the quasi-experimental methodology and point to few (16 works in 10 years) studies that deal with problem solving as a methodological alternative for teaching mathematics.