Greater emphasis must be placed on activities that promote innovative teaching methods in early childhood mathematics education in Poland. Our classrooms offer algorithmic and rote teaching methods, depriving students of important elements of successful mathematics learning. The aim of this action research was to investigate the relationship between a classroom environment that allows for dialogue and discovery and young children’s input into problem solving. Teaching six classes of elementary school within one academic year gave the author the opportunity to examine how dialogic teaching combined with a growth mindset approach can transform the attainment of knowledge, understanding and skills of learners, and how modern practices like number talks, solving open-ended tasks and group work can unleash students’ potential and activate them as thinkers and reasoners. The results confirmed that students who are challenged and offered concept-based learning opportunities not only genuinely engage in their tasks, but also help each other with deeper understanding of the concepts. They can cooperate with teachers in the creation of a new classroom in which students’ voices are heard and discoveries take place.
Problem posing and problem solving serve as a crucial element of classroom instruction in early mathematics education, and have long been a topic of study of many practitioners and researchers. Used as a powerful tool for differentiation, they affect the ways in which the practice of mathematics is perceived by students and also help teachers gauge children’s understanding of concepts. In the student-centered approach, problem posing and problem solving can successfully engage students in creative educational situations. This research has been part of a broader design research project, the aim of which was to investigate the relationship between a classroom environment that allows for dialogue and young children’s propensity to design and solve their own tasks. Methodology included taking field notes and photographs, followed by reflection sessions. Turning young mathematicians into independent inquirers helped them gain authentic ownership of their knowledge. Additionally, it aided in the development of the young children’s competencies in effective engagement in problem posing activities. The toolbox of instructional techniques for problem posing in the classroom evolved, transforming mathematical classrooms into inquiry polygons for all learners.
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