engleski

Advances in Research on Teaching Mathematics

Research presented in the papers collected for this Monograph deals with various aspects of teaching mathematics on different educational levels and across several European countries. The Monograph consists of three chapters. In the first chapter of the Monograph, the authors wrote about students’ knowledge and representations of knowledge in teaching mathematics. The first paper examines types of errors in students dealing with different aspects of fractions. The author cautions for teaching directed towards comprehension to reduce misconceptions and recognize mathematical concepts in a real-life context. The results of recent studies focussing on typical misconceptions when dealing with different aspects of fractions are present in the paper. In the second paper, the author compared geometry tasks in university entrance examinations across a period and found the content of the tasks decreasing in complexity. Throughout his survey, the author considered the commonly used five components of spatial intelligence as well as the mathematical content of the problems. The authors of the third paper in this chapter raise an interesting issue of managing dichotomies in mathematics education. They discuss and advise mindfully combining different teaching approaches to produce the best results depending on the educational context. Using the example of introducing students to the mathematical structure of division, they demonstrate different ways of knowledge transfer, the role and meaning of repetition, and the logic of including concrete representations. The fourth paper reports on teachers’ use of didactic manipulatives in primary mathematics education. In the final paper in this chapter, the authors conducted an experiment showing that visual representation facilitated problem-solving. The second chapter contains papers focused on teaching practice. The author of the first paper presents a theoretically supported method for introducing arithmetic operations in primary education. The concurrent method of teaching multiplication and division in elementary school is discussed. The second paper investigates interactions in children’s mathematical lessons. The authors found that the different classroom setting encourages mathematical communication and connecting pieces of mathematical knowledge. In the third paper, the authors describe the construction process and use of a novel game for mathematics education. It advantages students’ knowledge by describing and connecting different ideas encountered across the mathematics curriculum. The authors of the final paper in this chapter propose football-related tasks and activities across all grades of primary education. They argue for the popularization of mathematics by connecting to interesting and familiar realistic topics. The content of the third and the last chapter of the Monograph relates to technology in teaching mathematics. The first paper reports on prospective teachers’ familiarity and attitudes about participating in the eTwinning programme. The following papers address the consequences of online education during Covid-19 lockdown. The authors of the first paper examined the differences in grades obtained after onsite and online learning and the author of the second paper examined students’ attitudes and satisfaction concerning an online course. The final paper presents a result of mathematical modelling of population density data used for computer mobility simulations.

mathematics ; education ; ICT

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