Mathematical working space relations with conversions between representations and problem solving in fraction addition

The present study is focused on the cognitive level of Mathematical Working Space (MWS) and the component of the epistemological level related to semiotic representations in fraction addition. A test measuring students’ conversion and problem - solving ability in fraction addition was developed and administered to 388 primary and secondary school students (about 11-14 years old) three times. Multivariate analysis of variance (MANOVA) for repeated measures and implicative method revealed that the students’ performance improved as they move within primary school and within secondary school. A hiatus in performance progress is indicated, though, when the students moved from primary to secondary school. This finding is in line with a compartmentalized way of thinking indicated for this age group. Didactical implications are discussed

Mathematical creativity and geometry: The influence of geometrical figure apprehension on the production of multiple solutions

International audienceThe aim of the study is to investigate the creativity demonstrated by students in multiple-solution tasks (MSTs) in geometry taking into account the role of geometrical figure. To this end, the test that was administered among 149 eleventh graders consisted of two types of problems: a. with and b. without the relevant figure. Findings revealed that fluency and flexibility were higher when the verbal description of the problem was accompanied by the relevant figure. The originality of students' solutions, though, did not differ in the two types of problems. The similarity analysis suggested distinct student profiles: (a) poor fluency and flexibility, (b) moderate fluency and flexibility and (c) high fluency and flexibility. Although the majority of students belong to the first two groups, qualitative results provide evidence that students managed to improve and gain high fluency and flexibility. Findings also indicated that geometrical figure apprehension is a prerequisite for high levels of creativity in geometry

Mathematical creativity and geometry: The influence of geometrical figure apprehension on the production of multiple solutions

International audienceThe aim of the study is to investigate the creativity demonstrated by students in multiple-solution tasks (MSTs) in geometry taking into account the role of geometrical figure. To this end, the test that was administered among 149 eleventh graders consisted of two types of problems: a. with and b. without the relevant figure. Findings revealed that fluency and flexibility were higher when the verbal description of the problem was accompanied by the relevant figure. The originality of students' solutions, though, did not differ in the two types of problems. The similarity analysis suggested distinct student profiles: (a) poor fluency and flexibility, (b) moderate fluency and flexibility and (c) high fluency and flexibility. Although the majority of students belong to the first two groups, qualitative results provide evidence that students managed to improve and gain high fluency and flexibility. Findings also indicated that geometrical figure apprehension is a prerequisite for high levels of creativity in geometry

How could the Presentation of a Geometrical Task Influence Student Creativity?

This study aims to investigate high school students’ geometry learning by focusing on mathematical creativity and its relationship with visualisation and geometrical figure apprehension. The presentation of a geometrical task and its influence on students’ mathematical creativity is the main topic investigated. The authors combine theory and research in mathematical creativity, considering Roza Leikin’s research work on MultipleSolution Tasks with theory and research in visualisation and geometrical figure apprehension, mainly considering Raymond Duval’s work. The relations between creativity, visualization and geometrical figure apprehension are examined through four Geometry Multiple-Solution Tasks given to high school students in Greece. The geometrical tasks are divided into two categories depending on whether their wording is accompanied by the relevant figure or not. The results of the study indicate a multidimensional character of relations among creativity, visualization and geometrical figure apprehension. Didactical implications and future research opportunities are discussed

Fostering representational flexibility in the mathematical working space of rational numbers

The study focuses on the cognitive level of Mathematical Working Space (MWS) and the component of the epistemological level related to semiotic representations in two mathematical domains of rational numbers: fraction and decimal number addition. Within this scope, it aims to explore how representational flexibility develops over time. A similar developmental pattern of four distinct hierarchical levels of student representational flexibility in both domains is identified. The findings indicate that the genesis of the semiotic axis in fraction and decimal addition is not automatic, but a long process of developmental steps that could be referred to as MWS1, MWS2, MWS3, MWS4 (final). There is not a clear and stable correspondence between developmental levels of representational flexibility and school grades. Didactical implications in order to foster representational flexibility in the MWS of fraction and decimal addition are discussed

The Role of Representations in the Understanding of Mathematical Concepts in Higher Education: The case of Function for Economics Students

There are numerous studies about the teaching and learning of mathematics at different educational levels. In the case of higher education most studies were conducted at pedagogical departments for prospective teachers and mathematical departments. The present study concentrates on university students who attend a course on mathematics as part of a program at the Faculty of Economics and Management. It examines aspects of students’ affective and cognitive behavior in solving representation tasks concerning their understanding of exponential and logarithmic functions. Results confirmed the existence of a comprehensive model with significant interrelations among general beliefs, self-efficacy beliefs and cognitive behaviour about the use of representations in general and, in the case of the specific concept. Regression analysis indicated the predominant role the self-efficacy beliefs play in the use of representations in defining the concept of function and solving recognition and translation tasks. Implications about the teaching of mathematics in higher education are discussed

Early childhood teachers' awareness of the characteristics of picture books for learning mathematics

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