The Interplay of Processing Efficiency and Working Memory with the Development of Metacognitive Performance in Mathematics

The present study outlines a specific three level hierarchy of the cognitive system and especially the relations of specific cognitive and metacognitive processes in mathematics. The emphasis is on the impact of the development of processing efficiency and working memory ability on the development of metacognitive abilities and mathematical performance. We had used instruments measuring pupils´ metacognitive ability, mathematical performance, working memory and processing efficiency. We administered them to 126 pupils (8-11 years old) three times, with breaks of 3-4 months between them. Results indicated that the development of each of the abilities was affected by the state of the others. Particularly, processing efficiency had a coordinator role on the growth of mathematical performance, while self-image, as a specific metacognitive ability, depended mainly on the previous working memory ability

Play based activities for mathematical thinking at infancy: Nursery teachers’ and parents’ beliefs

Mathematics takes place in a major part of human life and mathematical concepts are used in every part of daily life, starting from the age of infancy. The present study concentrates on the age of 11 months to two years, during nursery education, when formal, informal and non-formal activities enable infants to have experiences related to mathematical concepts. Nursery teachers are expected to include play-based activities at every stage of the teaching process, while parents are recognized as young children’s first educators. We examined nursery teachers’ and parents’ beliefs and practices about the development of the infants’ mathematical skills through the use of play-based activities and their respective roles. The present study was conducted in Cyprus, where obligatory preschool education is only one year before primary education. Questionnaires, interviews and shared diaries with home activities were used for quantitative and qualitative data. Results indicated that both groups of participants expressed positive conceptions on the value of daily life play-based activities which could support mathematical learning. However, it seemed that in the case of parents there was a lack of relevant knowledge about the use of attractive and creative activities which could relate to plenty of mathematical concepts. Parents recognize the vital role of teachers and they asked for further guidance and support. We discuss how we can ensure the quality of early mathematics informal teaching and nonformal learning experiences can be offered for all infants. We discuss the role of the Curriculum in Mathematics at nursery school under a play-based context and the guided parental involvement

Inquiry-based teaching approach in mathematics by using the history of mathematics: A case study

International audienceThe use of the history of mathematics during an inquiry-based teaching approach is expected to multiply the positive effects on students' learning. The present work investigated a "typical" teacher's difficulties while trying to use the history of mathematics as a teaching tool during inquiry-based teaching activities. Two examples which were presented in the textbook of the 5 th grade of primary education were used to observe the teaching practices. Results indicated that the teacher had difficulties in understanding how students could investigate a mathematical concept by integrating the history of mathematics and how the study of the history would enable them to construct the new-acquired knowledge. The respective knowledge of the domain seemed to be a prerequisite in order to be able to use the history of mathematics fluently and flexibly in a learning environment which asked students to explore or investigate the mathematical concepts

Teaching the concept of function: Definition and problem solving

International audienceThe present study investigates students' abilities to understand the concept of function. Secondary education students were asked to (i) define the concept of function and present examples of functions, (ii) translate between different representations of a function and (iii) solve function problems. Findings revealed students' great difficulties in proposing a definition of function, in solving tasks of conversions between different modes of representation, and in solving function problems. Based on the students' abilities and misconceptions about functions, teaching practices for improving the students' understanding of functions 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