Florence Mihaela Singer

Petroleum - Gas University of Ploiesti · Educational Sciences

While patterning was commonly seen as evidence of mathematical thinking, interdisciplinary interest has recently increased due to pattern-recognition applications in artificial intelligence. Within two empirical studies, we analyze the analogical-transfer capability of primary school students when completing three types of bi-dimensional patterns,...

Affects are intuitively accepted as having a role in the key stages that determine success in problem-solving (PS) and problem-posing (PP). Two disjoint groups of prospective mathematics teachers with similar background and competences have been exposed to PS and PP activities, respectively, and they had to describe their affective states during th...

The links between research in mathematics education, psychology of creativity and research in gifted education started to gain more attention in the last decade, from researchers and the large public as well. The paper is intended to provide a concise survey of these links, with a focus on: frameworks for studying students’ creativity and giftednes...

Cognitive flexibility—a parameter that characterizes creativity—results from the interaction of various factors, among which is cognitive variety. Based on an empirical study, we analyze students’ and experts’ cognitive variety in a problem-posing context. Groups of students of different ages and studies (from primary to university) were asked to s...

Summary The general aim of the present thesis is to draw on possible strategies to improve learning for new generations of students who are exposed to the actual phenomenon of almost exponential increase of information in terms of both amount and accessibility. Can domain-specific expertise be enhanced with appropriate training, across ages? How d...

Creativity and giftedness in mathematics education research are topics of an increased interest in the education community during recent years. This introductory paper to the special issue on Mathematical Creativity and Giftedness in Mathematics Education has a twofold purpose: to offer a brief historical perspective on the study of creativity and...

The paper analyzes the results of activities undertaken by Mathematics students enrolled in a pre-service teacher-training program. Students were given the task to describe the way of building a figure from which one could get a box, to identify the geometric properties that allow producing the box, and to propose new models from which new boxes ca...

While a wide range of approaches and tools have been used to study children’s creativity in school contexts, less emphasis has been placed on revealing students’ creativity at university level. The present paper is focused on defining a tool that provides information about mathematical creativity of prospective mathematics teachers in problem-posin...

The aim of this Topical Survey is to give a brief overview of the current state of research on and activities for mathematically gifted students around the world, being of interest to educational researchers, research mathematicians, mathematics teachers, teacher educators, curriculum designers, doctoral students, and other stakeholders. The focal...

This Topical Survey offers a brief overview of the current state of research on and activities for mathematically gifted students around the world. This is of interest to a broad readership, including educational researchers, research mathematicians, mathematics teachers, teacher educators, curriculum designers, doctoral students, and other stakeho...

We use statistical data to identify the problems that appear to be difficult with students in a problem-solving contest counting 9,580 participants from grades 2 and 3. Our analysis considers the level of complexity of the reading and problem-solving processes, as well as the diversity of the forms the information is conveyed by. We found the stude...

This presentation introduces the Proceedings of the International Conference Education and Psychology Challenges - Teachers for the Knowledge Society – 3rd Edition (EPC-TKS 2015), which was held in Ploiesti, Romania, between May 8 - 10, 2015.

Effective communication in the classroom is a key element for learning, yet when and how future teachers should acquire such competence is not clear. In this article we explore students-prospective teachers’ written productions of a set of instructions in a learning situation. Through three emblematic cases we illustrate how a communication task fo...

The mathematical creativity of 4th to 6th graders, high achievers in mathematics, is studied in relation to their problem posing abilities. The study reveals that in problem-posing situations, mathematically high achievers develop cognitive frames that make them cautious in changing the parameters of their posed problems, even when they make intere...

The mathematical creativity of fourth to sixth graders, high achievers in mathematics, is studied in relation to their problem-posing abilities. The study reveals that in problem-posing situations, mathematically high achievers develop cognitive frames that make them cautious in changing the parameters of their posed problems, even when they make i...

Five themes from the fi rst 25 chapters of this book are identifi ed: (a) the object of mathematical investigation as the construction of the problem itself and not just as fi nding the solution to a problem; (b) problem posing as an agent of change in the mathematics classroom; (c) integrating problem posing into mathematics classrooms; (d) proble...

In the context of designing a new curriculum, the paper addresses the tension between integrating all subjects in an exploring- theme approach and a subject-based approach. Given the complexity of a curriculum reform, this opposite tension, faced by most current day change processes, cannot and should not be addressed by a firm option for one of th...

We look at dynamic thinking and static thinking in relation to mathematical problem solving. We examine the distribution of answers chosen by large samples of students to multiple-choice problems. Our empirical data suggest that static thinking activated by students in problem solving is likely to be responsible for a certain pattern of students’ r...

The links between the mathematical and cognitive models that interact during problem solving are explored with the purpose of developing a reference framework for designing problem-posing tasks. When the process of solving is a successful one, a solver successively changes his/her cognitive stances related to the problem via transformations that al...

As an introduction to the special issue on problem posing, the paper presents a brief overview of the research done on this topic in mathematics education. Starting from this overview, the authors acknowledge important issues that need to be taken into account in the developing field of problem posing and identify new directions of research, some o...

We analyse a student's creative expression in problem-posing situations. The findings suggest that a small but significant difference in creative behaviour at an interval of one year (from 11 to 12 years old) indicates a passage from cognitive variety to small incremental changes, under the constraints of a strong cognitive frame. We found a specia...

The survey described in this paper was developed in order to gain an understanding of culturally-based aspects of creativity associated with secondary school mathematics across six participating countries. All participating countries acknowledge the importance of creativity in mathematics, yet the data show that they take very different approaches...

This paper presents the results of an experiment in which fourth to sixth graders with above-average mathematical abilities modified a given problem. The experiment found evidence of links between problem posing and cognitive flexibility. Emerging from organizational theory, cognitive flexibility is conceptualized through three primary constructs:...

O prezentare succintă evidențiază pe bază de date concrete nivelul scăzut al cercetării în domeniul educațional în România. Sunt analizate cauze și consecințe ale acestui fapt, referitoare atât la învățământul preuniversitar cât și la cel universitar. Studiul converge spre importanța consolidării unei filiere de dezvoltare profesională în domeniul...

We study the relationship between creative tasks and the quality of learning. We found that when confronted with problem posing contexts, a high achiever in mathematics displays cognitive flexibility, and reaches a number of new understandings that allow deep learning. Consequently, efficient learning can be promoted in a context that combines prob...

The paper presents a qualitative analysis of the impact of a conversion program on the teaching activities of the participants. We found changes in conceptions and attitudes towards the new domain, and we interpreted them as evidence that the participants became aware of the importance of the specialized content knowledge in effective teaching. It...

This review highlights the importance of representational change (RC) for effective and creative learning. The RC capability has been deduced from three types of observations that concern respectively: children’s innate propensities, their cognitive endowment for recursive processes, and their spontaneous bridging ability. The introduction of RC as...

The paper presents some results of the first year implementation of an innovative master program that offers teacher training in a blended learning (BL) system. The strengths and the weaknesses of BL are emphasized by analyzing students’ projects and their learning outcomes. The following lessons for improving the BL process emerged along the study...

This pilot study shows that there is a direct correlation between academic self-efficacy and cognitive load within the academic environment. We have used a self-efficacy scale and mental load tests on a sample of 30 students. Statistical data were collected and were processed by calculating the correlation coefficients. Our hypothesis was confirmed...

Masterprof is a master program that was designed within and for a comprehensive partnership among faculty, graduate students and school teachers in order to give a consistent response to the social need for better educated teachers. This challenging aim requires top innovation at various levels of intervention. Therefore, Masterprof benefits from a...

This study provides evidence that pre-service teachers who develop and implement educational projects during their training are more likely to better understand the complexity of the teaching profession. The students-prospective teachers of our sample had to design small scale projects and to apply them in school settings. In addition, they had to...

We analyze the statistical distribution of the answers given by 2nd to 10th graders to a set of number line problems. To structure our analysis of students’ misconceptions, we identified three clusters of problems related to the number line. Our analysis shows that neglecting one of the main features of the number line can be a potential cause for...

When reasoning about infinite sets, children seem to activate four categories of conceptual structures: geometric (g-structures), arithmetic (a-structures), fractal-type (f-structures), and density-type (d-structures). Students select different problem-solving strategies depending on the structure they recognize within the problem domain. They natu...

This chapter focuses on a specific type of the child's mental activity: processing structures. The practice of structuring starts in the first years of the child's life, while she/he explores the environment within categorical learning, and it extends along cognitive development through the organization of spontaneous and aggregate structures. The...

This paper presents an exploration of the role of context, individual differences and motivation as related to creativity in school mathematics across several countries. We asked leading professionals in mathematics education from seven nations to take part in a thought experiment focusing on the following task: Imagine you were a policy maker (e.g...

What activities do children prefer in primary grades? Are these related to what the teacher effectively does in the classroom? How are the teaching stereotypes mirrored in the students' representations about the tasks? This article presents the outcomes of a survey on a national representative sample of four-graders that was focused on exploring th...

The system of testing, analyzing and reporting (star) underlies the following components: the development of collaborative databases of items in several languages, the assessment of students' knowledge and abilities in various school subjects by using tests from the databases, an individualized feedback to every student which is obtained by process...

We explore children’s strategies in comparing infinite sets of numbers, based on an empirical study. We report four categories of structures that the children identified during this process: geometrical-based structures, topological-based structures, fractal-type structures, and arithmetical-type structures. Using the identified structure, students...

A mechanism underlying the computational properties of the cognitive architecture is construed based on a minimal list of operational clusters. This general processing mechanism constitutes the dynamic infrastructure of mind (DIM). DIM consists in categories of mental operations foundational for learning that contain inborn components called inner...

During the last three decades, a large body of research was devoted to analyzing number representation in humans. The findings in neuroscience and their adequate interpretation in relation with cognition may reshape the traditional ways of teaching and learning. The paper synthesizes the following achievements of research on human cognition: there...

In the general framework of educational research, the present paper proposes a model of project management in terms of designing and implementing a distance learning program for Chemistry Field, implemented through the specific activities of the Rural Education Project. The paper is focused on the main steps in designing distance learning programs...

Based on an empirical study, we explore children’s primary and secondary perceptions on infinity. When discussing infinity, children seem to highlight three categories of primary perceptions: processional, topological, and spiritual. Based on their processional perception, children see the set of natural numbers as being infinite and endow Q with a...

This study attempts to analyze and synthesize the knowledge collected in the area of conceptual models used in teaching and learning during inquiry-based projects, and to propose a new frame for organizing the classroom interactions within a constructivist approach. The IMSTRA model consists in three general phases: Immersion, Structuring, Applying...

ABSTRACT— Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strat...

Do we need models in explaining the outer world and the self? What types of models might be helpful in school to explain both complexity and abstraction? What level of representation is appropriate? What dimensions of training should be focused on in constructing an inquiry-based learning? How could these dimensions be reflected in developing stude...

This chapter reports on the mechanisms activated by the reform of education at the confluence of economic, political and sociocultural factors in a system in transition to democracy and a functional market economy. The paper analyses the fluctuating balance between ideological and professional positions in the decision making process based on a cas...

The last decade brought about a vivid discussion concerning a competence-based curriculum in order to better train the students for the knowledge society. The present paper describes a cognitive model that aims at designing competences for secondary education. It consists in six operational categories which are combined based on epistemological and...

The paper is focused on recent researches in neuroscience and developmental psychology regarding mathematical abilities of infants. A model that tries to explain these findings is developed. The model underlies the mental operations that could be systematically trained to generate efficient school learning. The model is built from a cognitive const...

Dominating information by formation seems to be the only realistic solution to overcome the crisis generated by the higher and higher accumulation of information in each domain. The paper is proposing a model of building structured knowledge able to generate in the child's mind strategies for efficient processing of information.

The structural cognitive learning process of a domain implies three distinct stages: internalizing what we call basic learning units, constructing the specific mental structures and practicing them in order to develop specific competencies. Every school subject appears as a logical structure, which needs to be learned as a structure, with its natur...

The research is developed in the framework of a constructivist approach to learning. I suggest through the example of learning equations how recent developments in cognitive science could be connected to school learning. I propose a methodology of teaching practice consisting in the following three components: systematic training, focused on buildi...

We explore different types of behavior during the problem posing process by looking at the ways students value the problem data in solving and extending their own posed problems. Based on the outcomes of these analyses we explain the differences in students' success and failure in the problem posing approaches in relation to the level of understand...