Development Of Probabilistic Thinking Research Articles

FINANCIAL LITERACY OF THE MANAGEMENT STUDENTS – CZECH AND SLOVAK EXPERIENCE

Financial literacy is becoming one of the key competencies in the 21st century. In its absence, it is virtually impossible to navigate the market for financial products and services and thus ensure financial stability throughout the whole life. The author presents the results of a survey of the financial literacy of young future managers who are currently university students. Based on a questionnaire survey among full-time and part-time students, the author detects the positive impact of the practical experience of external students on their financial literacy. The author uses an innovative metric in the form of a personal finance index to assess financial literacy. In addition to overall success, this approach also makes it possible to analyze knowledge from the eight components of financial literacy. By comparing the results in individual areas, the author reveals that risk management is Achyla's heel of financial literacy. In addition to the knowledge component, the author also deals with the respondents' access to information sources. Based on these findings, the author formulates conclusions for the content of financial education. There is a need for a stronger link between the development of probabilistic thinking and the development of general numeracy with practical financial subjects. An important part of financial education is also the recognition of credible information sources.

The development of probabilistic thinking among children aged (6-11) years

The development of probabilistic thinking among children aged (6-11) years

GAME INVENTION AS MEANS TO STIMULATE PROBABILISTIC THINKING

In this paper, we make a qualitative analysis of didactic experiments performed with five 6 to 10-year-old children and five primary school teachers, starting from a structured game with probabilistic elements. The fundamental idea is to stimulate probabilistic thinking not only by playing a card game with decision making in uncertain situations, but by inventing games modifying the initial game. These experiments are grounded on the importance of emotions for learning, the subjective probability approach, and researches on problem posing. We have found that this activity of inventing games has a significant impact on the development of probabilistic thinking in children and teachers; it reduces the anxiety and it could be used in teaching strategies to foster statistical and probability literacy. Some of its positive effects are the strengthening of creativity, self-efficacy, self-esteem, the ability to ask questions, and the enjoyment of learning. First published February 2020 at Statistics Education Research Journal Archives

Semiotic Resources in the Development of Early Probabilistic Thinking When Teaching Mathematics as Storytelling

This article deals with the question of the development of probabilistic thinking in young students when teaching mathematics as storytelling. In this study, our research is framed by the theory of learning as an objectification process (Radford, 2008) that is accomplished by the interaction of material and ideational elements such as, mathematical objects, signs, speech, gestures, forms of imagination, action with signs. Results from this study reveal some patterns of probabilistic reasoning used by young students.

Intuitive and Informal Knowledge in Preschoolers’ Development of Probabilistic Thinking

Preschoolers develop a wide range of mathematical informal knowledge and intuitive thinking before they enter formal, goal-oriented education. In their everyday activities young children get engaged with situations that enhance them to develop skills, concepts, strategies, representations, attitudes, constructs and operations concerning a wide range of mathematical notions. Recently there is scientific interest in linking children’s informal and formal knowledge in order to provide them with opportunities to avoid biases aiming at formulating, perceiving, reflecting on and exercising probabilistic notions. The current study investigates preschoolers’ (N=90) intuitive understanding of the likelihood of events in a probabilistic task with spinners. Participants, at the age of 4 to 6, are tested on their predictions of the most probable outcome prior to and after an instructive session of reasoning. The probabilistic task, based on constructivist principles, includes methodological alterations concerning the sample space and the themes of the stimuli. Educational implications are further discussed under the general point of view that in order to link informal to formal mathematical learning in preschool classroom, the subject content and the cognitive capacity of children are important to match.

The relationship between probabilistic thinking and proportional reasoning among the students of secondary stage in Al-Dawaser valley governorate

The purpose of this study is to measure the level of probabilistic thinking and the level of proportional reasoning and identify the relationship between them among students in the first secondary grade in Wadi Al-Dwasir governorate.To achieve this goal, a test consisted of (21) items on probabilistic thinking was conducted. The test focused on three probability concepts: sample space, possibility event, and probability comparisons. Another test on proportional reasoning was conducted. It consisted of (21) items. The test was to address there concepts: proportionality, direct proportion and inverse proportion, and proportional division. The two tests were cheeked for validity and reliability by using appropriate methods.The researcher applied study tools to a sample of (290) students. They were randomly chosen from the first secondary grade in five public schools in Wadi Al-Dwasir governorate, saudi Arabia.The results of the study demonstrated that the level of probabilistic thinking and the level of proportional reasoning for the study population was, educationally, below the acceptance level. Also, there is, statistically, low direct proportional correlation at the significance level of (α = 0.05) for the study population.The study concluded that a considerable attention needs to be paid to the development of probabilistic thinking and proportional reasoning, the understanding of probability concepts, and concepts of proportionality. To this end, modern teaching strategies should be used, and more research to be conducted to discover and identify the factors and other variables that influence the development of probabilistic thinking among student in secondary level.Keywords: probability, probabilistic thinking, proportionality, direct and inverse proportional, proportional reasoning.

Designing probabilistic tasks for kindergartners

Recent research suggests that children could be engaged in probability tasks at an early age and task characteristics seem to play an important role in the way children perceive an activity. To this direction in the present article we investigate the role of some basic characteristics of probabilistic tasks in their design and implementation. In order to do so, we present the structure and the content of a series of tasks that were implemented in a kindergarten school focusing on two characteristics: the context and the materials used. In our case, the performance of the experiment together with the use of dice and spinners seemed to be critical in children's development of probabilistic thinking.

Thinking Science 프로그램의 확률 활동이 중학생의 확률적 사고 형성에 미치는 효과

이 연구의 목적은 중학생의 인지수준과 확률적 사고수준을 측정하여 그 관계를 분석하고 Thinking Science (TS) 프로그램의 확률 활동을 적용하여 그 효과를 분석하는 것이다. 중학교 1학년 219명을 실험집단과 통제집단으로 나누어, 실험집단에는 TS 프로그램의 확률 활동을, 통제집단에는 전통적인 과학 수업을 적용하였다. 결과에 의하면, 중학생의 인지수준은 대부분 구체적 조작기에 해당하였고, 많은 학생들의 확률적 사고수준은 확률 문제 해결에 양적 전략을 사용하면서 주관적 전략도 함께 사용하는 과도기적인 수준이었다. 또한, 인지수준이 높을수록 확률적 사고 수준도 높았으며, 확률의 구성요소 중에서 표본 공간과 한 사건에 대한 확률이 확률 비교와 조건부 확률보다 먼저 발달하였다. TS 프로그램의 확률 활동은 학생들이 확률 문제 해결에 양적 전략을 사용하도록 하는 데에 효과적이었다. 특히 사전에 확률 문제 해결에 주관적 전략과 양적 전략을 혼용하던 중기 구체적 조작기인 학생들이 사후에 양적 전략을 사용하도록 하고, 한 사건에 대한 확률을 인식하도록 하는 데에 효과가 있었다. The purposes of this study were to investigate the correlation between the cognitive level and the probabilistic thinking level and to analyze the effects of the probability activities in Thinking Science (TS) program on the development of probabilistic thinking. The 219 7th grade students were sampled in the middle school and were divided into an experimental group and a control group. The probability activities in TS program were implemented to the experimental group, while only normal curriculum was conducted in the control group. The results of this study showed that most of 7th grade students were in the concrete operational stage and used both subjective and quantitative strategy simultaneously in probability problem solving. It was also found that the higher the cognitive level of the students, the higher the probabilistic thinking level of them. The sample space and the probability of an event in the constructs of probability were first developed as compared to the probability comparisons and the conditional probability. The probability activities encouraged the students to use quantitative strategy in probability problem solving and to recognize probability of an event. Especially, the effectiveness was relatively higher for the students in the mid concrete operational stage than those in any other stage.

Understanding probabilistic thinking: The legacy of Efraim Fischbein

The study and analysis of probabilistic thinking, in particular its development in children, is a key element in our attempts to uncover the workings of the human mind and an essential foundation for the development of effective instruction in concepts central to modern models of scientific and social phenomena. This paper honours the contribution of Efraim Fischbein, who died in July 1998, to these endeavours. The first section summarises Fischbein's early work, culminating in his 1975 book ‘The Intuitive Sources of Probabilistic Thinking in Children’. The second focusses on three major themes prominent in that book, and elaborated in later work by Fischbein and his colleagues, namely: (a) The role of intuition in mathematical and scientific thinking, (b) The development of probabilistic thinking, and (c) The influence of instruction on that development. In the final section, suggestions are made as to how Fischbein's pioneering work can be built upon, in particular for improving the teaching of probability in schools.

Development of Probability Thinking in Children 5 to 12 Years Old

The purpose was to investigate the development of probabilistic thinking as outlined by Piaget and Inhelder, to clarify interrelations of different probabilistic tasks, and to examine the effects of IQ and gender on probabilistic thinking from 5 to 12 years. There were 240 subjects, boys and girls, medium in socio-economic status (SES) and IQ, of two cultural backgrounds, and of three age groups: 5 to 6 years, 8 to 9 years, and 11 to 12 years. Each subject was administered individually the Stanford-Binet and four Piagetian tasks assessing randomization, distribution of multiple discrete elements, odds estimation, and permutations. The responses were evaluated globally and in terms of specific measures. The results showed an increase in probabilistic performance that was mostly larger between the first two groups than the last two, positive interrelations among the tasks, partly different factorial structures in each age group with increasing factorial differentiation, more interrelations of IQ with global than specific measures and more in older than younger children, and more differences in favor of boys in older than younger groups. Discussion focuses on the degree of support for Piaget's claims and implications concerning the structure and development of probabilistic cognition.

The Development of Probabilistic Thinking in Children: A Comparison of Two Methods of Assessment

The Development of Probabilistic Thinking in Children: A Comparison of Two Methods of Assessment