Probabilistic Thinking Research Articles

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

Развитие вероятностного стиля мышления в условиях цифровизации математического образования

The stochastic knowledge, probabilistic style of thinking, the ability to build scientifi cally based forecasts — are becoming extremely popular in the socio-economic changes of modern society. They are of great importance in the natural Sciences and Humanities today. Such sciences as physics, cybernetics, biology, linguistics, chemistry, sociology and many others cannot do without statistical hypotheses, conclusions, forecasts, which in turn aff ects the improvement of the latest scientifi c trends based on the probabilistic and statistical methods of data processing. The article presents an essential characteristic of the development of the probabilistic thinking style of high school students in the study of the stochastic line in the school course of mathematics. The results of an experimental study are presented which help to identify the students’ level of abilities of physical-mathematical and social-humanitarian classes to operate with the concepts of the world of random processes and phenomena. As part of the digitization of mathematical education, the examples of work in the software environment “Mathematical designer” are considered.

فعالية استراتيجيات التفکير المتشعب في تنمية التفکير الاحتمالي لدى تلاميذ المرحلة الإعدادية *

هدف البحث الحالي إلى تحديد فعالية استراتيجيات التفکير المتشعب في تنمية التفکير الاحتمالي لدى تلميذات المرحلة الإعدادية، تکونت عينة البحث من (64)تلميذة من تلميذات الصف الثاني الإعدادي ،موزعين على مجموعتين: تجريبية (32)تلميذة، وضابطة(32)تلميذة، بمدرستين من مدارس إدارة منية النصر التعليمية، وتم تحقيق التکافؤ بينهما من حيث بعض المتغيرات الدخيلة، وأعدت الباحثة اختبارا لقياس التفکير الاحتمالي بالإضافة إلى دليل العلم في ضوء استراتيجيات التفکير المتشعب وکراسة الأنشطة في محتوى الرياضيات، وذلک خلال الفصل الدراسي الأول لعام 2018/2019 م. وتم التوصل إلى النتائج الآتية: يوجد فرق دال إحصائيا عند مستوى دلالة (0.01) بين متوسطي درجات تلميذات المجموعتين التجريبية والضابطة في الاختبار البعدي للتفکير الاحتمالي لصالح تلميذات المجموعة التجريبية. يوجد فرق دال إحصائيا عند مستوى دلالة (0.001) بين متوسطي درجات تلميذات المجموعة التجريبية في التطبيقين البعدي/ القبلي لاختبار التفکير الاحتمالي لصالح التطبيق البعدي. الکلمات المفتاحية: استراتيجيات التفکير المتشعب- التفکير الاحتمالي. The objective of this research is to determine the effectiveness of the neural branching strategies in the development the probabilistic thinking pupils in the preparatory stage,The sample consisted of (64) prep- school students, divided into two groups: experimental group(32) students, and control group( 32) students in two schools of Menia Al-Nasr Educational Administration, and their equivalence was achieved in terms of some variables, The researcher prepared a test to measure probabilistic thinking and guide teacher by the neural branching strategies &work sheets during the first semester of 2018/2019. The results: There is a statistically significant فرق difference ذو عند at مستو ى (the level (0.01) بين between متوسطيthe درجات degrees mean تلميذات the two groups التجريبية experimental و الضابطة and the control في in the post- التطبيقapplication البعدي لاختبار to test القدرة of ability على probabilistic thinking for المجموعة the التجريبية experimental . group students . There is a statistically significant فرق difference ذو عند at مستو ى (the level (0.001) بين between متوسطيthe درجات degrees mean تلميذات the التجريبية experimental groups و الضابطة in the post- التطبيقapplication and pre- application البعدي لاختبار to test القدرة of probabilistic thinking for theالتجريبية post application keywords :The Neural Branching Strategies– Probabilistic Thinking

Probability Distortions, Collectivism, and International Stock Prices

We introduce a novel composite probability distortion (CPD) score based on investors’ stock valuations derived from a pure-probability-weighting version of cumulative prospect theory and from salience theory. This measure is strongly and consistently priced in the cross-section of international stock returns: low-CPD-score stocks are underpriced while those with high scores appear overpriced. Individualism is the main driver of differences in the CPD premium across countries and U.S. states. Consistent with the substantially lesser degree of probabilistic thinking in collectivist cultures documented by the psychology literature, we find that the CPD premium is substantially higher in these than in individualist cultures.

Технология проектирования элективных курсов по математике при подготовке к ЕГЭ с целью развития вероятностного стиля мышления обучающихся

In today’s rapidly changing socio-economic conditions, people often have to face the problems, the solution of which is non-standard. A potentially possible means of the creative problem solving is a probabilistic style of thinking, which implies a departure from stereotypes. It is often connected with a refusal to act according to strictly determined rules, and a deviation of the negative attitude to the randomness of many phenomena and processes of the world. The order is born out of chaos as a result of self-organization. The article proposes a solution to the problem of achieving the quality and productivity of education through the development of schoolchildren’s probabilistic thinking style while training them for the Unifi ed State Examination in mathematics of the profi le level. A substantial component of the elective course “Probabilistic nature of mathematical problems of the Unifi ed State Exam” in mathematics in the system of general education is proposed. A group of tasks is presented which are done with the use of operations: the analysis and synthesis, combination, transposition, evaluation. The actualization of the components of the probabilistic style of thinking is aimed at improving the effi ciency of the learning process, improving the entire holistic system of development and self-development of the student’s personality. The main task of the informative fi lling of the elective course in mathematics in general education is to form a unifi ed scientifi c picture of the world in students, to develop a new culture of thinking, to identify interdisciplinary connections and to combine diff erent activities in the learning process. The reported study was funded by RFBR according to the research project № 18-313-20002 “Theoretical and methodical ensuring the fractal formation and development of the probabilistic style of thinking in the conditions of global informatization of education (on the example of teaching mathematics)”.

Mentoring model based on the levelling of probabilistic thinking to develop problem solving ability

This study aims to describe the probabilistic thinking level of mathematics education students in the topics of sample space, event, and the probability of the event. Many studies have produced different levels of probabilistic thinking, allowing for another new leveling structure of the probabilistic thinking.This study used a qualitative descriptive method involving 112 mathematics education students of Universitas Ahmad Dahlan who took elementary statistics subject in the second semester of 2017/2018 academic year as its subjects. The data analysis was conducted by describing the answers based on the probabilistic thinking leveling indicator.The results of the first stage of this study found a new leveling structure in probabilistic thinking, namely six levels of probabilistic thinking: (1) Level 0 (pre-subjective), with 23 students (20.54%); (2) Level 1 (subjective), with 18 students (16.07%); (3) Level 2 (transition), with 16 students (14.29%); (4) Level 3 (informal quantitative), with 17 students (15.18%); (5) Level 4 (formal quantitative), with 14 students (12.50%); and (6) Level 5 (numerical), with 24 students (21.43%). The second phase of the research will focus on the appropriate mentoring model based on the findings of this first stage research, improve the students’ ability to solve problems, and raise their level of probabilistic thinking to the next levels.

A different way of thinking about seismic risk

Seismic risk has traditionally been approached using probabilistic analysis. This dilutes the potential impact of low probability, extreme events that may lead to severe consequences including excessive land damage, building damage, injuries and death. The communication of risk in probabilistic terms is also not clearly understood by most audiences. Further, it is evident that few building developers, owners and users have a good understanding the implications of this and the capacity design of buildings, which may not be repairable after a severe event.
 There is also an adverse impact on planning and land use, where decisions that may affect many people are based on a limited view of adverse outcomes such as liquefaction, lateral spread and slope stability in severe earthquakes.
 A different way of thinking about seismic risk is proposed. An approach of using scenarios derived from a combination of deterministic as well as probabilistic thinking would prompt consideration of impacts over a range of events. This would allow full consideration of which outcomes are clearly not acceptable and which are. This may facilitate planning for both private and public sector, with a common understanding that is relatively easily communicated to both experts and lay people.
 This risk evaluation framework would also facilitate consideration of mitigation, by bringing focus on unacceptable outcomes of severe events that are currently obscured by pure probabilistic analysis. This was missing in Christchurch, which experienced the sort of event we can readily anticipate and should actively plan for in other parts of New Zealand.
 This would help us avoid future red zones and excessive damage and demolition. It will inform development of building codes and standards and will help us evaluate risk and provide resilience and redundancy across the range of interconnected infrastructure networks.
 Informed debate is needed with key decision makers to discuss the underlying objectives of our regulation and how these may be better met by such an approach, without engineers allowing themselves to be trapped in past thinking and assumptions.

CORRECTIONAL INFLUENCE OF THE SET ON PROBABILISTIC JUDGMENT

Relevant investigations of psychical mechanisms of probabilistic thinking revealed its bounded rationality reflecting of the specific of subjective comprehension of one other problem by the people. Such cognitive activity of the people plays an important role in the assessment of multiple alternatives and serves to satisfaction their different needs. Considering the main exploratory principles of General Set’s Theory, we assume that functioning of probabilistic judgments determined by relevant set formed in the process of purposive activity of the people. Take into consideration of temporary parameter two forms of the set defined: prospective (orientation on the results of future events) and situational (orientation on results of current events). Obtained experimental data showed: prospective set, compared with situational set, made significant corrective influence on erroneous probabilistic judgments. It indicates the importance of clear cognitive fixation by the subjects of instrumental dependence between primary and secondary expected results.

Toward a theoretical structure to characterize early probabilistic thinking

The role of probability in curricula for children has fluctuated greatly over the past several decades. Recently, some countries have removed probability from their preschool and primary curricula, and others have retained it. One reason for such lack of agreement is that theory about early probability learning is still relatively new and under development. The purpose of this report is to sketch a tentative theoretical structure with the potential to anchor curricular decisions and inform further research on early probability learning. Toward that end, we begin by reviewing existing literature. We attend, in particular, to the probabilistic thinking tendencies exhibited by children whom researchers consider to be in the earliest stages of learning the subject. We then use these tendencies to posit two different cycles for early probabilistic thinking. One of these cycles is compatible with disciplinary norms and supports normative thinking; thinking tendencies in this normative compatible cycle include attending to the position of objects in a container, forming images of random generators, attending to the operation of random generators, and thinking about past experiences playing games of chance. Thinking tendencies in the other posited cycle lead to belief systems that conflict with normative disciplinary practice; these belief systems include elements such as myths, superstitions, animism, and determinism. We illustrate the two cycles using empirical data from design-based research. We then reflect on how the two cycles comprising our structure of early probabilistic thinking (SEPT) framework can provide a basis for further curricular and theoretical work.

Investigation of Thai university students’ scientific reasoning abilities

The study aimed to explore scientific reasoning abilities of engineering freshmen in Thailand (N = 680) using 24 multiple-choice questions of Lawson’s Test of Scientific Reasoning (LTSR) and find its relation with high school grade. It was found that male students (N = 442; 73±16%) outperformed female (N = 238; 67±18%) for LTSR scores. Overall, dimension 1 of LTSR about the conservation of mass and volume (80±27%), and dimension 4 about the probabilistic thinking (80±24%) were the highest ability dimensions. In contrast, dimension 6 involving the hypothetical-deductive thinking and reasoning was the lowest ability dimension (50±27%). Moreover, the results revealed no correlation between the LTSR score and high school grade. The findings suggest improving classroom activities which not focus solely on science content knowledge but rather on the scientific reasoning abilities as crucial aspects needed for lifelong learning.

The Effects of Research-Inquiry Based Learning on the Scientific Reasoning Skills of Prospective Science Teachers

The aim of this study is to investigate the effect of research-inquiry-based learning approach on the Scientific Reasoning Skills of Science Education Prospective Teachers in the Nature of Science and Science History Course. The study was designed as a single group pre-test – post - test model. The study group consisted of 31 prospective teachers in the 3rd grade of Science Education program in a public university in the spring term of 2017-2018 academic year. For the scientific reasoning skills of prospective teachers "Scientific Reasoning Skills Test - SRST" was measured as a pre-test, then the Nature of Science and Science History course was conducted with the Research-Inquiry Based Learning Approach and SRST was applied as a final test. This test consists of 7 sub-dimensions and contains a total of 26 items. The findings of the sub-problems of the study can be expressed as follows; a significant difference was found between the SRST pre-test total scores and post-test total scores in favor of the post-test total scores according to the sub-dimensions of proportional thinking, correlative thinking and hypothetical thinking. There was no significant difference in the post-test total scores according to the sub-dimensions of conservation laws, identifying and controlling variables, combinatorial thinking and probabilistic thinking. There was no significant difference between SRST pre-test and post-test total scores of man and woman students. A significant difference was found only in the sub-dimension of combinatorial thinking in the total scores of the sub-dimensions of SRST.

Effects of the activities for five senses using folk games on the considerate behaviors and the probabilistic thinking of Young Children

Effects of the activities for five senses using folk games on the considerate behaviors and the probabilistic thinking of Young Children

THE EFFECTIVENESS OF EVIDENCE-BASED REASONING IN INQUIRY-BASED PHYSICS TEACHING TO INCREASE STUDENTS’ SCIENTIFIC REASONING

Evidence-Based Reasoning (EBR) is a framework of inquiry-based teaching for developing scientific reasoning. This research aims to analyze the effectiveness of EBR in inquiry-based Physics teaching to improve students' scientific reasoning. Applying Slovin formula for sample determination, the research involved 139 upper-secondary school students with similar prior knowledge. This research used one group pre-test post-test design with replication. The effectiveness of teaching on improving scientific reasoning was analyzed by using Paired Sample T-test. ANOVA was used to analyze the consistency of the teaching effectiveness across in test group. The findings indicated that EBR effectively improved students' scientific reasoning in inquiry-based Physics teaching based on two main grounds. On the first, the significance was ensured by N-gain category of scientific reasoning component, which proved (a) control of variables reaching high category, (b) proportional thinking at moderate category; c) probabilistic thinking reaching moderate category, (d) hypothetical-deductive reasoning attaining low category; and (e) correlational thinking achieving low category. In addition, the level of scientific reasoning has attained the experience characterized by slightly imperfect answers. Students voiced positive response to EBR, which stated that it helped them engage in scientific reasoning in Physics learning. They also voiced the general opinion on EBR and inquiry-based learning in general. Keywords: evidence-based reasoning, inquiry teaching, physics teaching, scientific reasoning.

Identify Students’ Scientific Reasoning Ability at Senior High School

This study aims to identify students’ scientific reasoning ability in SMAN 3 Surakarta. The ability of scientific reasoning is an important factor to encourage students’ thinking ability in learning. The method used in this study is a descriptive method with 88 students 11th-grade taken at random. The data of scientific reasoning obtained through written test using the Lawson classroom test of scientific reasoning (LCTSR), instrument test that used consists of 12 items two tier multiple-choice that contains 6 scientific reasoning domain 1) Conservation of Mass and Volume (CMV), 2) Proportional Thinking (PPT), 3) Control of Variables (CV), 4) Probabilistic Thinking (PBT), 5) Correlational Thinking (CT), and 6) Hypothetical-deductive Reasoning (HDR). The domains are used as the basis for grouping students’ scientific reasoning abilities into three levels: concrete reasoning, transitional, and formal reasoning. The results showed that 51.14% of the students were at the level of concrete reasoning, 42,05% at the transitional level, and 6,81% at the formal reasoning level. This can be a reflection of whether the physics learning that has been implemented is able to encourage students’ scientific reasoning ability. The information can be used as a consideration in the selection of appropriate models, methods, and physics learning media.

Прикладні задачі як засіб розвитку ймовірнісного мислення учнів

Прикладні задачі як засіб розвитку ймовірнісного мислення учнів

ANALISIS PENYELESAIAN TUGAS PROBABILITAS SISANALISIS PENYELESAIAN TUGAS PROBABILITAS SISWA SD DITINJAU DARI PERBEDAAN KEMAMPUAN MATEMATIKA DAN GENDER

This study is aimed to analyze probabilistic thinking of elementary school students based on math ability and gender differences. Descriptive explorative approach was used to describe in depth probabilistic thinking of boys with high, middle, low math ability and girls with high, middle, low math ability. The result showed that probabilistic thinking of boy with high math ability indicated multistructural because his thinking quantitative and proportional. While probabilistic thinking of boys with middle, low math ability and girls with high, middle, low math ability indicated unistructural because their thinking quantitative and non proportional. Beside that, boys’ thinking in solving probability tasks was more analytical and flexible than girls’ thinking. So, students with math ability difference, gave difference response in solving probability tasks. This result found new strategy in solving probability comparison task. This result could contribute to curriculum developer to introduce probability in elementary school level and teachers could use discussion method in teaching probability material.

Practical Teaching Strategies for Hypothesis Testing

ABSTRACTTeaching the concept of inferential statistics is one of the most challenging tasks for statistics educators. Often, students cannot make logical connections between inferential statistics and other topics such as descriptive statistics and probability. The source of difficulty may be that inferential statistics is based on complex ideas such as hypothetical reasoning, data analytic methods, and probabilistic thinking. This article presents classroom practices that teachers can easily adapt for their statistics classes to teach fundamental ideas of inferential statistics. The expected educational outcome is the conceptual understanding of the elements of statistical testing rather than learning about a specific testing methodology. Using the proposed practices, students are guided to propose their own hypotheses, collect actual data, and make their own inferences, rather than following a predetermined sequence of procedures. The practice material is divided into three subtasks, so that teachers can plan their curriculum effectively and perform formative assessments regarding students' progress.

Real probability and probabilistic thinking

Real probability and probabilistic thinking

Students’ difficulties in probabilistic problem-solving

There are many errors can be identified when students solving mathematics problems, particularly in solving the probabilistic problem. This present study aims to investigate students’ difficulties in solving the probabilistic problem. It focuses on analyzing and describing students errors during solving the problem. This research used the qualitative method with case study strategy. The subjects in this research involve ten students of 9th grade that were selected by purposive sampling. Data in this research involve students’ probabilistic problem-solving result and recorded interview regarding students’ difficulties in solving the problem. Those data were analyzed descriptively using Miles and Huberman steps. The results show that students have difficulties in solving the probabilistic problem and can be divided into three categories. First difficulties relate to students’ difficulties in understanding the probabilistic problem. Second, students’ difficulties in choosing and using appropriate strategies for solving the problem. Third, students’ difficulties with the computational process in solving the problem. Based on the result seems that students still have difficulties in solving the probabilistic problem. It means that students have not able to use their knowledge and ability for responding probabilistic problem yet. Therefore, it is important for mathematics teachers to plan probabilistic learning which could optimize students probabilistic thinking ability.