Probability Theory Course Research Articles

Problem-based learning for improving problem-solving and critical thinking skills: A case on probability theory course

Problem-based learning (PBL) has been widely applied as an alternative to improve learning outcomes, but it is still little studied in the context of the probability theory course. This study described how implementing the PBL model improves students’ problem-solving and critical thinking skills in probability theory course and evaluates its quality. This design research involved 58 undergraduate students and two probability theory course lecturers from two universities in Indonesia as participants. Data collection used observation to describe PBL implementation, then questionnaire and pretest-posttest to evaluate the quality of the model. This study produced a PBL model for the probability theory course which is implemented through five steps: i) Orienting students on problems; ii) Organizing students to study; iii) Assisting individual and group investigations; iv) Developing and presenting work or solutions; and v) Analyzing and evaluating problem solving processes. Lecturers and students consider that the implementation of PBL is practical. PBL implementation can also improve students’ problem-solving skills and critical thinking in the probability theory course. Thus, implementing PBL can be used as a solution to optimize learning outcomes in the probability theory course.

KEMAMPUAN REPRESENTASI MATEMATIS CALON GURU MATEMATIKA PADA MATA KULIAH TEORI PELUANG

In understanding mathematics learning, representation is considered an entry point in solving various complex mathematical problems. The ability of mathematical representation is related to the expression of mathematical ideas using various ways, including written language, spoken language, pictures, symbols, examples, diagrams, graphs, or other real examples as representations. The research design used is mixed research (Mixed Method). The subjects in this study were 17 prospective mathematics teacher students, but then 3 (three) people were selected as subjects to be interviewed. Consists of subjects with high category (S1), subjects with medium category (S2), and subjects with low category (S3). Data collection was carried out using test instruments in the form of description questions in the probability theory course. From the test results, after being examined, students were selected to represent each category. Furthermore, by using the results of student tests, interviews were conducted to compare the results of interviews with student answers. The results of the written test and the results of the interview test were then analyzed to determine the student's representational ability. The results of this study indicate that students' mathematical representation skills in the probability theory course are still relatively low, this can be seen in 3 (three) subjects after matching the results of the written test and the results of the interview test. Individuals with high categories can meet the indicators of expression representation or mathematical equations and verbal representations. Subjects in the medium category were able to fulfill the indicators of mathematical representation or expression. Low subjects were not able to fulfill one of the three indicators of mathematical representation ability

A Fresh Shot at Statistics in the Classroom: Three Perspectives Using World Cup Soccer Player Data

In this article, we outline several activities revolving around soccer players who participated in the 2018 FIFA World Cup and 2019 FIFA Women’s World Cup. Classroom activities are described from different perspectives, useful for a range of different statistics courses. In a first semester probability theory course, students investigate the counter-intuitive birthday paradox empirically and theoretically. For an introductory data science course, students practice their data wrangling skills using the statistical software R. Additional activities are shared for those instructors interested in emphasizing multivariable thinking in a second semester applied statistical modeling course. The activities shared will provide a range of opportunities for instructors to incorporate the FIFA World Cup data in their own courses. Supplementary files for this article are available online.

Students Abstract Thinking Abilities in terms of Mathematical Disposition

This research aims to describe students abstract thinking abilities in the probability theory course in terms of mathematical disposition. The research method used is descriptive research with a qualitative approach. The research subjects were 5th-semester students who took probability theory courses. Determination of subjects using purposive sampling techniques. Instruments used include test results of mathematical abstract thinking abilities, disposition questionnaires, interview guidelines, and researchers as the key instruments. Analysis data using the Miles model and Huberman includes data reduction, display data and conclusion drawing/verification. The research results are, Subject 1 (S1) is in the high mathematical disposition category, fulfills three indicators of abstract thinking abilities, namely transforming problems into symbols, manipulation process of abstract mathematical objects, and the formation of mathematical concepts related to other concepts. Subject 2 (S2) is in the medium mathematical disposition category, fulfilling two indicators of abstract thinking abilities, namely transforming problems into symbols and the manipulation process of abstract mathematical objects, the formation of mathematical concepts related to other concepts. Subject 3 (S3) is in the low mathematical disposition category, it only fulfills one indicator of the abstract thinking abilities, namely transforming problems into symbols.

КОМП’ЮТЕРНА ПІДТРИМКА ВИВЧЕННЯ ТЕМИ “КОРЕЛЯЦІЙНИЙ ЗВ'ЯЗОК, КОЕФІЦІЄНТ КОРЕЛЯЦІЇ” КУРСУ ТЕОРІЇ ЙМОВІРНОСТЕЙ ІЗ ЕЛЕМЕНТАМИ МАТЕМАТИЧНОЇ СТАТИСТИКИ

The article investigates the problem of developing the components of an effective computer-oriented methodological system for teaching the discipline "Probability theory with elements of mathematical statistics", which is provided for in the curriculum for training future mathematics teachers at a pedagogical university. The article contains methodological and procedural aspects of the organization of calculations in the process of establishing a correlation between the values of the features of a sample of the general totality in the mathematical software Mathcad. A detailed example of solving the problem of determining the correlation between the values of the features of a sample of the general totality, determining the sample correlation coefficient and its standard deviation, equations of direct regressions is given. The basics of the concepts of the correlation between the values of the features of the sample of the general totality, the sample correlation coefficient, the standard deviation of the sample correlation coefficient and the equation of direct regressions are briefly given. A brief review of educational, methodological and scientific literature used in teaching probability theory with elements of mathematical statistics is carried out, the expediency of using mathematical software environments when working with the content of this discipline and the development of test tasks of different levels of complexity in probability theory with elements of mathematical statistics for the purpose of objective assessment is substantiated knowledge of students. The article contains software implementations of the algorithm for establishing a correlation between the values of the features of a sample of the general totality in the software mathematical environment Mathcad, finding the sample correlation coefficient and its standard deviation, direct regression equations, as well as conclusions and directions for further scientific and pedagogical research in the field of implementation of computational methods of mathematical statistics for finding statistical estimates of a sample of values of random variables. The methodological and algorithmic materials presented in the article can be useful for students to organize and activate independent scientific and pedagogical activities, teachers of secondary educational institutions, leaders of optional and circle work of students, teachers of the probability theory course with elements of mathematical statistics of pedagogical higher educational institutions. Key words: correlation, sample correlation coefficient, standard deviation of the sample correlation coefficient, statistical sample, general totality, probability theory, mathematical statistics.

МЕТОДИЧЕСКИЕ АСПЕКТЫ ПОДГОТОВКИ СТУДЕНТОВ ПЕДАГОГИЧЕСКИХ НАПРАВЛЕНИЙ ПО ОСНОВНЫМ РАЗДЕЛАМ ТЕОРИИ ВЕРОЯТНОСТЕЙ

The article deals with the problem of formation of knowledge, skills and abilities of students-mathematicians, necessary for preparation for teaching probabilistic and statistical direction in the course of school mathematics. The study is conducted by reviewing and highlighting the characteristics of tasks included in the list of mandatory tasks at school. An example of the implementation of this task is the preparation of a mandatory list of various probabilistic problems necessary for the training of future mathematics teachers. Special attention is paid to the tasks included in the unified state exam. As a result, it was proposed to systematize the knowledge of the probability theory course according to a certain plan necessary for successful completion of pedagogical practice and teaching this course at school.

Forming a conceptual understanding of mathematics at students of technical universities

The global challenges that humanity is facing today pose the task of higher education to prepare a specialist with fundamental training and the ability to learn throughout life. Fundamentalization of education is not possible without the formation of students' conceptual understanding of the material studied. This problem is quite relevant in the study of mathematics due to the specific nature of this science. The researchers' lack of a unified point of view in determining the essence of the conceptual understanding of mathematics does not allow practitioners to develop tools for assessing the level of conceptual understanding among university students. The purpose the article is to identify and formulate the essential characteristics and pedagogical conditions for the formation of a conceptual understanding of mathematics, as well as to explore the possibilities and effectiveness of the integration of computer modeling as an instrument of forming a conceptual understanding in the process of teaching probability theory to students of technical universities. The study showed that a computer workshop, developed based on identified pedagogical conditions and taking into account the didactic capabilities of ICT in the educational process, is an effective means of developing conceptual understanding when studying a course in probability theory. Students whose curriculum included a workshop with elements of computer modeling have a more excellent knowledge of methodologically significant knowledge and the ability to relate previously learned material to new problems.

Analysis of Equilibrium Pre-service Teacher Trough Valsiner Zone Learning

This study aims to thoroughly investigate how the equilibrium of pre-service teacher in the probability theory course through learning based on Valsiner theory. The method used is descriptive qualitative by taking as many as one experimental class as a sample to be traced. It was concluded that through observations and short interviews it could be shown that in the first and second meetings, students were still experiencing cognitive conflict so that there was no equilibirium in students. then at the third, fourth meeting and the next meeting students have shown a positive response so that a balance or equilibrium can be seen from each student representative’s response through the given teaching material and also through inter-group discussions between groups so that there is uniformity of knowledge and no longer heterogeneous

Improving Mathematical Beliefs of Pre-service Teacher Trough Valsiner Zone Learning

This study aims to comprehensively analyze the increase in mathematical beliefs of pre-service teacher of mathematics education at Siliwangi Tasikmalaya University through learning based on the Valsiner Zone in total and based on Mathematical Preliminary Ability (MPA). The method used in this research is quasi experiment, with research population that is pre-service teacher of mathematics education at Siliwangi University of Tasikmalaya and the sample is student who follow course of probability theory in semester V consisting of one experiment class with amount of 42 people and one control class which amounted to 40 people in the Mathematics Education Study Program. Random sampling by class. Data collection techniques are questionnaires of mathematical belief scale. Descriptive analysis there is an improvement of mathematical belief of student in probability theory course, both at theory valsiner class and control class. Further improvement in student mathematical belief with theory valsiner class modeling was higher than that of control class, from the average gain of normalized students in upper, middle and lower MPA categories in the experimental group compared with the mean of normalized student gain in upper, middle and lower MPA categories with the control group although both groups were in the moderate category.

Increasing Creative and Innovative Thinking Ability through The Strengthening of Character Education in Probability Theory Course

The purpose of this study was how to improve the ability to think creatively and innovatively through strengthening character education in the probability theory course. The sample of this study was 29 students of the fifth-semester of Mathematics Education. The method of research experimented, and the form of analysis is quasi-experimental. Data collection techniques are measurement techniques, creative and innovative thinking skills test and character education scale. The results increase in the ability of creative and innovative thinking through strengthening character education by providing learning in religious character education, being responsible both in groups and individually, discipline, honesty, tolerance for others, hard work, independence, having a high sense of curiosity in solving a problem related to Probability Theory.

Several Attempts on Probability Theory Courses Under Trinity Mode

Guiding forward to "Trinity Model" of education, to mould value, to foster ability and to transfer knowledge, for Tsinghua students, a few attempts have been tried on an important series of probability theory course including Probability Theory, Mathematical Statistics and Random Processes. These attempts are that the value shape and vitality stimulate learning interest; accurate concepts promote the level of imparting knowledge and cognizing knowledge; closing to practical problems leads to important probability distribution and enhances ability to solve practical problems; inserting some problems being researched to extend the ability to solve practical problems and to innovate in approaching scientific research; some strengthening links to further enhance and develop such ability.

If at First You Don’t Succeed, Try, Try Again

Previous research has considered sequential item response theory (SIRT) models for circumstances where examinees are allowed at least one opportunity to correctly answer questions. Research suggests that employing answer-until-correct assessment frameworks with partial feedback can promote student learning and improve score precision. This article describes SIRT models for cases when test takers are allowed a finite number of repeated attempts on items. An overview of SIRT models is provided and the Rasch SIRT is discussed as a special case. Three applications are presented using assessment data from a calculus-based probability theory course. The first application estimates a Rasch SIRT model using marginal maximum likelihood and Markov chain Monte Carlo procedures and students with higher latent variable scores tend to have more knowledge and are better able to retrieve that knowledge in fewer attempts. The second application uses R to estimate growth-curve SIRT models that account for individual differences in content knowledge and recovery/retrieval rates. The third application is a multidimensional SIRT model that estimates an attempt-specific latent proficiency variable. The implications of SIRT models and answer-until-correct assessment frameworks are discussed for researchers, psychometricians, and test developers.

Boris Vladimirovich Gnedenko: a classical scholar in probability, statistics, queueing, and reliability

BorisVladimirovichGnedenko (1912–1995) (Fig. 1).was a famousRussian/Ukrainian scientist in the field of asymptotical methods of probability theory and statistics, and also numerous applied sciences, especially queueing and reliability theory. He wrote many monographs and textbooks; the most well known of them are “Limit Theorems for Sums of Independent Random Variables” (together with A.N. Kolmogorov) and a textbook “A Course in Probability Theory.” For many years, Gnedenko was the Head of the Probability Chair at the Moscow State University. For 15years, from 1945–1960, Gnedenko worked in Ukraine (Lvov, Kyiv). He was a member of the Academy of Sciences of Ukraine, a founder of probability schools in Ukraine and Eastern Germany, and one of the best-known experts in queueing theory and reliability theory. B.V. Gnedenko was a member of the Royal Statistical Society (United Kingdom) and Honored Doctor of Humboldt Berlin University and the University of Athens.

A basic course in probability theory

A basic course in probability theory

Chance and probability: What do they mean to university engineering students?

The great interest aroused by the incorporation of Statistics and Probability into curricular projects has been accompanied by considerable evidence of significant difficulties in the meaningful learning and application of the concepts. These difficulties have been the subject of many studies, mostly concerning secondary school students. This study seeks to investigate the level of understanding of random phenomena, in a group of university students, on the second year of a Technical and Industrial Engineering Degree at the University of the Basque Country, in Spain. The students, who had all undertaken an introductory course in Probability Theory, were tested through both written questionnaires and one-to-one interviews, where they were presented with situations that demanded the ability to apply the knowledge they had learnt, at a high level, to a range of situations and to justify their reasoning. The results show that the vast majority of students had a poor understanding of random phenomena, applying alternative ideas to the ones taught on their course in Probability. The need to improve teaching strategies in Probability and Statistics, so that students can develop skills in constructing probabilistic models, is highlighted.

A Course in Probability Theory

A Course in Probability Theory

A course in probability theory (2nd edition), by Kai Lai Chung. Pp xii, 365. £7·20. 1974. SBN 012174650 X (Academic Press)

A course in probability theory (2nd edition), by Kai Lai Chung. Pp xii, 365. £7·20. 1974. SBN 012174650 X (Academic Press)

Design and tests of computer-furthered instruction

This paper discusses the philosophy of computer-furthered instruction (CFI), the design of a particular CFI system used in the required undergraduate course in probability theory and statistics taught in the School of Business at the University of Kansas, and performance and process tests of the effects of introducing the CFI system. The purpose of CFI systems is not to replace traditional methods used in teaching (i.e. lectures, discussions, reading assignments, homework exercises, etc.) but rather to take advantage of some of the unique attributes of real time computing to allow the students to see and perform assignments otherwise impossible. After contrasting CFI and CAI systems, we discuss the course in its standard format, the traditional problems usually encountered in teaching this course, and the package of programs used. Some sample CFI conversations are included. Statistical tests of performance and process changes induced by the CFI system are presented; their significance and implications are examined.

CHUNG, K. L.: A course in probability theory. Harcourt & Brace, New York 1968. VIII, 331 S.

Biometrische ZeitschriftVolume 15, Issue 5 p. 367-368 Buchbespreehungen CHUNG, K. L.: A course in probability theory. Harcourt & Brace, New York 1968. VIII, 331 S. H. Ahrens, H. AhrensSearch for more papers by this author H. Ahrens, H. AhrensSearch for more papers by this author First published: 1973 https://doi.org/10.1002/bimj.19730150517AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume15, Issue51973Pages 367-368 RelatedInformation

A Course in Probability Theory. By K. L. Chung. Pp. vii, 331. £6·20. 1968. (Harcourt, Brace and World.) - Introduction to Probability and Statistics. By M. Goldman. Pp. xv, 546. £5·50. 1970. (Harcourt, Brace and World.) - Probability and Statistical Inference. By R. G. Krutchkoff. Pp. xiv, 306. £5·25. 1970. (Gordon and Breach.)

A Course in Probability Theory. By K. L. Chung. Pp. vii, 331. £6·20. 1968. (Harcourt, Brace and World.) - Introduction to Probability and Statistics. By M. Goldman. Pp. xv, 546. £5·50. 1970. (Harcourt, Brace and World.) - Probability and Statistical Inference. By R. G. Krutchkoff. Pp. xiv, 306. £5·25. 1970. (Gordon and Breach.)