Understanding Of Probability Concepts Research Articles

Measuring Students’ Understanding in Probability Concept between Two Different Cohort using Rasch Measurement

The students’ level of proficiency in any particular course is individually distinctive. Therefore, it is necessary for the educators to be able to address their student’s level of ability in understanding of the course they enrolled. Particularly, educators should be able to design a set of questions which suits the level of their students’ ability. For this reason, this study is concentrated on identifying the level of student’s ability in understanding probability concepts that has been included in the statistics course (STA150: Probability and Statistics 1). This course was enrolled by two groups of students (Group A and Group B) from the Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Perak branch. Group A enrolled the course in December 2015 until March 2016 whilst Group B enrolled in June until November 2016 sessions. Since the aims of this study are to investigate the difference in students’ conceptual knowledge and understanding of probability concepts, as well as to examine which concepts were found most difficult by the students, hence the Rasch measurement approach was used to explore those aims. An instrument consists of 20 items in a test based on the “Counting Rule” topic was formed by an experienced lecturer to measure the level of student’s ability between the two groups. Based on the findings, it was found that there is a high reliability index of 0.93 (Group A) and 0.88 (Group B) which suggests the suitability of the instrument developed in this study to be replicated to the other samples, even though, the person student’s responses to the items for both groups appeared differently in terms of their difficulties in understanding the probability concepts which represents the student’s ability on this particular topic.

On visualizing the number comparison scheme in grey extent analysis

PurposeThe purpose of this paper is to illustrate an alternative number comparison process to the original procedure utilized under the grey extent analysis.Design/methodology/approachNumber comparison process is visualized on simple diagrams constructed on a Cartesian coordinate system. Discernable areas to assist related probability calculation were sought according to compliance with desired dominance conditions.FindingsBy visualization, the author was able to obtain exactly the same probability information as those attainable by using the original number comparison process.Research limitations/implicationsReach of this methodology is merely constrained by the limitation of original method where whitenization values of interest uniformly distribute over the domains of related grey numbers.Originality/valueNumber comparison with visualization is easy to comprehend and practice, does not require resorting to probability formulas and an understanding of probability concepts.

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.

Graphing Calculator for Probability Students: How Was It Perceived?

Most students see Mathematics as one of the most challenging and stressful subjects, which if given an option, would rather opt out than undertake it. With low motivation and interest levels, the thought of undertaking a course in Mathematics can be worrying for some. Consequently, teachers are faced with disinterested students, who are passive in class, which makes teaching of the subject even more challenging. At times, with non participative students, Mathematics classrooms appear 'solemn'. Through the years, teachers have been experimenting or 'trying out' various approaches/techniques, in their attempt to develop students' interest and motivation. With the advent of information technology tools, teachers have now attempted to adopt more innovative approaches and incorporate ICT tools into Mathematics classrooms as well. One such tool is the graphing calculator (GC), which is adopted in this study. The incorporation of GCs into Malaysian Mathematics classrooms is at its infant stages. The study examined the students' reactions toward the incorporation of GCs into Probability lessons as well as the subject itself. Findings favor the adoption of GC in learning Probability, particularly in terms of calculator usage, quality of output, understanding of Probability concepts, confidence in solving problems, enhanced communication abilities and positive attitudes towards GC. Recommendations made aimed at assisting educators, policy-makers and researchers in enhancing the quality of the teaching and learning of Probability.

Levels of understanding of probability concepts among secondary school pupils

This paper provides an insight into the levels of understanding of probability concepts of Malaysian secondary school pupils and the relationship among their probabilistic understanding and the independent variables of sex, form and mathematical ability. Information related to the levels of understanding of probability concepts is essential to curriculum design in this branch of mathematics. A study was conducted on a representative sample of 1266 form four and six (lower) pupils from fifteen secondary schools located in the suburban district of Klang, Selangor Darul Ehsan, Malaysia. A probability concepts test was administered and data collected and analysed to obtain factual information regarding the understanding of probability concepts among Malaysian pupils. This paper discusses the performance of pupils on intuitive and taught probabilistic concepts, describes the establishment of a probability concepts hierarchy and considers probabilistic understanding in relation to the independent variables sex, form and mathematical ability. A scale compromising three levels was set up. The results of the distribution of levels showed that generally Malaysian pupils were at Level 2. The study also revealed that boys, form six pupils and pupils with a higher mathematical ability performed better than their counterparts. Finally, several implications for educational practice are suggested.

Push-Penny: What Is Your Expected Score?

Probability is concerned with predicting the results of random phenomena. An understanding of randomness and its consequences is fundamental to the study of probability. Mathematics-education researchers have given considerable attention to the subjective understanding of probability concepts. The literature contains numerous articles that relate this type of research to the teaching of probability and statistics (see Shaughnessy and Bergman [1993] for a review of this literature).

Children's understanding of probability concepts: Some ideas for the classroom

Children's understanding of probability concepts: Some ideas for the classroom

Children's understanding of adverbs denoting degree of likelihood

Two studies were conducted to examine children's understanding of three terms that denote different degrees of likelihood: possibly, probably and definitely. In Study I, children in preschool, and first, third and fourth grade completed a comparison task involving pairs of likelihood terms. Twelve stories were created that described the likelihood that each of two children would participate in an activity, and subjects judged which of the two children actually participated. In Study 2, children in preschool, and first, third and fifth grade evaluated separate statements describing three different children, each of whom was said to have a different estimate of the likelihood that a scary event depicted in a movie would actually occur. Subjects rated how scared each of the three children felt. The results of the two studies revealed that preschoolers showed very little comprehension of the meaning of any of the three words, but by fourth grade the majority of children distinguished among all three terms. Children understood the distinction between definitely and both of the other terms (possibly, probably) better than they understood the distinction between possibly and probably. This finding is consistent with research on the development of children's understanding of probability concepts. Unexpectedly, the distinction between probably and definitely seems to emerge at a younger age than the distinction between possibly and definitely. The findings are discussed in terms of their implications for communicating verbal messages to children.

The teaching of the concepts of statistical tests of hypotheses to non-statisticians

The logic underlying the formulation of statistical tests of hypothesis can be counterintuitive for the non-mathematician, e.g. to test whether two treatments are different, why suppose they are equal? When introducing the topic of hypothesis testing, it is easy to present the formal fiamework for the testing procedure without explaining the logic behind it. In courses for statisticians, one may often (unjustifiably) rely on the understanding of probability concepts as a foundation for understanding statistical inference, but in courses taught to non-statisticians where there is minimal discussion of probability, it is essential that explanations must be based on concepts the students can readily understand. The method proposed here for teaching the concept of hypothesis testing makes an analogy to the judicial system, whereby a person is assumed innocent until sufficient evidence warrants a verdict of guilty. Analogies for the different elements of statistical tests are presented and discussed, together with a classroom fiamework for discussion of statistical tests.