From Static to Dynamic Representations of Probability Concepts

International Journal of Information and Communication Technologies in Education, 2019

The probability is exceptional in the teaching of mathematics because students often have difficulties to understand the basic terms and the problem solving strategies. Understanding lacks of the probability concept and various types of misconceptions arise from the misleading intuition and misinterpretations of experience with the stochastic phenomena. The probability concept seems too abstract to some students therefore it is advisable to use mathematical problems based on real-life ideas, such as drug efficacy testing, tests for diagnosing of diseases in medicine, sports competitions, and games. By eliminating misconceptions and improving understanding of the problem solving strategies, it is possible to use various types of visualization to solve problems from this field of mathematics. Tables and different types of graphic diagrams can help students to understand the basic rules and problem solving techniques. This paper describes the main objectives and the structure of an int...

Eurasia Journal of Mathematics, Science and Technology Education

The importance of visual representations in education and mathematics is well known. Probabilities are a domain in mathematics that uses many visual representations since their theory consists of a variety of diagrams and graphs. In the past, many studies have shown that the use of various representations in teaching probabilities can greatly improve learning. Of course, the use of a visual representation or a visual tool when teaching or solving an exercise can have a variety of roles. The present work is based on the ancillary and informative role of the image. The following research examines the extent to which students, by solving a probability problem, have the need to use a visual representation or image. Additionally, the differences in student performance are investigated, given the role of the image in the activity. This knowledge can improve the teaching methods of probabilities and, with their appropriate use, school textbooks. The results show that there are more perspec...

Australian Mathematics Teacher, 2004

From experience, we know there are several difficulties to convey different concepts in statistics and probability as well as being assimilated by the learner. Looking to contribute in the solution of this problem, a technology development, named CalEst, has been accomplished. It aims to provide a set of tools with an educational approach to assist the teaching/learning process. This development generates information in a visually-attractive manner, improving enormously the understanding of the concepts and motivating the learning of statistics and probability. Probability notions play a crucial role in the analysis and interpretation of statistical data. Accordingly, this project incorporates several animations to illustrate and experiment several probability concepts. Furthermore, CalEst assists in an animated approach to calculate probabilities; hence illustrating the concepts of density and cumulative distribution functions for a diverse number of distributions. Other concepts a...

this paper is to explore some of the relationships between probability and the graphics calculator, in order to provide a more extensive justification of these sorts of claims. The history of probability in the school curriculum is relatively short, and generally unfortunate. In most states, aspects of probability have only appeared in the last generation, unlike, say, algebra, geometry, trigonometry and calculus, which have been taught in schools for several generations now. Until quite recently, much of the work has been excessively formal, with a focus in the senior school on the use of an algebra of probabilities. Research, anecdotal evidence and the observations of both teachers and public examiners have generally suggested that students find the formal study of probability rather difficult, and insightful learning seems to be rare. While a formal approach is ultimately essential in the undergraduate years, it is more questionable at the school level, particularly in the lower ...

2016

This thesis is a summary of a pilot study adopting the design experiment methodology investigating alternative approaches to the teaching of probability – the classical approach (called “Laplace approach” in our study) and the axiomatic approach (called “Properties approach”) – and alternative pedagogical treatments of these approaches: with or without explicit refutations of common misconceptions by the teacher. Four short video-lessons were designed, focused on Bernoulli trials: “Laplace-exposition”; “Laplace-refutation”; “Properties-exposition” and “Properties-refutation “. The primary misconception addressed in the study was the erroneous application of proportionality models: the misconception called “illusion of linearity” in the context of probability. The design and layout of the videos’ visuals and audio were informed by the principles of cognitive load theory in multimedia to ensure optimal learning potential. Each lesson was tried with one volunteer participant, a post-co...

Modern classrooms have access to a range of potential technologies, ranging from calculators to computers to the Internet. This paper explores some of the potential for such technologies to affect the curriculum and teaching of probability in the secondary school and early undergraduate years, rather than relying on the classical and formal approaches focusing on set theory and counting techniques. Different approaches to probability, including the study of risk, are identified. We describe some of the ways in which the teaching of probability might be supported by the availability of various forms of technology, including calculators, computer software and the Internet. We consider especially the role of simulation as a tool for both teachers and students, focusing on activities that are not possible without the use of technology. Modern technology provides an excellent means of exploring many of the concepts associated with probability. Many of these opportunities for learning wer...

This classroom note illustrates how dynamic visualization can be used to teach conditional probability and Bayes' theorem. There are two features of the visualization that make it an ideal pedagogical tool in probability instruction. The first feature is the use of area-proportional Venn diagrams that, along with showing qualitative relationships, describe the quantitative relationship between two sets. The second feature is the slider and animation component of dynamic geometry software enabling students to observe how the change in the base rate of an event influences conditional probability. A hypothetical instructional sequence using a well-known breast cancer example is described. (Contains 3 figures.)

This study examined the problem-solving behavior of four students from an urban, middle school as they used computer simulation software to solve probability tasks, by generating and interpreting computer data and representations to make decisions about fairness and adequacy of sample size. The questions that guided the study were: (1) How are data generated by the students from computer simulations interpreted with respect to (a) fairness and (b) significance of sample size? (2) What decisions about fairness and adequacy of sample size do students make on the basis of evidence that they collect? and (3) How are student ideas influenced, if at all, by their computer-generated representations and others? The students were video-taped during five sessions which occurred on two days of a summer institute, a component of the Informal Mathematical Learning (IML) Project at Rutgers University. Data consisted of discussions between and among students as they worked in pairs on the task, conversations between students and researchers, screen-shots of computer representations that students selected and discussed, and students' written work recorded on CDs. These were analyzed using the Powell, Francisco & Maher v (2003) model for investigating the development of mathematical knowledge using video data.

Advances in Mathematics Education, 2014