Computer Programming to Support Probability Education: An Empirical Approach (original) (raw)
Related papers
2017
The paper presents a proposal of a teaching practice aimed at higher secondary school students, which intends to enhance discussion on the meaning and interpretation of probability, a topic which is often neglected in Italian schools. The authors are convinced that turning the traditional teaching method upside down-that is, proceeding directly to a problem solving approach with the aid of computers as programming tools-better develops in the students the ability to analyse and address uncertain situations correctly, and consolidates a probabilistic mentality. The chosen method was a phenomenon-inductive approach with the help of simulations, which encouraged the formulation of hypotheses and speculation concerning random phenomena.
Teaching and Learning Probability in an Age of Technology
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...
The graphics calculator and the curriculum: The case of probability
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 ...
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.
Analysing Probability Teaching Practices in Primary Education: What Tasks do Teachers Implement
Mathematics, 2021
This study analyses probability tasks proposed by primary education teachers to promote probabilistic literacy. To this end, eight class sessions at various levels of the Chilean educational system were recorded on video and analysed through the "probability tasks" dimension from the "Observation Instrument for Probability Classes" (IOC-PROB), which includes five components: use of resources, probabilistic contexts, cognitive challenge, procedures and strategies, and probability meanings. The results show that probability tasks focus mainly on technical knowledge, causing the probability class to become an arithmetic class in which only formulas are applied, mechanically and with no meaning. As a result, we see no use of technological resources, a low use of physical materials, and an absolute predominance of solving decontextualised exercises. We conclude that it is necessary to enhance the probability teaching practices based on lesson plans that consider a wide variety of resources and contexts to gradually advance towards a representation of probabilistic knowledge that relies on conventional procedures and notations.
2010
In Quebec secondary schools, the teaching of probabilistic concepts is mandatory, but most teachers feel insufficiently prepared. Furthermore, middle school students are confronted to gambling activities at a young age, without necessarily understanding the underlying probability. In order to analyze the development of a more realistic and mathematically correct understanding of gambling activities, we conducted a one-year design experiment involving 4 high school teachers. We trained the participants in various concepts of probability and accompanied them to prepare classroom situations, which they used in their classrooms. In this paper, we analyze how the participating teachers used a simulation software we provided them. Mainly, the teachers used the software to show that gambling activities do not pay off over the long term. However, it was more difficult for the teachers to discuss probabilistic concepts through the simulation software.
Teaching Elementary Probability: Not Leaving it to Chance
This paper considers the role of content knowledge and pedagogical content knowledge in the teaching of probability to Grade 5 students. Le ssons of two teachers were studied to determine the activities and teaching strategies us ed to bring out ideas associated with chance, and examine how probability understanding is developed in class. The lessons are shown to be rich in deep probabilistic ideas. The c omplex interplay between these concepts was sometimes handled well by the teachers, whereas on other occasions gaps in content and pedagogical content knowledge had the potential to cause misconceptions for students. Since the 1990s much research attention has focused on the pedagogical content knowledge of teachers. At the same time, chance and data have become more significant components of the curriculum, particularly at the p rimary school level. This report takes a closer look at the way two teachers use both conten t and pedagogical content knowledge to help Year 5 students d...
Teaching and Learning of Probability
The Proceedings of the 12th International Congress on Mathematical Education, 2015
Probability has strong roots in the curricula of many countries but is relatively new in others. And although probability has been introduced into the mainstream school mathematics curricula in many countries, research does not necessarily support a rapid inclusion into the curriculum because many problems in teaching and learning probability are still unsolved. For example, should probability be taught to all students? When should students be introduced to probability? What is probability literacy? How is probability literacy developed? What kind of knowledge do teachers need in order to teach probability in more concrete, meaningful and effective ways? How do we facilitate the development of such teaching knowledge? How could investigating students' conceptions of probability from various perspectives further inform our teaching? At ICME 12 in Seoul, Topic Study Group 11 provided a forum for presentations and discussion from an international view about the current state and important new trends in research and practice related to the teaching and learning of probability. Traditionally, the teaching of probability concerns two different interpretations of probability: (1) a classical conception, where probability is based on combinatorics or formal mathematics, and (2) a frequency conception, where probability is
Re-connecting probability and reasoning about data in secondary school teaching
2011
The teaching of probability and of statistics in secondary schools in the UK, as in most countries, takes place rightly or wrongly in mathematics classes. As the mathematics curriculum becomes increasingly influenced by software developments that facilitate a focus on drawing inferences by manipulating and representing data as in Exploratory Data Analysis, probability retreats into an isolated world of coins, dice and spinners. Secondary school students are not being encouraged to see the wider relevance of probabilistic thinking. Very recent software developments promise the re-connection of probability and reasoning about data by offering probability as a modelling tool. Opportunities are now available to review how these developments might redirect the curriculum including the wider and earlier use of probability as a subjective measure of chance. This paper will review some of these possibilities. Int. Statistical Inst.: Proc. 58th World Statistical Congress, 2011, Dublin (Sessi...