Probability has been researched since 1972. What do these researches tell us about the learning and teaching probability? If you want to know more, here are references lists for you to explore about it. Hope it helps.
Bognár, K. and T. Nemetz (1977). "On the Teaching of Probability at Secondary Level." Educational Studies in Mathematics 8(4): 399-404.
Castro, C. S. (1998). "Teaching Probability for Conceptual Change La Enseñanza de la Probabilidad por Cambio Conceptual." Educational Studies in Mathematics 35(3): 233-254.
This work presents a theoretical proposal for a methodology for the teaching of probability theory. The theoretical proposal has a dual inspiration: (1) the epistemological approach of Lakatos (1978b) regarding the quasi-empirical nature of mathematical theories; (2) the perspective of conceptual change for the teaching-learning process, as formulated by Strike and Posner (1992). The scientific content taught and the didactic methods used in the classroom should, according to this proposal, respect and conform to this dual inspiration. We also present an evaluation of the methodology in a real context: six Spanish high school classes of students aged 14-15. The main purpose of the research was to answer this question: Is our didactic proposal more effective than traditional methodology? We operatively identify the concept of traditional teaching, and establish several indicators of effectiveness: the mastery of elementary probability calculations, the quality of intuitive reasoning in probability, and the conceptual and attitudinal change produced. We found significant differences on all indicators, except for attitudinal change, in favour of the group that followed our proposal.
Dooren, W. V., D. D. Bock, et al. (2003). "The Illusion of Linearity: Expanding the Evidence towards Probabilistic Reasoning." Educational Studies in Mathematics 53(2): 113-138.
Previous research has shown that - due to the extensive attention paid to proportional reasoning in mathematics education - many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the 'illusion of linearity'. For example, in geometry it is known that many students believe that if the sides of a figure are doubled, the area is doubled too. In this article, the empirical evidence for this phenomenon is expanded to the domain of probabilistic reasoning. First, we elaborate on the notion of chance and provide some reasons for expecting the overgeneralization of linear models in the domain of probability too. Afterwards, a number of well-known and less-known probabilistic misconceptions are described and analysed, showing that they have one remarkable characteristic in common: they can be interpreted in terms of the improper application of linear relations. Finally, we report on an empirical investigation aimed at identifying the ability of 10th and 12th grade students to compare the probabilities of two binomial chance situations. It appears that before instruction in probability, students have a good capability of comparing two events qualitatively, but at the same time they incorrectly quantify this qualitative insight as if the variables in the problem were linked by a linear relationship. Remarkably, these errors persist after instruction in probability. The potential of this study for improving the teaching and learning of probability, as well as suggestions for further research, are discussed.
Falk, R., R. Falk, et al. (1980). "A Potential for Learning Probability in Young Children." Educational Studies in Mathematics 11(2): 181-204.
Sixty-one children, from 4 to 11 years old, were presented with two sets, each containing blue and yellow elements. Each time, one colour was pointed out as the payoff colour (POC). The child had to choose the set from which he or she would draw at random a POC element in order to be rewarded. The sets were of varying sizes with different proportions of the two colours. The problem was to select the higher of the two probabilities. Three kinds of materials were used: Pairs of urns with blue and yellow beads, pairs of roulettes divided into blue and yellow sectors, and pairs of spinning tops, likewise divided into two colours. Roughly around the age of six, children started to select the greater of the two probabilities systematically. The dominant error was selecting the set with the greater number of POC elements. Verbal concepts of probability and chance were explored and some 'egocentric' thought processes were described. The study indicates that probability concepts could be introduced into school teaching even in the first grades. The deterministic orientation in the instruction for young ages should be attenuated, permitting concepts of uncertainty right from the beginning.
Fischbein, E. and A. Gazit (1984). "Does the Teaching of Probability Improve Probabilistic Intuitions?: An Exploratory Research Study." Educational Studies in Mathematics 15(1): 1-24.
The paper analyzes the effects of a teaching programme in probability devised for junior high school pupils (grades 5, 6 and 7). It was found that most of the notions were too difficult for the fifth grade pupils. In contrast, about 60-70% of the sixth graders and about 80-90% of the seventh graders were able to understand and use correctly most of the concepts contained in the programme. It was also found that, as an indirect effect the course on probability had a beneficial effect on some intuitively based misconceptions of the subjects, like: the "representiveness" effect; the positive recency effect; the notion of "a lucky choice"; the superstitious belief in the possibility of influencing the course of events by some particular behaviour.
Fischbein, E., M. S. Nello, et al. (1991). "Factors Affecting Probabilistic Judgements in Children and Adolescents." Educational Studies in Mathematics 22(6): 523-549.
Six hundred and eighteen pupils, enrolled in elementary and junior-high-school classes (Pisa, Italy) were asked to solve a number of probability problems. The main aim of the investigation has been to obtain a better understanding of the origins and nature of some probabilistic intuitive obstacles. A linguistic factor has been identified: It appears that for many children, the concept of "certain events" is more difficult to comprehend than that of "possible events". It has been found that even adolescents have difficulties in detaching the mathematical structure from the practical embodiment of the stochastic situation. In problems where numbers intervene, the magnitude of the numbers considered has an effect on their probability: bigger numbers are more likely to be obtained than smaller ones. Many children seem to be unable to solve probability questions, because of their inability to consider the rational structure of a hazard situation: "chance" is, by itself, an equalizing factor of probabilities. Positive intuitive capacities have also been identified: some problems referring to compound events are better solved when addressed in a general form than when addressed in a particular way.
Freudenthal, H. (1974). "The Crux of Course Design in Probability." Educational Studies in Mathematics 5(3): 261-277.
Garet, M., S., A. Porter, C., et al. (2001). "What makes professional development effective? Results from a national sample or teachers." American Educational Research Journal 38(4): 915.
Hawkins, A. S. and R. Kapadia (1984). "Children's Conceptions of Probability: A Psychological and Pedagogical Review." Educational Studies in Mathematics 15(4): 349-377.
This paper identifies a number of key questions concerning children's understanding of probability. A selection of psychological and pedagogical research studies is evaluated. Attention is drawn to the various definitions of probability assumed by their authors, indicating the relevance of these to an understanding and synthesis of the reported findings. The possibility of basing relevant classroom practice on subjective rather than theoretical concepts of probability is discussed.
Jones, G. A., C. W. Langrall, et al. (1997). "A Framework for Assessing and Nurturing Young Children's Thinking in Probability." Educational Studies in Mathematics 32(2): 101-125.
Based on a synthesis of the literature and observations of young children over two years, a framework for assessing probabilistic thinking was formulated, refined and validated. The major constructs incorporated in this framework were sample space, probability of an event, probability comparisons, and conditional probability. For each of these constructs, four levels of thinking, which reflected a continuum from subjective to numerical reasoning, were established. At each level, and across all four constructs, learning descriptors were developed and used to generate probability tasks. The framework was validated through data obtained from eight grade three children who served as case studies. The thinking of these children was assessed at three points over a school year and analyzed using the problem tasks in interview settings. The results suggest that although the framework produced a coherent picture of children's thinking in probability, there was 'static' in the system which generated inconsistencies within levels of thinking. These inconsistencies were more pronounced following instruction. The levels of thinking in the framework appear to be in agreement with levels of cognitive functioning postulated by Neo-Piagetian theorists and provide a theoretical foundation for designers of curriculum and assessment programs in elementary school probability. Further studies are needed to investigate whether the framework is appropriate for children from other cultural and linguistic backgrounds.
Kaufman, B. and L. Råde (1973). "Relations and Probability." Educational Studies in Mathematics 5(1): 49-64.
Kazima, M. (2007). "Malawian Students' Meanings for Probability Vocabulary." Educational Studies in Mathematics 64(2): 169-189.
The paper discusses findings of a study that investigated Malawian students' meanings for some probability vocabulary. The study explores the meanings that, prior to instruction, students assign to some words that are commonly used in teaching probability. The aim is to have some insight into the meanings that students bring to the classroom. The sample for the study consisted of 154 students in their first year of secondary school education and whose first language was Chichewa. The paper demonstrates that many of the students' preconceived meanings for probability vocabulary were distant from established conventional probability meanings. In addition, there was a wide range of meanings associated with each of the words. An attempt is made to analyse the students' meanings and to explain their possible sources, some of which are rooted in the students' first language. The paper highlights the importance of having an awareness of students' preconceived meanings, and also stresses the importance of language in learning probability.
Nikiforidou, Z. and J. Pange (2010). "The notions of chance and probabilities in preschoolers." Early Childhood Education Journal 38(4): 305-311.
Chance, randomness and probability constitute statistical notions that are interrelated and characterize the logicomathematical thinking of children. Traditional theories support that probabilistic thinking evolves after the age of 7. However, recent research has underlined that children, as young as 4, may possess and develop basic notions, through mental mechanisms and/or through intuitive processes. In the current study, preschoolers ( N = 200) aged 4–6, participated in two diverse probability tasks related to the likelihood of events and the graphical representation of randomness. The aim of this study was to test whether children, at this young age, have the ability to predict the most probable outcome in a probabilistic game with animal cards and whether they can mark symbols randomly distributed in a 5 × 5 matrix. Preschoolers infered correctly the most likely outcome and showed a minimal understanding of randomness by preferring the uniform rather than random distribution of items. Such findings have both methodological and educational implications for further research as already the notions of chance and probabilities are integrated in Preschool Mathematics Curricula worldwide.
Shaughnessy, J. M. (1977). "Misconceptions of Probabilty: An Experiment with a Small-Group, Activity-Based, Model Building Approach to Introductory Probability at the College Level." Educational Studies in Mathematics 8(3): 295-316.
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