Concerns about the influence of misconceptions, culture and social setting on probabilistic reasoning of teacher trainees led to a study in this area to explore the reasoning of preservice teachers from a college of education in Ghana. This study investigates preservice teachers' misconceptions and difficulties in probabilistic problems solving…

Assessing students' conceptions related to independence of events and determining probabilities from a sample space has been the focus of research in probability education for over 40 years. While we know a lot from past studies about predictable ways students may reason with well-known tasks, developing a diagnostic assessment that can be used by…

Students studying statistics often misunderstand what statistics represent. Some of the most well-known misunderstandings of statistics revolve around null hypothesis significance testing. One pervasive misunderstanding is that the calculated p-value represents the probability that the null hypothesis is true, and that if p < 0.05, there is…

Several studies revealed that probability misconceptions were widespread among students, but the activities for addressing the misconceptions has been lacking. This study designed activities that reflect real life situations for addressing equiprobability bias, positive and negative recency effects, belief bias and representativeness bias for…

In the author's experience with this activity, students struggle with the idea of representativeness in probability. Therefore, this student misconception is part of the classroom discussion about the activities in this lesson. Representativeness is related to the (incorrect) idea that outcomes that seem more random are more likely to happen. This…

This paper is based on research that investigated the development of probabilistic language and thinking by students 10-12 years old. The focus was on the adequate use of probabilistic terms in social practice. A series of tasks was developed for the investigation and completed by the students working in groups. The discussions were video recorded…

Mike Shaughnessy is Professor Emeritus of Mathematics and Statistics at Portland State University in Oregon. He served as co-chair for the Board for the Special Interest Group for Research in Mathematics Education of the American Educational Research Association from 2005-2007. A member of the Board of Directors of the National Council of Teachers…

Probability is receiving increased coverage in all levels of education. Knowledge of the Law of Large Numbers may be an important factor in developing a true understanding of the subject. Study results evidence a lack of awareness of this fundamental principle among teachers of mathematics. Study results also suggest that additional probability…

In three studies we looked at two typical misconceptions of probability: the representativeness heuristic, and the equiprobability bias. The literature on statistics education predicts that some typical errors and biases (e.g., the equiprobability bias) increase with education, whereas others decrease. This is in contrast with reasoning theorists'…

Using a new method of data analysis (statistical implication) and a method of postcorrelative treatment reveals students' preconceptions in conditional probability stemming from concrete references and makes explicit the procedures of problem solving that reflect these conceptions. (24 references) (Author/MKR)

Reports on a study in which anchoring probability situations that are conceptually analogous to misconception-prone target probability situations were generated and tested with secondary mathematics students. Reports that a follow up test showed that 65% of the reconstructed knowledge was retained after six months. (Author/MM)

Discusses students' preconceptions of randomness and offers an alternative way to think about the concept using the idea of complexity. That is, the randomness of a sequence can be measured by the difficulty of encoding it. Methods of judging complexity and implications for teaching are discussed. (Contains 30 references.) (MKR)

A sample of 134 sixth-grade students who were using the Connected Mathematics curriculum were administered an open-ended item entitled, Vet Club (Balanced Assessment, 2000). This paper explores the role of misconceptions and naive conceptions in the acquisition of statistical thinking for middle grades students. Students exhibited misconceptions…

Previous research has shown that--due to the extensive attention spent 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…

Presents research findings related to students' intuitive ideas about the concepts of chance to inform teachers how students form their concepts of probability and statistics. Discusses adolescents' conceptions of uncertainty, judgmental heuristics in making estimates of event likelihood, the conjunction fallacy, the outcome approach, attempts to…