Mathematical language (or the content-specific words in mathematics) has repeatedly shown to be related to mathematical abilities in preschool and in the early grades of primary education. Research in this field has predominantly focused on young children's quantitative and spatial language. At the same time, recent research has discovered that…

Problems teaching probability in Tonga (in the South Pacific) led to the question on how language and culture affect the understanding of probability and uncertainty. The research uses a discursive approach to identify the endorsed narratives which underlie Tongans' reasoning in situations of uncertainty. I aim to justify the claim that the Tongan…

The aim of this study is to explore Israeli high school graduates' mathematical explanations for the spread of the coronavirus, given that the mathematics required to do so was part of their school curriculum. An online questionnaire consisting of two sections provided a variety of potential framings for explaining the phenomenon. The first…

Currently, instruction pays little attention to the development of students' sampling variability reasoning in relation to statistical inference. In this paper, we briefly discuss the especially designed sampling variability learning experiences students aged about 15 engaged in as part of a research project. We examine assessment and…

The purpose of this study is to contribute insights into how collaborative activity can help promote students' mathematical understanding. A group of six high school students (15- to 16-year olds) worked together on a challenging probability task as part of a larger, after-school, longitudinal study on students' development of mathematical ideas…

Presents a theoretical proposal of a methodology for the teaching of probability theory. Discusses the importance of the epistemological approach of Lakatos and the perspective of the conceptual change. Discusses research using a proposed didactic method with Spanish high school students (N=6). Concludes that significant differences on all…

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…

The effects of a teaching program in probability devised for students in grades five to seven were analyzed. Most of the notions were too difficult for fifth graders; 60-70 percent of the sixth graders and 80-90 percent of the seventh graders were able to understand and use correctly most of the concepts. (MNS)

Presents two case studies of learners attempting to understand the concept of normal distribution, specifically why physical phenomena such as height fall into normal distributions. Draws conclusions about a Connected Mathematics learning environment that enables confrontation with epistemological anxiety and the features of modeling languages…

Presents a framework for assessing probabilistic thinking based on validated data obtained from eight third grade children who served as case studies. Major constructs were sample space, probability of an event, probability comparisons, and conditional probability. Levels of thinking appear to agree with the levels of cognitive functioning…

Describes a study to determine middle school children's representational strategies to form part-whole or part-part relationships for relational numbers such as proportions, ratios, or fractions. Quantitative and qualitative analysis revealed that children prefer a part-part representation to solve relational quantity problems. (15 references)…

Reviews research indicating that students' cognitive models hold random events to be equiprobable Examined 87 students between the ages of 15 and 17 to determine whether masking a random event using geometric figures would affect the students' view of the event as equiprobable. Results indicated that masking overcame the equiprobable bias of the…

An attempt is made to elaborate on the connections and differences between the objective and subjective elements of mathematical knowledge using case study analysis relative to how an epistemological perspective about probability and randomness impacts upon a short classroom teaching episode. (19 references) (Author/JJK)

To investigate the origins and nature of intuitive obstacles affecting the learning of elementary probability theory, 618 Italian elementary and middle school students were interviewed about their methods of solution for several problems dealing with probability. The discussion focuses on four varieties of obstacles to learning prevalent within…