Coordination of theoretical probability and relative frequency estimates is challenging in probability teaching and learning. Modeling is one of the ways of teaching and learning that facilitates inquiry between these two perspectives. Given that, we designed a modeling activity to support fifteen secondary students in investigating theoretical…

The multi-faceted nature of mathematics knowledge for teaching, including pedagogical content knowledge (PCK), has been studied widely in elementary classrooms, but little research has focused on senior secondary mathematics teaching. This study utilised the Knowledge Quartet (Rowland et al., "Research in Mathematics Education," 17(2),…

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…

This study reports the results of a study examining how easily students are able to transfer frequency solutions to conditional probability problems to novel situations. University students studied either a problem solved using the traditional Bayes formula format or using a natural frequency (tree diagram) format. In addition, the example problem…

This article is a systematic reflection on a sequence of episodes related to teaching probability. Our central claim is that reducing problems to a consideration of the sample space, which consists of equiprobable outcomes, may not be in accord with learners' initial ways of reasoning. We suggest a "desirable pedagogical approach" in which the…

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…

We present a view of knowledge construction processes, focusing on partially correct constructs. Motivated by unexpected and seemingly inconsistent quantitative data based on the written reports of students working on an elementary probability task, we analyze in detail the knowledge construction processes of a representative student. We show how…

The study focused on the interaction between two secondary school students while they were working on computerized mathematical investigation tasks related to probability theory. The aim was to establish how such interaction helped the students to learn from one another, and how it may have hindered their learning process. The assumption was that…

The purpose of this study is to investigate the ways in which Swedish seventh grade students (12 and 13 years old) handle chance encounters. Four groups of students working in pairs participated in the study. In the group discussions, which were tape-recorded and fully transcribed, the students were encouraged to explore strategies for winning a…

Identifies key questions concerning children's intuitions and conceptions of probabilistic notions. Research on the theoretical framework for probability studies, misconceptions and strategies, and pupil attainment is reviewed, and the methodology is evaluated. Finally, implications for classroom practice are discussed. (MNS)

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…

Features and tools to outline and shape the long-term learning process for ratio are presented, with examples. Ratio-anticipating activity and creating visual models and schemes are stressed, with the basis for a theory of teaching and learning ratio presented. (MNS)

This study, conducted with children 4 to 11 years old, indicates that probability concepts could be introduced early in the elementary grades. (MK)

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)