Journal Article

  • 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 and complemented by the students’ written notes. The analysis was carried out under a historical-cultural perspective. We have identified how some notions about frequency, chances, possibility and probability are intuitive and how others are mistaken. Subjectivist probabilistic thinking is present in students’ ideas, and this indicates the need to develop teaching approaches that confront and overcome these ideas.

  • The inclusion of statistics and probability in the mathematics curriculum has always generated challenges to mathematics teachers of elementary schools. This article discusses activities that promote the professional development of such teachers. We present part of a doctoral research study of 16 teachers in which we discuss two case studies of teachers who planned teaching activities focusing on probabilistic simulations. Results demonstrated that the joint elaboration and discussion, within an educational space marked by collaboration, afforded teachers greater security when addressing the subject, and allowed them to develop new knowledge and ideas on teaching and learning statistics and probability. However, diverse pedagogical beliefs could drive different teachers’ attitudes in classes and influence their focus while implementing their practices.

  • Information on the HIV/AIDS epidemic in Southern Africa is often interpreted through a veil of secrecy and shame and, I argue, with flawed understanding of basic statistics. This research determined the levels of statistical literacy evident in 316 future Mathematical Literacy teachers’ explanations of the median in the context of HIV/AIDS survival times. Drawing on the three-tiered statistical literacy hierarchy proposed by Watson (1998, 2006) and the SOLO taxonomy (Biggs & Collis, 1982), a categorization framework was constructed. About half the teachers were classified below the level of basic understanding of the median. Misunderstandings included confusion of the median survival time with the maximum survival time, and a failure to consider the spread of the data along with the centre.

  • This paper presents discussions on stochastic education in early childhood, based on two doctoral research projects carried out with groups of preschool teachers from public schools in the Brazilian cities of Suzano and São Paulo who were participating in a continuing education program. The objective is to reflect on the analysis of two didactic situations related to the learning of statistics in mathematics classes. The results show evidence of the mathematics learning of the teachers who teach mathematics in early childhood. They also highlight the mathematical and statistical relations that children are able to establish when carrying out stochastic activities included in their childhood context.

  • This study is an exploration of teachers’ engagement with concepts embedded in the normal distribution. The participants were a group of 290 in-service teachers enrolled in a teacher development program. The research instrument was an assessment task that can be described as an “unknown percentage” problem, which required the application of properties of the standard normal distribution curve. Responses to the task were analyzed using the Action, Process, Object, Schema (APOS) framework that specified a standardization and a probability layer of understanding. The success rates were 27% and 14% in the two questions, with most teachers experiencing problems in the probability layer because of a failure to link the probability values with the area covered by the curve.

  • In this paper, we report on the impact of four activities and two interviews on the organization of an introductory statistics course attended by future mathematics teachers at the University of Sao Paulo, Brazil. The activities were designed to enhance students’ learning and collaborative knowledge construction, based on Vygotsky’s Socio-Historical Theory. Data were collected in the course through the activities and the interviews. Analysis of the data suggests that the course improved students’ initiative, collaboration and intentional action, as well as their attitude as future mathematics teachers. Quantitative results comparing 2013 with earlier offerings of the course are also discussed. The transformation discussed here could be applied in other introductory statistics courses, and may lead to practical pedagogical improvements.

  • This paper aims to contribute to the emerging literature on capacity-building in statistics education by examining issues pertaining to the readiness of teachers in a developing country to teach basic statistical topics. The paper reflects on challenges and barriers to building statistics capacity at grassroots level in a developing country, based in part on lessons learnt from the design of an in-service intervention for teachers in South Africa, and on illustrative data about teachers’ attitudes, collected as part of this intervention. The paper reflects on implications for future design of interventions, as well as on research needs that can inform future capacity-building in statistics education in developing countries.

  • This study explored threshold concepts and areas of troublesome knowledge among students enrolled in a basic biostatistics course at the university level. The main area of troublesome knowledge among students was targeted by using technology to improve student learning. A total of 102 undergraduate students who responded to structured questionnaires were included in this study. The results suggest that threshold concepts regarding “statistics” and “random sample” need to be better understood. “Confidence interval” and “hypothesis testing” were the two most frequent troublesome areas among the participants. The pedagogical role of technology in teaching and learning statistics, and the mechanisms whereby technology may improve student learning were discussed.

  • This study aimed to gain knowledge of students’ beliefs and difficulties in understanding p-values, and to use this knowledge to develop improved teaching programs. This study took place over four consecutive teaching semesters of a one-semester were used to inform the instructional design for the following semester, the introduction of hypothetical probabilistic reasoning using a familiar context, and the use of alternative representations. The students were also encouraged to write about their work. As the interventions progressed, a high proportion of students successfully defined and used p-values in Null Hypothesis Testing procedures.

  • This study examined a random stratified sample (n=62) of teachers’ work across eight institutions on three tasks that utilized dynamic statistical software. We considered how teachers may utilize and develop their statistical knowledge and technological knowledge when investigating a statistical task. We examined how teachers engaged in trans-numerative activities with the aid of technology through representing data, using dynamic linking capabilities, and creating statistical measures and augmentations to graphs. Results indicate that while dynamic linking was not always evident in their work, many teachers took advantage of software tools to create enhanced representations through many trans-numerative actions. The creation and use of such enhanced representations of data have implications for teacher education, software design, and focus for future studies.