To ensure the learning of mathematics, teachers must be able to analyse their students' mathematical practices when solving tasks, interpret the difficulties that students encounter, and decide how to manage students' difficulties. This competence in didactic analysis and intervention allows teachers to adapt their teaching to meet individual…

The aim of this study is to reveal and evaluate the attending and interpreting skills of student thinking of prospective teachers, as well as their instructional suggestions as responding skills. The current study was conducted with 29 prospective mathematics teachers (PMTs) within a qualitative design in the context of probability. First, three…

Employing a statistical modeling inspired pedagogy is becoming a widespread practice in the statistics education community. Many have incorporated the practice of formulating conjectures in their modeling-enhanced educational designs and have reported on its benefits. We further elucidate the mechanism through which students' conjecturing may be…

In this paper, we investigate the ways in which 15 year-old students conceive interrelated issues of randomness. We deal with these issues of randomness as a whole and not separately from each other, in contrast to the research so far. In order to analyse the students' ways we introduce a modification of Kyburg's Schema [(1974). "The logical…

The aim of this study is to explore the judgments and reasoning in probabilistic tasks that require comparing two probabilities either with or without introducing an additional degree of uncertainty. The reasoning associated with the task having an additional condition of uncertainty has not been discussed in previous studies. The 66 undergraduate…

A mysterious conflict of solutions emerged when a group of tenth- and eleventh-grade students were studying a seemingly ordinary problem on combination and probability. By investigating the mysterious "conflicts" caused by multiple randomization procedures, students will gain a deeper understanding of what it means to perform a task…

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…

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…

An interview with a sixth-grade student illustrates how her number sense and understanding of variability relate to her ability and proclivity to apply a frequentist (statistical) approach to probability tasks. A general suggestion for teaching about mathematics of uncertainty through the gradual strengthening of estimation, as per the historical…

We analyze probability content within middle grades (6, 7, and 8) mathematics textbooks from a historical perspective. Two series, one popular and the other alternative, from four recent eras of mathematics education (New Math, Back to Basics, Problem Solving, and Standards) were analyzed using the Mathematical Tasks Framework (Stein, Smith,…

This paper summarizes the thinking of 84 middle school mathematics students' about variability in three stochastics tasks that involve repeated trial. Differences in students' acknowledgment of variability were found, depending on whether the task was from a sampling environment, or a probability environment. Students tended to neglect variability…