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…

This research aimed to generate a learning trajectory in an introduction to early mathematics, precisely to measure learning using educational games and Realistic Mathematics Education (RME) and to describe young children's curiosity in learning early mathematics. Children need to have an understanding to take a measurement and use a learning…

It was shown previously that observers can learn to exploit an uneven spatial distribution of singleton distractors to better shield visual search from distractors in the frequent versus the rare region (i.e., distractor location probability cueing; Sauter, Liesefeld, Zehetleitner, & Müller, 2018). However, with distractors defined in the same…

In learning, errors are ubiquitous and inevitable. As these errors may signal otherwise latent cognitive processes, tutors--and students alike--can greatly benefit from the information they provide. In this paper, we introduce and evaluate the Systematic Error Tracing (SET) model that identifies the possible causes of systematically observed…

Pedagogical Content Knowledge (PCK) is a powerful construct for examining the complexity of teacher knowledge. Together with teachers' moment-by-moment choices of action, it provides insight into teachers' knowledge and its influence on student learning. This paper investigates the PCK experienced by a senior secondary mathematics class during a…

This study attempted to develop a literature-informed discourse-based instructional approach and evaluated its effects on eleventh-grade students' conceptual and procedural understandings in probability and statistics. To this end, a quasi-experimental study that involved two control groups and one experimental group was used. One-way analysis of…

The objective of this qualitative research is to study the mathematical work when solving a mathematical task in the domain of probability presented by Chilean high school mathematics teachers in pre-service and in-service training. We consider as theoretical support the Mathematical Working Space model and methodological design of a collective…

Chinese opera performance proceedings can be divided into two types. The first is 'visible proceedings', which can be directly seen and heard in the performance, and the second is 'invisible proceedings', which arrange the story and performance of the opera using procedural thinking. The research methods of this study were mainly used to analyze…

This study aims to analyse the reasoning that children and adults with the same school level use to assess and justify the fairness of games, considering aspects of probability such as randomness, sample space, and comparison of probabilities. Data collection included a Piagetian clinical interview based on games of chance. The results showed that…

Preparing for the future during ongoing activities is an essential skill. Yet it is currently unclear to what extent we can prepare for the future in parallel with another task. In two experiments, we investigated how characteristics of a present task influenced whether and when participants prepared for the future, as well as its usefulness. We…

Small private online courses (SPOCs) have influenced teaching and learning in China's higher education. Learning management systems (LMSs) are important components in SPOCs. They can collect various data related to student behavior and support pedagogical interventions. This research used feature engineering and nearest neighbor smoothing models…

This study analyzed how the earliest teaching and learning of probability was organized in Singapore, the US, and Indonesia through an analysis of textbook as an intended mathematics curriculum. An analytical framework was developed comprising four perspectives: representational forms, cognitive demand levels, contextual features, and organization…

A fundamental aspect of statistical inference is representation of real-world data using statistical models. This article analyzes students' articulations of statistical models and modeling during their first steps in making informal statistical inferences. An integrated modeling approach (IMA) was designed and implemented to help students…

Students explored variation and expectation in a probability activity at the end of the first year of a 3-year longitudinal study across grades 4-6. The activity involved experiments in tossing coins both manually and with simulation using the graphing software, "TinkerPlots." Initial responses indicated that the students were aware of…

Traditionally, Canadian Inuit have lived in the circumpolar regions of Canada and those who still live in these regions, have their own cultures, which they tend to celebrate in their educational curricula. Inuit culture reflects their traditional lifestyle, when they were nomadic, and hunted and fished to survive in incredibly difficult…