The uniformly most accurate (UMA) is an important optimal approach in interval estimation, but the current literature often introduces it in a confusing way, rendering the learning, teaching and researching of UMA problematic. Two major aspects cause this confusion. First, UMA is often interpreted to maximize the accuracy of coverage, but in fact,…

The field of Linguistics has long been interested in the verb meanings of intransitive verbs and their argument structure, specifically the breakdown of intransitive verbs into unaccusative and unergative verb types. Despite extensive research, a universally applicable explanation for this breakdown remains elusive due in part to the variability…

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 adaptive learning problem concerns how to create an individualized learning plan (also referred to as a learning policy) that chooses the most appropriate learning materials based on a learner's latent traits. In this article, we study an important yet less-addressed adaptive learning problem--one that assumes continuous latent traits.…

The teaching of mathematics is mostly done with tasks that learners and teachers do or solve, in and outside of class. These tasks, which are used to illustrate concepts in mathematics, are referred to in this paper as examples in mathematics. Examples that teachers choose and use are fundamental to what mathematics is taught and learned, and what…

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…

Emphasis in teaching and learning statistics has shifted from memorizing formulas and procedures to investigating situations, creating models, and using data to understand problems. The Common Core State Standards for Mathematics (CCSSM) (NGA Center and CCSSO 2010) Grade 8 Statistics and Probability content standards drive this point home.…

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…

We examine the challenges of teaching probability through the use of modelling. We argue how an integrated modelling approach might facilitate a coordinated understanding of distribution by marrying theoretical and data-oriented perspectives and present probability as more connected to the social lives of modern-day students. Research is, however,…

The current study was conducted with the goal of helping to address the research gap of improving preservice teachers' pedagogical knowledge about probability by investigating how preservice teachers explored concepts of probability during aleatoric music composition, as well as their contemplation process during follow-up reflections focused on…

There is currently a consensus in mathematics education that favors constructivist instructional models, which are based on the inquiry of knowledge by students. There are, however, different views that consider objectivist models, based on knowledge transmission (direct or explicit teaching) more effective in the teaching of scientific…

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…