Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article…

Emotions are a fleeting experience, sometimes lasting only moments before dissipating. Prior research in SLA has either ignored emotions, underestimated their relevance, or has studied them as a relatively stable individual difference variable. In contrast, the present study takes an idiodynamic approach to examine the rapidly changing…

The move from additive to multiplicative thinking requires significant change in children's comprehension and manipulation of numerical relationships, involves various conceptual components, and can be a slow, multistage process for some. Unit arrays are a key visuospatial representation for supporting learning, but most research focuses on 2D…

The purpose of this case study was to describe how one band director used pedagogical content knowledge while working with beginning-band students to help them develop the skill of playing brass lip slurs. Data were generated from (1) video recordings of each class over two different weeks during the school year, (2) "think aloud"…

The purpose of this exploratory study was to identify the analytic frames children (ages 9 to 11) employed as they worked together to make sense of an ill-structured problem, what those same children did when their frames collided in the context of deliberative dialogue, and what they learned from the process of negotiation. Data included pre- and…

This mixed-methods study investigates writers' task representation and the factors affecting it in test-like and non-test-like conditions. Five advanced-level L2 writers wrote two argumentative essays each, one in test-like conditions and the other in non-test-like conditions where the participants were allowed to use all the time and online…

In this article, we examine children's (aged 9-11) experience of deliberative dialogue in which they sought to reach consensus around a shared problem with their peers. Through analysis of pre- and post-task interviews as well as videotapes of the sessions, we explore the pedagogical nature of children's engagement. In light of shifting trust…

Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic…

This study aims to describe the constructive metacognitive activity shift of eleventh graders in solving a mathematical problem. Subjects in this study were 10 students in grade 11 of SMAN 1 Malang. They were divided into 4 groups. Three types of metacognitive activity undertaken by students when completing mathematical problem are awareness,…

Students' opportunities to learn how to think are embedded in the instructional tasks with which they are invited to engage in the classroom. Prior research has revealed that the selection and use of cognitively demanding tasks does not guarantee high-level student thinking during their enactment. To address this challenge, we designed and…

Spatial visualisation is a subset of spatial ability and is exemplified in predicting whether or not a net will fold to form a target solid. The researchers examined video of interviews to explore the schemes of Year 5 students for determining the validity of nets for a cube and pyramid. Findings suggest the significance of imaged actions, shown…

The present study provides an in-depth, longitudinal account of an undergraduate student's L2 discourse socialization in an academic exchange program in Canada. By invoking Rogoff's (1995) notion of participatory appropriation, this qualitative case study examined an L2 student's task-related strategies and performance as they evolved over time in…

In recent years there has been an increased emphasis on algebraic reasoning in primary school classrooms. This includes introducing students to the mathematical practices of making conjectures, justifying and generalising. Drawing on findings from a classroom-based study, this paper explores one teacher's journey in shifting her task design and…

This research focused on a new method in the development of animation story content, which could shorten the creation process and arouse new ideas. Two phases of experiments were conducted to explore this reversed model. The first phase is a pretest of participants' creativity, which was a base for further examination the relationship between…

Two studies were conducted to investigate whether context variations were suitable to improve metacognitive judgments in children in a complex, everyday memory task. In the first phase of each experiment, participants were shown a short event (video) and gave judgments-of-learning (JOLs), that is, rated their certainty that they would later be…