Spurred by Kilpatrick's (1987) "Where do good problems come from?", this study explores problem-posing triggers of experienced problem posers for mathematics competitions. Triggers are conceived as instances of noticing, where an impulse draws a poser's attention and "triggers off" a mathematical re-action, one of the outcomes…

In calculus, related rates problems are some of the most difficult for students to master. This is due, in part, to the nature of the problems, which require constructing a nuanced mental model and a solid understanding of the function. Many textbooks present a procedure for their solution that is unlike how experts approach the problem and elide…

Adaptive expertise represents the combination of both efficient problem-solving for clinical encounters with known solutions, as well as the ability to learn and innovate when faced with a novel challenge. Fostering adaptive expertise requires careful approaches to instructional design to emphasize deeper, more effortful learning. These teaching…

This study was carried out to develop a test to assess algorithmic thinking skills. To this end, the twelve steps suggested by Downing (2006) were adopted. Throughout the test development, 24 middle school sixth-grade students and eight experts in different areas took part as needed in the tasks on the project. The test was given to 252 students…

Feedback on how students progress through completing subgoals can improve students' learning and motivation in programming. Detecting subgoal completion is a challenging task, and most learning environments do so either with "expert-authored" models or with "data-driven" models. Both models have advantages that are…

This study explores talent-development trajectories of early-career chemical engineers to identify key components for success in the field using the talent development megamodel as a theoretical framework. Interviews with 12 recent PhD graduates reveal a trajectory across four developmental stages: (a) math ability and science ability, (b)…

Purpose: Second and foreign language (SL/FL) teachers' informal problem-solving has received little explicit research attention while it is widely acknowledged that problem-solving is crucial to expertise development in any complex knowledge domain. To develop a clearer understanding of the role of informal problem-solving in SL/FL teachers'…

Sourcing is the ability to evaluate information by analysing source parameters such as author's expertise on a given topic. Past research, mostly based on school-related materials and tasks, shows that adolescents do not pay attention to source parameters when evaluating online scientific information. However, recent research has suggested that…

The purpose of this study was to examine the career experiences of three music teachers through the lens of expertise theory. An additional purpose was to discover how the participants viewed success in the field of music education. Using an instrumental case study design, three experienced music teachers--who served as the case--were interviewed…

This study was inspired by the following question: how is mathematical creativity connected to different kinds of expertise in mathematics? Basing our work on arguments about the domain-specific nature of expertise and creativity, we looked at how participants from two groups with two different types of expertise performed in…

The ability to solve authentic real-world problems in science, engineering, and medicine is an important goal in post-secondary education. Despite extensive research on problem solving and expertise, the teaching and assessing of advanced problem-solving skills in post-secondary students remains a challenge. We present a template for creating…

Addressing food, energy, and water issues through a systems approach is essential for Native American communities, where climate change, natural disasters, and pandemics further strain access to these vital resources. Tribal communities experience a disproportionate impact from these global crises, which heightens and exposes existing…

Statistics students' conceptions of the work of statisticians and the discipline of statistics may play an important role in the topics to which they attend and their interest in pursuing further study. To learn about students' conceptions, we collected open-ended survey responses from 44 undergraduate students who had completed introductory…

Problem solving followed by explicit instruction, as suggested by productive failure and several other instructional theories, indicates long-term learning benefits, whereas explicit instruction followed by problem solving has been consistently demonstrated as superior within the framework of cognitive load theory. However, the effectiveness of…

Problem solving is a critical skill in many disciplines but is often a challenge for students to learn. To examine the processes both students and experts undertake to solve constructed-response problems in genetics, we collected the written step-by-step procedures individuals used to solve problems in four different content areas. We developed a…