This study focuses on computer-based formative assessment for supporting problem solving and reasoning in mathematics. To be able to assist students who find themselves in difficulties, the software suggested descriptions - diagnoses - of the encountered difficulty the students could choose from. Thereafter, the software provided metacognitive and…

Extant research has demonstrated that problem-posing and problem-solving mutually affect one another. However, the exact nature and extent of this relationship requires a detailed elaboration. This is especially true when adidactical problem-posing arises within a problem-solving context. In this study, we analyze the scripting journey used by two…

Spatial visualization--the ability to mentally imagine and manipulate objects--has frequently been measured using the Paper Folding Test (PFT). In this task, participants view diagrams of a paper being folded and a hole being punched. They then identify the resulting punch pattern. Although task instructions promote mentally unfolding the paper,…

This study explored the use of heuristics in the design space by novice and expert engineers in the initial ideation of a design solution. Verbal protocol analyses were conducted with four engineering students and four professional engineers as they generated ideas to solve a design problem. Overall, both experts and novices used various types of…

Much of our real-life decision making is bounded by uncertain information, limitations in cognitive resources, and a lack of time to allocate to the decision process. It is thought that humans overcome these limitations through "satisficing," fast but "good-enough" heuristic decision making that prioritizes some sources of…

Students' opportunities to struggle with mathematical ideas have long been considered paramount to learning. However, there's little research on how teachers; (1) draw on and make sense of the discourses of perseverance; (2) enact it in classroom; and (3) develop an expansive view of perseverance. To contribute to these lines of research, we build…

A transition from "doer" to "teacher" for prospective teachers requires them to reorient from thinking about how they do mathematics to engaging with students and their work, understanding student representations, and planning instruction accordingly. To scaffold a transition, we developed a five-step mathematics as teacher…

In spite of having deficits in various areas of social cognition, especially in mindreading, Machiavellian individuals are typically very successful in different tasks, including solving social dilemmas. We assume that a profound examination of neural structures associated with decision-making processes is needed to learn more about…

We compared the performance of three heuristics with that of subjects on variants of a well-known combinatorial optimization task, the Traveling Salesperson Problem (TSP). The present task consisted of finding the shortest path through an array of points from one side of the array to the other. Like the standard TSP, the task is computationally…

The topic of teaching troubleshooting is examined as an example of the teaching of cognitive strategies for technical problem solving. The traditional behavioral approach to teaching troubleshooting has essentially been algorithmic. Recent cognitive research suggests an approach founded first on task analysis and characterized by: (1) analysis of…

Corporate and educational settings increasingly require decision making, problem solving and other complex cognitive skills to handle ill-structured, or heuristic, tasks, but the growing need for heuristic task expertise has outpaced the refinement of task analysis methods for heuristic expertise. The Heuristic Task Analysis (HTA) Method was…

Applying and adapting a variety of appropriate heuristic strategies is one of the accepted standards of problem solving (NCTM, 2000). Thinking through a solution to a non-routine mathematical task, experts in problem solving call into play many sophisticated strategies (almost) without conscious efforts, while novices need to be taught how to do…

Presents thinking-aloud protocols from secondary pupils solving arithmetic story and geometrical problems and analyzes their protocols by using interpretation models founded on a general problem-solving model. A word problem solving simulation is also used to further explicate processes pupils use to solve mathematical tasks. (Author/MBR)

Discussion of instructional design models focuses on a study concerned with developing effective instruction in heuristic-based problem solving for computer programing. Highlights include distinctions between algorithms and heuristics; pretests and posttests; revised instructional design procedures; student attitudes; task analysis; and…