In this paper, we present a case study of a secondary mathematics teacher, Isaac (pseudonym), and his considerations for teaching with multiple methods for solving missing-value problems. While his students preferred methods that drew more closely on their intuitive understanding of proportionality, Isaac emphasised the algorithmic…

Novice programmers need well-designed instruction and assessment informed by research and critical perspectives to conquer the historical challenges associated with completing introductory computer programming courses successfully. These issues include high dropout and failure rates, the struggle to acquire and retain basic programming knowledge,…

This study examined if and how thinking time, defined as the time from the start of the problem to the students' first action to solve, influences their problem-solving efficiency, defined as the number of steps taken to solve the problem, using Graspable Math, a web-based mathematical tool. We found that: (1) students who took longer to think…

We recently developed the "Framework of Achievement Bests" to explain the importance of effective functioning, personal growth, and enrichment of well-being experiences. This framework postulates a concept known as "optimal achievement best," which stipulates the idea that individuals may, in general, strive to achieve personal…

What if you could challenge your 11th graders to figure out the best response to a partial meltdown at a nuclear reactor in fictional Gammatown, USA? With this volume in the "STEM Road Map Curriculum Series," you can! "Radioactivity" outlines a journey that will steer your students toward authentic problem solving while…

Background: This study investigated learning outcomes and user perceptions from interactions with a hybrid intelligent tutoring system created by combining the AutoTutor conversational tutoring system with the Assessment and Learning in Knowledge Spaces (ALEKS) adaptive learning system for mathematics. This hybrid intelligent tutoring system (ITS)…

Clinical reasoning is a central skill in diagnosing cases. However, diagnosing a clinical case poses several challenges that are inherent to solving multifaceted ill-structured problems. In particular, when solving such problems, the complexity stems from the existence of multiple paths to arriving at the correct solution (Lajoie, 2003). Moreover,…

This paper presents a simplified approach for the application of material efficiency metrics to linear and convergent synthesis plans encountered in organic synthesis courses. Computations are facilitated and automated using intuitively designed Microsoft Excel spreadsheets without invoking abstract mathematical formulas. The merits of this…

The goals of this study were to investigate the timing and the mechanism by which two types of model-centered instruction (MCI)--expert modeling (EM) and self-guided modeling (SGM)--might be made increasingly effective, efficient, and engaging for learners with different levels of expertise. The 62 pre-service and in-service evaluators who…

This study evaluates the effects of an intervention aimed at improving representational flexibility in linear-function problems. Forty-nine students aged 13-16 participated in the study. A pretest-intervention-posttest design with an experimental and control group was used. At pretest, both groups solved a choice test, where they could freely…

Nowadays we need to teach students how to become flexible problem solvers in a dynamic world. The pace in which technology changes and complexity increases requires increased efficiency in learning and understanding. This requires the engineers of tomorrow to quickly gain knowledge and insight outside their prime area of expertise. To transfer…

It is argued that efficient use of cognitive strategies also involves domain-specific knowledge, metacognition, and motivation. Issues concerning cognitive strategy instruction are explored, and it is concluded that a hybrid model representing a compromise between the notion of cognitive strategies and current connectionism may best portray human…

Many students find it difficult to learn the kinds of knowledge and thinking required by college or high school courses in mathematics, science, or other complex domains. Thus they often emerge with significant misconceptions, fragmented knowledge, and inadequate problem-solving skills. Most instructors or textbook authors approach their teaching…

This study compared the efficiency (time) and accuracy of two representations of instructional algorithms--list versus flow chart--for the task of using indexes to search for document numbers in the U.S. Documents Monthly Catalog. Participants were 55 undergraduates and 5 adults at the Virginia Military Institute. Two sets (flow charts and lists)…