Design research (DR) promises to simultaneously solve practical problems of education and develop theory to guide future interventions. However, educational DR remains paradigmatically underdeveloped, making it difficult to train new researchers, to agree upon what makes a theoretical contribution, and to promise clear outputs to funders--all of…

Today, experts agree that the level of cognitive development of modern young people affects the long-term life goals and outcomes that they set for themselves. During the course of numerous studies experts have identified such key competencies as problem solving, information literacy, and critical thinking. However, there are still many unanswered…

This article reports on a project that used a game-creation tool to introduce middle-school students ages 10 to 13 to problem-solving strategies similar to those in computer science through the lens of studio-based design arts. Drawing on historic paradigms in design pedagogy and contemporary educational approaches in the digital arts to teach…

Building on Dörner's (1996) theory of complex problem-solving, a learning scenario for teacher students was created and tested. Classroom management is interpreted as a complex problem, which requires the integration of competing interests and tackling multiple, simultaneous tasks under time pressure and with limited information. In addition,…

In response to a desire to strengthen the economy, educational settings are emphasizing science, technology, engineering, and mathematics (STEM) curriculum and programs. Yet, because of the narrow approach to STEM, educational leaders continue to call for a more balanced approach to teaching and learning, which includes the arts, design, and…

Today's engineers, designers, and technologists are often thrust into the role of problem solver, from the initial design phase of a product or process all the way to final development. Many engineers in manufacturing environments are tasked with solving problems and continuously improving processes to enhance company profitability, efficiency,…

When dividing one fraction by a second fraction, invert, that is, flip the second fraction, then multiply it by the first fraction. To multiply fractions, simply multiply across the denominators, and multiply across the numerators to get the resultant fraction. So by inverting the division of fractions it is turned into an easy multiplication of…

This aim of this study is to describe the process of local conjecturing in generalizing patterns based on Action, Process, Object, Schema (APOS) theory. The subjects were 16 grade 8 students from a junior high school. Data collection used Pattern Generalization Problem (PGP) and interviews. In the first stage, students completed PGP; in the second…

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

In 2009, we reported on a new Intelligent Tutoring Systems (ITS) technology, example-tracing tutors, that can be built without programming using the Cognitive Tutor Authoring Tools (CTAT). Creating example-tracing tutors was shown to be 4-8 times as cost-effective as estimates for ITS development from the literature. Since 2009, CTAT and its…

The desire to persuade students to avoid strictly memorizing formulas is a recurring theme throughout discussions of curriculum and problem solving. In combinatorics, a branch of discrete mathematics, problems can be easy to write--identify a few categories, add a few restrictions, specify an outcome--yet extremely challenging to solve. A lesson…

When a second-grade class struggled to make sense of the algorithms for multidigit addition and subtraction, attitude and morale were down, and student discourse was at an all-time low. When daily mathematics class started, the teacher was hearing an overall class moan. The instructed needed to turn it around, to find a way to help excite and…

Although most tasks that STEM professionals engage in--like identifying problems, making models, and testing those models--involve inquiry, many STEM classes still rely on direct instruction. Stephan argues that even as new resources for active learning are being developed for STEM instruction, many teachers aren't using these resources and tasks…

Recognizing and using mathematical structure are key components of mathematical reasoning. The authors believe that one productive way to support students' use of structure is by identifying opportunities to address structure in the context of what teachers are already doing, rather than developing additional tasks or new curriculum materials. The…

Introduction of a pedagogical concept, Kubus, in a problem oriented learning context--analysed within the framework of an activity system--indicates what might happen when offering tools tempting to influence and regulate students' learning approach and hereby neglecting the importance of existing habits and values. Introduction of this new…