The purpose of the present study was to gather data regarding the implementation of Prodigy in elementary schools in a mid-sized school district in the southern United States. Prodigy is a free, adaptive mathematics game provided by Prodigy Education. The program integrates curriculum-aligned mathematics content (Grades 1-8) in a game-based…

Background: Problem solving is considered to be a central activity of engineering practice. While some studies have shown how various beliefs affect students' abilities to solve problems, studies are needed that explicitly examine the beliefs and assumptions students bring to the problem-solving process. Purpose/Hypothesis: The purpose of this…

Educators across the nation are now well under way in implementing the Common Core State Standards (CCSS; National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA & CCSSO], 2010) for mathematics. The emerging literature regarding CCSS mathematics instruction for students with disabilities urges…

Hubka's theory of technical systems (TTS) is briefly outlined. It describes commonalities in all engineering devices, whatever their physical principles of action. This theory is based on a general transformation system (TrfS), which can be used to show engineering in the contexts of society, economics and historic developments. The life cycle of…

The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In…

Research on language processing has shown that the disruption of conceptual integration gives rise to specific patterns of event-related brain potentials (ERPs)--N400 and P600 effects. Here, we report similar ERP effects when adults performed cross-domain conceptual integration of analogous semantic and mathematical relations. In a problem-solving…

This brief "Math for Real" article introduces Ohanna, a seventh grader who lives in New York City and regularly takes the bus to get around the city. Ohanna pays $2.50 per bus ride when using her MetroCard. She earns a 5% bonus when she refills the card with a minimum of $5.00. For example, if she adds $10.00 on her MetroCard, her…

This investigation presents students with the challenge of determining the total number of eggs in a photograph of a stack of egg trays. The perspective of the photograph does not allow students to count all the individual eggs in the top tray but does allow them to see the number of eggs in one row and one column of the top tray. During this…

The solution of simple kinetic equations is analyzed without referencing any topic from differential equations or integral calculus. Guided by the physical meaning of the rate equation, a systematic procedure is used to generate an approximate solution that converges uniformly to the exact solution in the case of zero, first, and second order…

Ill-structured problems can be regarded as one of the measures that meet recent social needs emphasizing students' abilities to solve real-life problems. This study aimed to analyze the mathematical abstraction process in solving such problems, and to identify the mathematical abstraction level ([I] Recognition of mathematical structure through…

Help seeking is an important process in self-regulated learning (SRL). It may influence learning with intelligent tutoring systems (ITSs), because many ITSs provide help, often at the student's request. The Help Tutor was a tutor agent that gave in-context, real-time feedback on students' help-seeking behavior, as they were learning with an ITS.…

Screen inferiority in performance and metacognitive processes has been repeatedly found with text learning. Common explanations for screen inferiority relate to technological and physiological disadvantages associated with extensive reading on screen. However, recent studies point to lesser recruitment of mental effort on screen than on paper.…

Reduction is one of the key techniques used for problem-solving in computer science. In particular, in the theory of computation and complexity (TCC), mapping and polynomial reductions are used for analysis of decidability and computational complexity of problems, including the core concept of NP-completeness. Reduction is a highly abstract…

The main goal of the Russian professional education becomes the preparation of competent, qualified graduates, who are able not only to put their knowledge and skills to use, but also make original nonstandard decisions in the situations happening in their professional activities. The process of the design students' creativity development requires…

The aim of this paper is to present "the three steps method" of the self-formation of collaborative groups in a problem-based learning environment. The self-formation of collaborative groups is based on sharing of accountability among students for solving instructional problems. The steps of the method are planning collaborative problem…