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…

Introducing challenging tasks in such a way that makes them accessible, rather than daunting, to students is a challenge for teachers. Solving challenging tasks involves students having to grapple with the problem. The role of the teacher is to motivate and clarify the problem rather than showing students how to solve the problem.

How do high school students approach academic and creative challenges? This study compares the content of academic and creative challenges for 190 high school students, and examines students' intentions to persist. Students reported experiencing academic and creative challenges in different areas: academic challenges were described primarily in…

The relative age effect (RAE) has been demonstrated in many youth and professional sports. In this study, we hypothesized that there would also be a RAE among youth chess players who are typically involved in a complex cognitive task without significant physical requirements. While typical RAEs have been observed in adult chess players, in this…

In the process of learning mathematics, students practice various forms of thinking activities aimed to substantially contribute to the development of their different cognitive structures. In this paper, the subject matter is a "cognitive obstacle", a phenomenon that occurs in the procedures of solving mathematical tasks. Each task in…

Developing students' 21st century skills, including creativity, critical thinking, and problem solving, has been a prevailing concern in our globalized and hyper-connected society. One of the key components for students to accomplish this is to take part in today's participatory culture, which involves becoming creators of knowledge rather than…

Self-regulation has been shown as a critical factor in learning in a regular classroom environment (e.g. Wolters and Pintrich in "Instr Sci" 26(1):27-47, 1998. doi: 10.1023/A:1003035929216). However, little research has been conducted to understand self-regulation in the context of collaboration (Dinsmore et al. in "Educ Psychol…