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…

In this work, we examine students' ways of thinking when presented with a novel linear algebra problem. Our intent was to explore how students employ and coordinate three modes of thinking, which we call computational, abstract, and geometric, following similar frameworks proposed by Hillel (2000) and Sierpinska (2000). However, the undergraduate…

In this article the connection between transfer, interaction and reflective thinking is analyzed, especially within the context of learning mathematics. Attention is paid to the question of how to use or to explore the knowledge that has already been acquired. It may be relevant to make a distinction between the "classical" concept of…

In this paper, we describe a framework for data analysis that can be embedded into a base application. Since it is important to analyze the data directly inside the application where the data is entered, a tool that allows the scientists to easily work with their data, supports and motivates the execution of further analysis of their data, which…

A considerable number of children rely on counting to solve single-digit addition problems when they are expected to use accurate retrieval-based strategies. There are different reasons why this may be so. Children may use inefficient counting strategies, produce errors when applying backup strategies or lack sufficient confidence to just state…

In this exploratory study we considered how one teacher's understanding of proportional reasoning related to his teaching. We relied on Knowledge in Pieces as a lens for considering the teacher's knowledge organization as a way to make sense of his understanding. We did so by collecting data from two instruments and using Epistemic Network…

We have been incrementally adding data-driven methods into the Deep Thought logic tutor for the purpose of creating a fully data-driven intelligent tutoring system. Our previous research has shown that the addition of data-driven hints, worked examples, and problem assignment can improve student performance and retention in the tutor. In this…