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…

This paper explores how a group of pre-service elementary school teachers training to become mathematics teachers for elementary schools arrived at generalizations based on patterns. Two representative problems were investigated with these preservice teachers. The focus of this study was how these preservice teachers analyze and symbolize…

According to Geary's evolutionary approach, humans are able to easily acquire primary knowledge and, with more efforts, secondary knowledge. The present study investigates how primary knowledge contents can facilitate the learning of formal logical rules, i.e., secondary knowledge. Framing formal logical problems in evolutionary salient contexts…

Creating explanations is an important process for students, not only to make connections between novel information and background knowledge, but also to be able to communicate their understanding of any given topic. This article explores students' explanations in the context of computational science and engineering, an important interdisciplinary…

A critical assumption made in Kapur's ("Instr Sci" 40:651-672, 2012) productive failure design is that students have the necessary prerequisite knowledge resources to generate and explore solutions to problems before learning the targeted concept. Through two quasi-experimental studies, we interrogated this assumption in the context of…

The current study examined if preschoolers' understanding of fantasy and reality are related to their learning from educational videos. Forty-nine 3- to 6-year-old children watched short clips of popular educational programs in which animated characters solved problems. Following video viewing, children attempted to solve real-world problems…

This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…

While information theory is typically considered in the context of modern computing and engineering, its core mathematical principles provide a potentially useful lens through which to consider human language. Like the artificial communication systems such principles were invented to describe, natural languages involve a sender and receiver, a…

Despite a cognitive disadvantage when interpreting into one's B language, strategy use and awareness of norms allow interpreters to be resourceful and efficient in achieving communicative goals. There is a need to incorporate strategy training in interpreter education, especially when teaching into-B interpreting. However, strategy taxonomies…

Analytical thinking is the competency needed by students in order to compete and achieve success in the professional field for the 21st Century. Research that aims to examine the most optimal learning model in empowering students' analytical thinking needs to be done since many students have low ordered thinking skills. Through this…

Children in a first-grade class who were taking their first steps in formal mathematical knowledge were given a sequence of five modelling tasks during their regular mathematics lessons. These tasks were different in nature from the problems they encountered in their textbooks. They are more complex and challenging, requiring analysis of the…

According to humanistic psychology, human beings have the potential to shape and change their lives. People are self-determining creatures capable of making decisions about what their existence will be like and who they will become. We interpret this specifically human feature as an empowerment to design one's life and also to influence…

Contextualization is a method used for mathematics curriculum design within lesson plans and as a pedagogical practice in face-to-face classes. Many researchers are studying the effects of using contextualization in the teaching and the learning process for mathematics (Bottge & Cho, 2013; Perin, 2011; Young, Hodge, Edwards, & Leising,…

Formal coach education has been described as an activity which promotes conformity from course attendees. To date, however, few studies have looked at how coach education has been socially constructed over time. The present study addresses this gap and provides a Freirean account of English Football Association (FA) coach education since 1967.…

There are many choices for learning mathematics for engineering students with courses available in face-to-face, blended and fully online modalities. Students are demanding more flexibility in their programs, however the temptation to misuse this flexibility to avoid mathematical studies until it is too late can be an unfortunate side effect. A…