The presented article is dedicated to a new way of teaching substitution in algebra. In order to effectively master the subject matter, it is necessary for students to perceive the equal sign equivalently, to learn to manipulate expressions as objects, and to perceive and use transformations based on defining their own equivalences. According to…

To learn content knowledge in science, technology, engineering, and math domains, students need to make connections among visual representations. This article considers two kinds of connection-making skills: (1) "sense-making skills" that allow students to verbally explain mappings among representations and (2) "perceptual…

MathCheck is a relatively new online tool that gives students feedback on their solutions to elementary university mathematics and theoretical computer science exercises. MathCheck was designed with constructivism learning theory in mind and it differs from other online tools as it checks the solutions step by step and shows a counter-example if…

This study explores kindergarten students' early notions of mathematical equivalence in the United States. In particular, it uses qualitative methods to examine the understandings children hold about the equal sign prior to formal instruction and how these understandings shift throughout an 8-week classroom teaching experiment designed to develop…

According to the views of social constructivism, learning takes place when individuals engage socially to talk about and act on shared problems or interests. In recent years, this approach has been very popular for the teaching and learning of mathematics in primary and secondary education. On the contrary, in tertiary education, it seems that…

Pre-service teachers need to develop habits of mind that allow them to grow as new teachers. This article describes an elementary mathematics methods course in which teaching as an experiment was used a framework for pre-service teachers to participate in action research by developing learning goals, observing and analyzing student thinking,…

Using a students' workshop as a laboratory, this article summarises the observation of three years' implementation of a new study module for a Bachelor Program in Engineering Design (Interior and Furniture Design) at the University of Forestry, Sofia, Bulgaria. The article offers an analysis of group dynamics and the difficulties and issues…

Adults adopt the traits of characters in narratives, but little is known about whether children do so. In Study 1, 7- and 10-year-olds (N = 96) heard a 2.5-minute recording about a professor or cheerleader. Reporting higher engagement in the professor narrative related to more time playing with an analytical toy (a Rubik's cube), whereas reporting…

Research indicates that students find open educational resources (OER) favorable, but there is no research regarding students' perceptions of faculty who use open textbooks. In the present study we examined this topic experimentally with two undergraduate psychology courses at a small public university. Participants read two passages--one about an…

The advancement of computer and communication technologies has enabled students to learn across various real-world contexts with supports from the learning system. In the meantime, researchers have emphasized the necessity of providing personalized learning guidance or support by considering individual students' status and needs in order to…