These proceedings contain the papers of the 12th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2015), October 24-26, 2015, which has been organized by the International Association for Development of the Information Society (IADIS), co-organized by Maynooth University, Ireland, and endorsed by the…

Against the backdrop of half a century of research in mathematics problem solving, Polya's last stage is especially conspicuous--by the scarcity of research on it! Much of the research focused on the first three stages (J.M. Francisco and C.A. Maher, "Conditions for promoting reasoning in problem solving: Insights from a longitudinal…

Previous studies have reported that students employed different problem solving approaches when presented with the same task structured with different representations. In this study, we explored and compared students' strategies as they attempted tasks from two topical areas, kinematics and work. Our participants were 19 engineering students…

What are the nature, forms, and roles of metaphors in mathematics instruction? We present and closely analyze three examples of idiosyncratic metaphors produced during one-to-one tutorial clinical interviews with 11-year-old participants as they attempted to use unfamiliar artifacts and procedures to reason about realistic probability problems.…

Online collaborative learning allows discussion to occur at greater depth where knowledge can be constructed remotely. However students were found to construct knowledge at low-level where they discussed by sharing and comparing opinions; those are inadequate for new knowledge creation. As such, this research attempted to investigate the students'…

Collaborative learning has placed an emphasis on co-constructing knowledge by sharing and negotiating meaning for problem-solving activities, and this cannot be accomplished without governing the self-regulatory processes of students. This study employed a Web-based tool, Google Docs, to determine the effects of Web-based collaboration on…

This article describes how teachers address issues and tensions that students meet in learning division of fractions. First, students must make sense of division of fractions on their own by working individually and in small groups, using concrete or pictorial representations, inventing their own processes, and presenting and justifying their…

This study examined how toddlers gain insights from source video displays and use the insights to solve analogous problems. Two- to 2.5-year-olds viewed a source video illustrating a problem-solving strategy and then attempted to solve analogous problems. Older but not younger toddlers extracted the problem-solving strategy depicted in the video…

Children are naturally curious and want to make sense of their world. To implement mathematical tasks that nurture children's desire to reason, it is valuable for teachers to have experienced for themselves comparable tasks and learning environments (Ball and Bass 2000). In this article, the author describes three strategies to facilitate…

Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

This study is set in the context of a Post Graduate course for Teacher Education where the participants were exposed to a systematic reflective learning strategy facilitated by a structured interactive e-learning platform. The e-platform was used for students to share, reflect and they had demonstration of skills in class. The researcher intended…

A combination of regular classroom teaching with the use of resources available on the Moodle platform has been designed to foster the development of skills for learning to learn for students in an undergraduate general chemistry course. The use of the Moodle platform essentially aimed at strengthening the students' prior knowledge of…

Three mid-level mathematics teachers (grades 7 and 8) and a university mathematics educator formed a year-long professional learning community. The objective was to collectively look at how they were promoting the Standards for Mathematical Practice (SMP) (CCSSI 2010) in their classes. The monthly discussions followed an iterative cycle in which…

The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…