This study took a broad view of generalization, exploring how classroom instruction within opportunities of implicit generalization may be related to students' abilities to generalize. From an integrated perspective of generalization and problem solving, we investigated twelve lessons of two middle level teachers based on three pattern-based…

Crime Scene for Mathematics Investigation (CSMI) was created as a small group, cooperative, self-selective grouping strategy to allow students to explore mathematics based on their own understanding and perceived readiness, much like the concept and application of literature circles in language arts. In essence, these self-chosen small groups met…

In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…

Which potato chip is healthiest: (1) regular; (2) baked; or (3) sour cream and onion? This problem requires critical and numerical skills in order to read and compare nutrition labels. The question has applications in mathematics and science classrooms but also in teachers' lounges and school cafeterias. It is a problem that addresses the five…

Purpose: Student/trainee perception of their performance can sometimes be inaccurate. This study aims to look at the accuracy of perception to actual performance in short-term intervention style training/instruction. Design/methodology/approach: Two studies conducted using university students in problem solving exercises compared the performance…

This phenomenographic study documented changes in student-held electrical concepts the development of meaningful learning among students with both low and high prior knowledge within a problem-based learning (PBL) undergraduate electrical engineering course. This paper reports on four subjects: two with high prior knowledge and two with low prior…

Justification is a core mathematics practice. Although the purposes of justification in the mathematician community have been studied extensively, we know relatively little about its role in K-12 classrooms. This paper documents the range of purposes identified by 12 middle grades teachers who were working actively to incorporate justification…

Reasoning and sense making are at the heart of mathematics teaching and learning throughout the K-12 mathematics curriculum. Focusing on these skills gives students the opportunity to analyze, interpret, and critically think about the mathematics they learn. The terms "reasoning" and "sense making" are frequently used to describe the wide range of…

Many approaches to instruction focus on helping people learn to recognize "the old in the new"--to turn what would otherwise be novel problems into familiar patterns that can be solved efficiently through the reuse of prior learning. Instruction that leads to efficient transfer is important, but it can also promote what we call "overzealous"…

The idea of learning through games isn't necessarily new. In fact, over the past decade, researchers have been espousing the use of games to help both children and adults learn. But it's only been recently that games have begun to make serious inroads into classrooms. As the world becomes more and more driven by mobile apps and tablet…

This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

The Common Core State Standards (2010) involve the demonstration of conceptual knowledge of numbers and operations. For students who struggle with mathematics and have not responded to instruction, it is important that interventions emphasize this understanding. In order to address conceptual understanding of numbers and operations in meeting the…

This paper reports a study that explored the overall pattern of metacognitive awareness of reading strategy use and its possible relationship with reading comprehension. Moreover, the study investigated the influence of gender and proficiency level on the use of these strategies. The Survey of Reading Strategies Questionnaire (SORS), the…

Despite it being the second decade of the 21st century, there still exists a range of definitions of what a 21st century learning environment is. This can be troublesome for teacher educators as we strive to prepare teachers for environments we can't clearly describe. In order to describe a 21st century learning environment, we developed an IC Map…

We report on a project to introduce interactive learning strategies (ILS) to physics classes at the Université Pierre et Marie Curie, one of the leading science universities in France. In Spring 2012, instructors in two large introductory classes, first-year, second-semester mechanics, and second-year introductory electricity and magnetism,…