Thirty-seven third graders and thirty-two first graders engaged in solving a tangram puzzle in the shape of a fox. They had five minutes to solve the puzzle, and after this time, they received guidance on the particular piece they had difficulties with. Through the lenses of navigating flexible abstraction, reinterpretation, combinations, and…

Mastering the ability for learning to learn is the most ambitious goal of modern educators. A distinction is made between two relatively independent components of this expertise: (a) the reflective component of the learning to learn ability that allows a person comprehend what knowledge and skills he or she lacks to act in the new situation; (b)…

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…

Early elementary school students are expected to solve twelve distinct types of word problems. A math researcher and two teachers pose a structure for thinking about one problem type that has not been studied as closely as the other eleven. In this article, the authors share some of their discoveries with regard to the variety of…

A teaching team of three teachers aims to prepare students for 21st Century Learning Outcomes, which includes critical thinking, problem solving, and communication skills. Yet classroom experience has taught them that one of the most difficult aspects of teaching young children is that they have few experiences or prior knowledge to make sense of…

"Focus in Grade 1: Teaching with Curriculum Focal Points" describes and illustrates learning paths for the mathematical concepts and skills of each grade 1 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate…