Vectors have important applications both within and outside mathematics, but the concept of vectors is often taught to students in a less-than-engaging way, leading to students feeling inadequate and frustrated. This article describes the use of a mathematical microworld, "Driving with Vectors," to explore vectors using equitable…

The authors share the results of a research project involving the use of mathematics to develop students' Numeracy General Capabilities. The current article delves into an example of a teacher supporting 'good habits of mind' through focussing on the Critical Learning Disposition of accuracy.

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…

Learning a second language (L2) is not merely mastering an additional linguistic system, but rather learning a new way of conceptualizing the world. Grammatical development does not always align simultaneously with conceptual development in L2. That explains why L2 learners may produce sentences that are grammatically correct, but pragmatically…

The domain of motion or kinematics is important because it forms the basis of mechanics, an important branch of physics. By studying kinematic phenomena in the laboratory, high school students are likely to develop a better understanding of kinematics concepts as well as elements of the scientific approach to study natural and constructed…

Assessing student learning traditionally involves determining whether students can solve a certain percentage of problems correctly, under the assumption that this achievement indicates they have the knowledge and understanding they need to progress to new topics. This article explores what teachers can learn from looking closely at student…

This column provides ideas and techniques to enhance your science teaching. This month's issue discusses using the 5E learning cycle to create coherent storylines. The 5E learning cycle provides an important framework to help teachers organize activities. To realize the full potential of the 5E framework for student learning, lessons must also…

A distinguishing feature of all the formative assessment probes in the "Uncovering Student Ideas" series is that each probe has two parts: (1) a selected answer choice that usually mirrors the research on commonly held ideas students have about concepts or phenomena; and (2) an explanation that supports their answer choice. It is this…

In this paper I look at a set of teaching techniques and practices that I experienced as a student of traditional hula over the past twenty years. I explain the practices of ho'ike (testing by showing what one knows), 'aiha'a (getting grounded), pa'a ka waha/ ho'olohe (hold the mouth/ listen), and learning without palapala (paper) as I have…

"Improving Mathematics in the Early Years and Key Stage 1" reviews the best available evidence to offer five recommendations for developing the maths skills of 3-7-year olds. Recommendations include integrating maths into different activities throughout the day -- for example, at registration and snack time -- to familiarise children…

Thoughtful implementation of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) presents an opportunity for increased emphasis on the development of mathematical understanding among students. Granted, ascertaining the mathematical understanding of an individual student is highly complex work and often exceedingly difficult.…

The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics--how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings--and how to use these insights to improve instruction and student learning. In this…

"Theoretical Foundations of Learning Environments" provides students, faculty, and instructional designers with a clear, concise introduction to the major pedagogical and psychological theories and their implications for the design of new learning environments for schools, universities, or corporations. Leading experts describe the most…

This collection of 58 articles from the recently-published third edition of the International Encyclopedia of Education focuses on learning, memory, attention, problem solving, concept formation, and language. Learning and cognition is the foundation of cognitive psychology and encompasses many topics including attention, memory, categorization,…

The goal of this article is to examine students' mathematical development that occurs as a teacher works within each of 2 zones of learning: students' zones of proximal development (ZPD) and students' zones of potential construction (ZPC). ZPD, proposed by Vygotsky, is grounded in a social constructivist perspective on learning, whereas ZPC,…