The notion of temporal range is introduced and discussed in this paper. Two dimensions of temporal range are identified: mathematical temporality relating to mathematical ideas, their precursors and horizons; and a mathematical learning temporality where what students say/do provides the ground on which future learning can be built. These…

In this article, we share our learning experience as a Lesson Study team. The Research Lesson was on Figural Patterns taught in Year 7. In addition to helping students learn the skills of the topic, we wanted them to develop a problem-solving disposition. The management of these two objectives was a challenge to us. From the lesson observation and…

This paper demonstrates, following Vygotsky, that language and tool use has a critical role in the collaborative problem-solving behaviour of school-age children. It reports original ethnographic classroom research examining the convergence of speech and practical activity in children's collaborative problem solving with robotics programming…

I discuss a pedagogical strategy in which we ask students to write about science. Such writing is to be done regularly and often, in class and out of class, in the format of brief "letters to a friend" and longer essays. The goal of this technique is not to teach students how to write; it is to use their writing to help them learn the science.…

Knowledge sharing and transfer are essential for learning in groups, especially when group members have different disciplinary expertise and collaborate online. Computer-Supported Collaborative Learning (CSCL) environments have been designed to facilitate transactive knowledge sharing and transfer in collaborative problem-solving settings. This…

There are at least five different equivalent definitions of the absolute value concept. In instances where the task is an equation or inequality with only one or two absolute value expressions, it is a worthy educational experience for learners to solve the task using each one of the definitions. On the other hand, if more than two absolute value…

Means-end actions are an early-emerging form of problem solving. These actions require initiating initial behaviors with a goal in mind. In this study, we explored the origins of 8-month-old infants' means-end action production using a cloth-pulling training paradigm. We examined whether highlighting the goal (toy) or the means (cloth) was more…

The focus of the article is the validation of an instrument to assess gifted students' affect after mathematical problem solving tasks. Participants were 225 students identified by their district as gifted in grades four to six. The Chamberlin Affective Instrument for Mathematical Problem Solving was used to assess feelings, emotions, and…

This paper explores the relation between problem solving learning environments (PSLEs) and assessment concepts. The general framework of evidence-centered assessment design is used to describe PSLEs in terms of assessment concepts, and to identify similarities between the process of assessment design and of PSLE design. We use a recently developed…

Intellectual engagement is an absorbing, creatively energized focus resulting in a deep personal commitment to exploration, investigation, problem-solving and inquiry over a sustained period of time. In this article, the authors argue that participatory learning environments with a focus on knowledge building offer clear learning benefits to…

A better understanding of the basic mechanisms of the Problem-solving/Response to Intervention (PS/RtI) framework will help educators address students' diverse learning and behavioral needs. It will also help educators who may view PS/RtI as a compliance matter rather than an informative educational process that helps children reach their goals.…

Perceptual characteristics of mathematical equations may influence solvers' problem solving. For example, in a study of equations involving addition and multiplication, Landy and Goldstone (2010) showed that participants tended to perform narrowly spaced operations first, suggesting that spacing affects how symbols are grouped for problem solving.…

This paper describes the learning trajectory for Early Equations and Expressions (EELT), one of the 18 learning trajectories presented at www.TurnOnCCMath.net, developed to interpret the Common Core Standards for Mathematics based on research on student learning. The EELT is foundational for introducing concepts of early algebra and setting the…

Everyday financial dilemmas require us to draw on social, interdisciplinary, and mathematical understandings simultaneously and in synergy if we are to make informed financial decisions. Financial literacy is enjoying an elevated status across the "Australian Curriculum." This paper reviews some of the literature on financial literacy,…

When planning and teaching, attention is generally given to cognition while the effect of mood and emotion on cognition is ignored. But students are not emotionless thinkers and the effect can make a difference to their thought. This is particularly evident when attempting to foster creative thinking. This article draws on research to describe…