As they prepared for the 2016-2017 school year, administrators and teachers at Design Tech High School ("d.tech"), a public charter school in Northern California, decided they needed a deeper understanding of how students learn. According to Nicole Cerra, Director of Learning, "Obviously you need to get to know students…

Identification and development of giftedness is a major task of mathematics teachers worldwide. An early identification of gifted children in mathematics can have a number of benefits, like, providing opportunities for the nourishment of their talent, saving them from burnout, and proper utilisation of mathematical talent in future. As creativity…

This article is an attempt to tell the story of action research as it has developed over the last half century. Action research has become an important part of a number of research programs, especially in the field of education. Action research is a powerful idea centering on humans' ability to break free from deleterious social habits…

"A cage-buster can't settle for ambiguity, banalities, or imprecision," writes well-known educator and author Rick Hess. "These things provide dark corners where all manners of ineptitude and excuse-making can hide." Hess suggests that leaders need to clearly define the problems they're trying to solve and open…

More is known now than ever about the range and nature of alternate conceptions that children hold, but educators are not yet sure of the best way to support effective development of children's scientific understanding. The coherence of science as perceived by the student matters in learning. That is, what the child brings to a learning task can…

An industrial-type distillation column, including appropriate pumps, heat exchangers, and automation, was used as a unit operations experiment to provide a link between classroom teaching and real-world applications. Students were presented with an open-ended experiment where they defined the testing parameters to solve a generalized problem. The…

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…

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.…

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…

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.…

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…

There has been a major shift in educational learning goals--as seen most recently by Goal 4.7 of the Sustainable Development Goals--focused on global citizenship education and education for sustainable development. The shift concerns recognition of the need for education systems to equip learners with competencies such as problem solving,…

This is mathematics in action, in context, in real life, and in detail. Begin the journey with Archimedes, and travel alongside the likes of Fermat, Fibonacci, Coxeter, and Adler. There is much to consider and opportunities to make links to things that might be "known", but maybe not well appreciated. On the way you will come across an angular…

As with so many aspects of mathematical enquiry, there is little that is "original", or "brand new", but that does not diminish the outcome of work that borrows from "those who have gone before". In this piece the author "borrows" from the work of Desargues, Monge, Ceva, Menelaus, van Aubel, and Gergonne. This novel approach to providing a proof…