Do young children understand the complex mathematics in the petals of a daisy, the Fibonacci sequence in the spiral of a pinecone, the fractal geometry in the leaves of a fern, or the "golden ratio" in the seed pattern of a sunflower? Probably not, but they certainly can observe and recognize the patterns and compare them to similar…

Freedom is a basic human desire. It is a central idea behind historic human rights movements and a sign of human flourishing. In this article, the author highlights five freedoms that are central to doing mathematics: (1) The freedom of knowledge; (2) The freedom to explore; (3) The freedom of understanding; (4) The freedom to imagine; and (5) The…

Studies indicate thoughtfully planned chants integrated with shared book reading help young children remember concepts and vocabulary they hear in literature, capture children's imagination, develop their rhyming acuity, and background knowledge, and increase their sense of story structure, understanding of story sequence, phonological awareness,…

This paper presents a new theoretical model of creative imagination and its applications in early education. The model sees creative imagination as composed of three inter-related components: vividness of images, their originality, and the level of transformation of imageries. We explore the theoretical and practical consequences of this new…

How can physics teachers help students develop consistent problem solving techniques for both simple and complicated physics problems, such as those that encompass objects undergoing multiple forces (mechanical or electrical) as individually portrayed in free-body diagrams and/or phenomenon involving multiple objects, such as Doppler effect…

Critical thinking pedagogy is misguided. Ostensibly a cure for narrowness of thought, by using the emotions appropriate to conflict, it names only one mode of relation to material among many others. Ostensibly a cure for fallacies, critical thinking tends to dishonesty in practice because it habitually leaps to premature ideas of what the object…

Imagination is a powerful engine that can drive people to bring their ideas, dreams, and desires to reality. The imagination constructs stories that lead people to create. Combining imagination with engineering knowledge creates inventions which initially might seem fantastic. The authors provide in this article a brief overview of a successful…

Over her 23 years of teaching elementary school, Vera, a third grade teacher (and co-author of this article), had often fallen into the familiar rhythm of the fall social studies curriculum, with its predictable narrative of discovery, bravery, heroism, and thanksgiving. Her journey to becoming a more reflective, thoughtful, and equitable teacher…

Picture books are often seen as a valuable tool for younger readers. In this article, the author suggests that the multiple literacies required to read a picture book can provide scaffolding and transmission of additional concepts for older readers.

Presents a short biography of one of the winners of the American Psychological Association's Award for Distinguished Scientific Early Career Contributions to Psychology (2012). Thomas L. Griffiths won the award for bringing mathematical precision to the deepest questions in human learning, reasoning, and concept formation. In his pioneering work,…

This essay employs the images and voices of children to describe how their learning about the world is supported as they engage in experiences that invoke creativity and imagination. The author states his belief that this "imagining," this giving body and substance to the nature of "imagination" is one of the foundations of knowing, a means of…

The international trend to increase the cognitive achievement of early childhood children has generated a need for better understanding how concept formation occurs within play-based programs. Yet the theories of play for supporting early childhood professionals were originally not conceptualized with this need in mind. In this article, concepts…

Stories that are presented through literature or popular media can be used to invite students into the world of math; stir their mathematical imaginations; and enhance their ability to read about, write about, and discuss math. This article explores how literature ("Flatland," the book and the movie) and an existing seventh-grade unit…

We introduce Lesson Play as an imaginary interaction between teacher and students presented in a form of a dialogue or play. We suggest that lesson plays are a valuable professional development tool in preparing for teaching that can be juxtaposed with, or used as a replacement for, traditional lesson planning. The article begins with an…

In the context of learning theories the problem of the passage from the psychological dimension governed by images to the "scientific" dimension dominated by concepts needs to be reformulated. The starting point of the question should be recognition that at a "deep" level, between the two dimensions, there is a bridge, the design of which can be…