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…

Science and engineering practices (SEPs) and crosscutting concepts (CCs) constitute a significant part of "A Framework for K-12 Science Education" (NRC 2012). As teachers, the role of the authors is to highlight the pivotal role that both scientific knowledge and the practices used to generate knowledge play in learning. This article…

Early understanding of base-10 concept has been shown to be associated with superior mathematical achievement among East Asian children. In addition to their base-10 structured number system, teacher support in kindergarten is also crucial to children's development of this complex mathematical concept. Therefore, this study examined how Japanese…

The concrete-representational-abstract (CRA) approach is an instructional framework for teaching math wherein students move from using concrete materials to solve problems to using visual representations of the materials, and finally abstract concepts. This study provides a literature synthesis and meta-analysis of the effectiveness of the CRA…

We describe here lessons learned in designing an early algebra curriculum to measure early algebra's impact on children's algebra readiness for middle grades. The curriculum was developed to supplement regular mathematics instruction in Grades K-5. Lessons learned centered around the importance of several key factors, including using conceptual…

Fostering students' bidirectional conception of the equal sign (viewing the equal sign as indicating an equivalence of two sides rather than a 'show result' symbol) is challenging, and students' misconception of the equal sign is persistent. Some studies mention that in China, the pedagogical approach to introducing the equal sign supports…

"Productive Uncertainty in Science Education" provides the support that teachers and students need for more complex science investigations. Science is driven by the need to manage uncertainty--uncertainty about how to explain the world, but also how to represent the world in an investigation, what to measure, and how to convince peers to…

This article focuses on an approach to the concept of historical time in early childhood education through the lens of cognitive psychology. It consists of three parts: (1) theoretical approaches, inspired by three broad scientific fields -- cognitive psychology, pedagogy and history; (2) the presentation of educational examples, formed by…

This study investigated the noticing of teachers who teach mathematics at different grade levels in the context of lesson study. The study specifically focused on teachers' noticing during the planning phase of the lesson. For this, the lesson planning phase of a group of four teachers consisting of kindergarten and primary school 1st grade…

How are religiously based eating regulations navigated in kindergarten, and how does the pedagogical context influence the children's understandings of religion and nationality? This article builds on a qualitative case study involving observations and group interviews with children in a Norwegian kindergarten. At mealtimes, some children ate…

Knowledge of conservation and conflict resolution is crucial for young children's academic and socio-emotional success. Dialogic instruction implemented in kindergarten classrooms is essential for young children's cognitive development and problem-solving abilities. Storybooks incorporate content knowledge and real-life experiences enhance…

The following paper continues the previous part, and examines the influence of crystallography on Fröbel's conception of mathematics. In this part we focus on yet unpublished material. These unpublished notes of Fröbel underline the visual transfer of drawing and images of crystals, mainly developed by Haüy, which were widespread at the turn of…

Equivalence is a concept that comes up across the entire K-12 grade span and in many different areas of mathematics. Students who are bureaucratically designated as "English Learners" can explore equivalence across their K-12 academic careers while developing language to connect ideas. Drawing on what is known generally from theory and…

This article examines the mathematical activity of five-year-old Liam to explore the difference between the mathematics games designed for children and the children's games that emerge through playful activity. We propose that this distinction is a salient one for teachers observing mathematical play for evidence of mathematical sense making.

Friedrich Fröbel is known as the founder of the modern kindergarten and for his development of novel learning materials called Gifts and Occupations. One of the foci of Fröbel's programme was mathematical education, which he addressed and taught through various activities that encouraged the largely implicit transmission of mathematical…