Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

The COVID-19 pandemic has affected student learning; according to the National Assessment of Educational Progress (2022), scores for students in the United States have shown a decline in mathematics. . One way educators can strengthen students' current mathematical knowledge and bridge to new content is through Number Talks. Number Talks are brief…

Students come to class with ideas about science content and the practices used to generate knowledge. Their lived experience provides them with basic ideas about how the world works. Tapping into their innate understandings and testing their ideas allows them to construct a more accurate understanding. Research shows that all students are ready to…

The ideas students bring to class and their perspectives on what is happening in the classroom change constantly. Keeping track of these changes is useful for adapting lessons, nurturing student self-reflection, increasing student ownership of learning, and building a teaching practice responsive to learners' needs. In this article, the authors…

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…

As teachers working with students in entry-level algebra classes, authors Amy Nebesniak and A. Aaron Burgoa realized that their instruction was a major factor in how their students viewed mathematics. They often presented students with abstract formulas that seemed to appear out of thin air. One instance occurred while they were teaching students…

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…

An operational understanding of the equal sign can hinder learning its relational meaning. After providing examples that illustrate the folly of expecting students who know the operational meaning of the equal sign to intuit the sign's relational meaning, this article provides teachers with strategies that will help them effectively introduce…

"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…

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…

The nature of science is a complex theme, and continues to be the subject of advanced and ongoing scholarship, drawing upon a range of disciplines. Therefore, whatever is presented in school science as being "the" nature of science must at best be a simplification, and so there is a need to form judgements about which simplifications are…

Since Widodo, Duit and Muller (2002) addressed that there is a gap between teacher's theoretical knowledge and their practical classroom constructivist behavior, we presented a sample teaching activity about Endothermic-Exothermic Reactions for teacher usage. Therein, the aim of this study is to design a 5E model to include students' alternative…

"Working Smarter, Not Harder: Reaching the Tough to Teach" is the topic of an exclusive four-part series by Sylvia Rockwell for the "Kappa Delta Pi Record." Part I describes the characteristics of students at risk of school failure, provides an overview of research-based principles found to be effective with all students and essential for students…

This book shows educators how to rethink teaching by challenging their beliefs about knowledge and learning. It helps teachers organize for student learning rather than plan for teacher telling by applying constructivist learning theory in the classroom. It presents a constructivist perspective on how to arrange classroom events for student…

Examines the development of students' understandings about fractions during six weeks of instruction. Reports that all students possessed informal knowledge disconnected from their knowledge of fraction symbols and procedures and that knowledge of rote procedures often interfered with students' attempts to build on their informal knowledge.…