When exposed to principal components analysis for the first time, students can sometimes miss the primary purpose of the analysis. Often the focus is solely on data reduction and what to do after the dimensions of the data have been reduced is ignored. The datasets discussed here can be used as an in-class example, a homework assignment, or a…

This chapter focuses on the development of concepts that children draw on as they work toward understanding negative numbers. Framed from a conceptual change lens, I discuss different interpretations children have of minus signs, numerical order, numerical values, and addition and subtraction operations and how children draw on these varied…

Literature on learning trajectories is reviewed, and challenges in developing designs to support responsive instruction are highlighted. A distinctive form of design called a "multi-dimensional instructional framework" is introduced. These frameworks span key dimensions of mathematisation, such as notating and distancing the setting,…

Mathematical modeling involves using mathematics to represent, analyze, and make predictions or decisions about real- world situations. Garfunkel and Montgomery (2016) elaborate on six components of the mathematical modeling process, including identifying the problem, making assumptions and identifying variables, doing the math, analyzing and…

A Common Core expectation of high school mathematics students is to analyze functions using different representations. One type of function to be analyzed is piecewise-defined functions. The author has found most approaches to the study of piecewise functions to be abstract, disconnected from any context, and difficult for students to understand.…

Practical problem solving is not common in many mathematical classes in Malaysian upper secondary schools. Usually, students receive the mathematical concepts through abstract materials (students cannot see some of them in their daily life). Thus some students believe that 'mathematics is not necessary for human life'. In this article, the…

Scientists understand that no result is more important than the welfare of the investigators and the people around them. Safety culture is an integral part of industrial and academic jobs; however, safety training has only recently been added to chemistry classroom and laboratories. Chemistry laboratories expose workers to a variety of hazards,…

In this article, Fishbone-based advanced computational thinking (FACT) pedagogy is proposed by fusing fishbone pedagogy and computational thinking pedagogy for enhancing teaching-learning process while teaching engineering and science courses, for engineering and science students respectively. The proposed FACT pedagogy has been implemented using…

Technology and Engineering Education (T&EE) includes "engineering design challenges" to establish a connection to designing and problem-solving indicative of being an Engineer. Engineering design challenges involving bridges (or towers) have been a common feature of the discipline. These bridge design challenges ask students to…

What do people need to learn to engage actively in social action for neighbourhood improvement or development? How important is emergent learning relative to planned learning in this context? Where does first-person knowledge fit into the body of knowledge required for success in bringing about change for the better in neighbourhoods through…

In this article, the authors introduce the "Pre-K-12 Guidelines for Assessment and Instruction in Statistics Education II (GAISE II): A Framework for Statistics and Data Science Education" report. This report, which was published by the American Statistical Association (ASA) and endorsed by the National Council of Teachers of Mathematics…

The National Council of Teachers of Mathematics (NCTM 2014) takes a clear stance that each and every student should have rich experiences in mathematics classrooms. In 2015, the Every Student Succeeds Act noted that Universal Design for Learning (UDL) is an evidence-based, scientifically valid framework that fosters access to instruction for all…

Guided-inquiry experiments are an important tool for helping students develop scientific practices such as hypothesizing and problem solving. In organic chemistry, these types of experiments can help students learn how to connect the theory of the reaction to the observation and data to decide how the reaction is proceeding or if it needs…

In response to increasing teacher interest in how to design and implement effective challenging tasks, James presents the Launch/Explore/Discuss model that builds on the work of leading Australian educators and researchers Peter Sullivan, Doug Clarke, and Charles Lovitt.

Space is a key area of science that is often taught in year 5 (ages 9-10) in English schools and related to this is gravitational force. Almost without exception children enjoy learning about the solar system and beyond. This article introduces a series of activities for children to explore the formation of impact craters in the solar system. The…