This study aims at exploring processes of flexibility and coordination among acts of visualization and analysis in students' attempt to reach a general formula for a three-dimensional pattern generalizing task. The investigation draws on a case-study analysis of two 15-year-old girls working together on a task in which they are asked to calculate…

In the western half of the United States, fire bombers are not an uncommon sight. During the "fire season," which can extend from June through November, these specially modified aircraft are used to drop fire retardant chemicals or water on wildfires. It can be an entertaining and instructive classroom exercise to use pictures of these…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

When thinking of models for sinusoidal waves, examples such as tides of the ocean, daily temperatures for one year in your town, light and sound waves, and certain types of motion are used. Many textbooks [1, p. 222] also present a "Ferris wheel description problem" for students to work. This activity takes the Ferris wheel problem out of the…

Engineering is prominently included in the "Next Generation Science Standards" (Achieve Inc. 2013), as it was in "A Framework for K-12 Science Education" (NRC 2012). The National Research Council, authors of the "Framework," write, "Engineering and technology are featured alongside the natural sciences (physical…

National Council of Teachers of Mathematics' (NCTM's) (2000) Connections Standard states that students should "recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect ...; [and] recognize and apply mathematics in contexts outside of mathematics" (p. 354). This article presents an in-depth…

Having returned to teaching the basics of pricing fixed-income securities after several years, the author recalls the difficulty students have in understanding the total return provided by fixed-income securities that are purchased at either a discount or premium from face value. This teaching note attempts to clarify the concept by suggesting…

This study attempts to determine if authentic learning strategies can be used to acquire knowledge of and increase motivation for computational thinking. Over 600 students enrolled in a computer literacy course participated in this study which involved completing a pretest, posttest and motivation survey. The students were divided into an…

This study explores the utility of a set of tablet-based personal computers in the K-12 science, technology, engineering, and mathematics classroom. Specifically, a lesson on food-chain dynamics and predator-prey population controls was designed on the Apple® iPad platform and delivered to three sophomore-level ecology classes (roughly 30 students…

This is the second of three articles that draw on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation". The report was soundly based on research about how children learn mathematics, much of it done in the UK in the '80s. Most of the findings about algebra are very…

Cosmic ray count rates with a set of portable Geiger counters were measured at different altitudes on the way to a mountain top and aboard an aircraft, between sea level and cruise altitude. Basic measurements may constitute an educational activity even with high school teams. For the understanding of the results obtained, simulations of extensive…

Advances in technology have caused high schools to update their computer science curricula; however there has been little analogous attention to technology-related education in middle schools. With respect to computer-related knowledge and skills, middle school students are at a critical phase in life, exploring individualized education options…

A common textbook problem asks students to calculate the total distance traveled by a bouncing ball, from its initial release until it comes to rest, under the assumption that the height of each bounce is some fixed proportion "r" of the height of the previous bounce. The solution is found by inserting information about "r" and the height from…

Now in a fully updated second edition, "Unlocking Mathematics Teaching" is a comprehensive guide to teaching mathematics in the primary school. Combining theory and practice, selected experts outline the current context of mathematics education. They suggest strategies, activities and examples to help develop readers understanding and confidence…

Sampling, very generally, is the process of learning about something by selecting and assessing representative parts of that population or object. In the inquiry activity described here, students learned about sampling techniques as they estimated the number of trees greater than 12 cm dbh (diameter at breast height) in a wooded, discrete area…