The world of man-made design is all around, in everyday objects and appliances people use without a second thought. In this exercise, students have an opportunity to challenge the common refrigerator's design--and improve it. This approach can be used with many other appliances.

Writing is an important content area that pervades all subject areas and is required for post-school success, yet many students with autism spectrum disorders (ASD) often struggle in written expression. In this article we discuss the characteristics of students with ASD that make writing difficult, and the strengths, such as the use of technology,…

Individuals' perceptions of their own level of cognitive ability are expressed through self-estimates. They play an important role in a person's self-concept because they facilitate an understanding of how one's own abilities relate to those of others. People evaluate their own and other persons' abilities all the time, but self-estimates are also…

This guide attempts to address an aspect of secondary CTE (Career and Technical Education) that has received little attention; the assessment literacy of educators. School leaders need to go beyond ensuring routine compliance with external and internal regulatory forces to identify ways in which CTE program teachers might better understand…

The King-Altman method of deriving rate equations for enzymatic reactions is applied to the derivation of the Michaelis-Menten equation, along with an explanation for how (or why) the King-Altman method works in this case. The slightly more complicated cases of competitive inhibition and a two-substrate enzyme-catalyzed reaction are then treated…

This classroom note is presented as a suggested exercise--not to have the class prove or disprove Goldbach's Conjecture, but to stimulate student discussions in the classroom regarding proof, as well as necessary, sufficient, satisfied, and unsatisfied conditions. Goldbach's Conjecture is one of the oldest unsolved problems in the field of number…

Young adult literature (YAL) is one of the most engaging and effective tools to promote the goal of lifelong literacy for middle and high school students. This article addresses the stakes of exploring--or failing to explore--common perceptions and misperceptions of YAL. Readers' lives as family members, consumers, and students play roles in their…

Transformations are a central organizing idea in geometry. They are included in most geometry curricula and are likely to appear with even greater emphasis in the future, given the central role they play in the "Common Core State Standards" for K-12 mathematics. One of the attractions of geometry is the ability to draw and construct the…

In the elementary grades, students learn procedures to compute the four arithmetic operations on multidigit whole numbers, often by being shown a series of steps and rules. In the middle grades, students are then expected to perform these same procedures, with further twists. The Reasoning and Proof Process Standard suggests that students need to…

In this article, the authors show how students can form familiar geometric figures on the calculator keypad and generate numbers that are all divisible by a common number. Students are intrigued by the results and want to know "why it works". The activities can be presented and students given an extended amount of time to think about…

This article reports findings from a multi-year study of teachers' conceptual change coincident with the development of instructional expertise among teachers involved in educational reform efforts in schools in Santiago, Chile. Conceptual change in teachers is important because recent research indicates that students of teachers who function at…

In this article, we suggest an instructional intervention to help students understand statements involving multiple quantifiers in logical contexts. We analyze students' misinterpretations of multiple quantifiers related to the epsilon-N definition of convergence and point out that they result from a lack of understanding of the significance of…

In this article, we discuss the importance of measurement literacy and some issues encountered in teaching introductory measurement courses. We present results from a survey of introductory measurement instructors, including information about the topics included in such courses and the amount of time spent on each. Topics that were included by the…

Dimensional analysis is a simple, clear and intuitive method for determining the functional dependence of physical quantities that are of importance to a certain process. However, in physics textbooks, very little space is usually given to this approach and it is often presented only as a diagnostic tool used to determine the validity of…

The goal of this practice guide is to offer educators specific, evidence-based recommendations that address the challenge of teaching early math to children ages 3 to 6. The guide provides practical, clear information on critical topics related to teaching early math and is based on the best available evidence as judged by the authors. The guide…