Approximate mathematical treatments are commonly taught in undergraduate chemistry, but the validity ranges of these approximations have rarely been properly defined. We present error contour plots of commonly used quadratic approximations for calculating equilibrium proton concentrations of monoprotic acids. Students and instructors can easily…

By analysis of student use of mathematics in responses to conceptual physics questions, as well as analogous math questions stripped of physical meaning, we have previously found evidence that students often enter upper-level physics courses lacking the assumed prerequisite mathematics knowledge and/or the ability to apply it productively in a…

Middle school students need to know about energy concepts and how they can reduce their energy use. New energy-monitoring tools provide powerful opportunities for students to engage in authentic investigations rich in the science practices described in "A Framework for K-12 Science Education" (NRC 2012), while at the same time advancing their…

This study examined the written work of students in the introductory calculus-based electricity and magnetism course at the University of Arkansas. The students' solutions to hourly exams were divided into a small set of countable features organized into three major categories, mathematics, language, and graphics. Each category was further divided…

Students at the middle school level are expected to use appropriate tools and techniques, including mathematics and graphing, to analyze and interpret data and communicate experimental findings. Measures of central tendency (mean, median, and mode--see sidebar for definitions) are often used as descriptive statistics when students conduct…

Describes a continuous sequence of development of arithmetical and ratio reasoning capacity which very few students now attain in introductory science courses. Sequence progresses from verbal interpretation of ratio of two numbers, to arithmetical reasoning involving division, coupling arithmetical reasoning to graphical representation, and to…

Describes a series of activities without conclusions to introduce scientific reasoning in a ninth grade physical science course. Uses popcorn popping to get students to think about the concepts of graphing, histograms, frequency, probability, and scientific methodology. (CW)

Introduces an activity that involves nature transects and requires students to use their process skills. Indicates the possible use of transects for student evaluation and examines the implementation of transects in the elementary curriculum in a multidisciplinary approach. Provides details of the activity. (YDS)