An important step in learning to use math in science is learning to see symbolic equations not just as calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and of organizing physics knowledge structures. In this paper, I propose "anchor equations" as a…

Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification--that physical quantities can be assigned specific numbers (with a unit). A second is to develop an intuition for…

North Korea's development of nuclear weapons and, more recently, intercontinental ballistic missiles (ICBMs) has added a grave threat to world order. The threat presented by these weapons depends critically on missile range, i.e., the ability to reach North America or Europe while carrying a nuclear warhead. Using the limited information available…

Professional problem-solving practice in physics and engineering relies on mathematical sense making--reasoning that leverages coherence between formal mathematics and conceptual understanding. A key question for physics education is how well current instructional approaches develop students' mathematical sense making. We introduce an assessment…

Science students should use mathematical and computational thinking to explain phenomena, but few examples of teachers engaging students in this important scientific practice have been found. This article describes a strategy for enhancing a lesson in which students use a mechanistic model to explain friction by adding mathematical and…

Many students struggle with the use of mathematics in physics courses. Although typically well trained in rote mathematical calculation, they often lack the ability to apply their acquired skills to physical contexts. Such student difficulties are particularly apparent in undergraduate electrodynamics, which relies heavily on the use of vector…

The branch of biology that studies ecosystems, habitats, their developments, and the equilibrium of species is called conservation biology (Soule 1986). It is important to study this balance of species within an ecosystem, where species might live for a short period of time (such as mosquitoes, the main source of food for frogs) or live for…

"The Language of Mathematics in Science" is an ASE/Nuffield project aimed at supporting teachers of 11-16 science in the use of mathematical ideas in the science curriculum. Two publications have been produced. This article focuses on the first of these, "The Language of Mathematics in Science: A Guide for Teachers of 11-16…

The terms "concreteness fading" and "progressive formalization" have been used to describe instructional approaches to science and mathematics that use grounded representations to introduce concepts and later transition to more formal representations of the same concepts. There are both theoretical and empirical reasons to…

A simple activity using cheap and readily available materials is described that allows students to experience first hand many of the concepts of measurement, uncertainty and graph drawing without laborious measuring or calculation. (Contains 9 figures.)

Observing the way a watering hose is wrapped on a rotating cylinder, a catenary shape is detected for the suspended portion of the hose. We calculate the angle [alpha] the tangent to the curve at the highest point of the suspended portion makes with the horizontal. By means of this quantity, the length of the suspended and dragged portions of the…

The present study examined whether multiple opportunities to learn math were associated with smaller socioeconomic status (SES) disparities in fifth-grade math achievement using data from the NICHD Study of Early Child Care and Youth Development (SECCYD; N = 1,364). High amounts of procedural math instruction were associated with higher…

We study different ways of determining the mean distance (r[subscript n]) between a reference point and its nth neighbour among random points distributed with uniform density in a D-dimensional Euclidean space. First, we present a heuristic method; though this method provides only a crude mathematical result, it shows a simple way of estimating…

Students need to achieve automaticity in learning mathematics without sacrificing conceptual understanding of the algorithms that are essential in being successful in algebra and problem solving, as well as in science. This research investigated the relationship between science-contextualized problems and computational fluency by testing an…

In earlier columns, the celestial coordinate system of hour circles of right ascension and degrees of declination was introduced along with the use of an equatorial star chart (see SFA Star Charts in Resources). This system shows the planets' motion relative to the ecliptic, the apparent path the Sun follows during the year. An alternate system,…