At the heart of the debate about the place of standard arithmetic algorithms is the practice of teaching subtraction through decomposition. One welcome feature of the national numeracy strategy in both its initial and current incarnations has been the introduction of a focus upon a variety of mental strategies supported by jottings. In this…

Mathematical computation consists of both written computation and mental computation. The strategies for mental computation can be used to check the reasonableness of written computations. Mental computation has two distinguishing characteristics: "it produces an exact answer, and the procedure is performed mentally, without using external…

Within the framework of a laboratory-focused, guided-inquiry pedagogy, students discover the Nernst equation, the spontaneity of galvanic cells, concentration cells, and the use of electrochemical data to calculate equilibrium constants. The laboratory experiment we describe here is a continuation of curriculum reform and pedagogical innovation at…

This article describes an activity that can be performed with an inexpensive plastic toy popper. The activity builds skill at analysing motion and results in the calculation of a surprisingly extreme acceleration. (Contains 1 figure.)

In this article we provide two detailed examples of how we incorporate biological examples into two mathematics courses: Linear Algebra and Ordinary Differential Equations. We use Leslie matrix models to demonstrate the biological properties of eigenvalues and eigenvectors. For Ordinary Differential Equations, we show how using a logistic growth…

Mobile synchronous learning is a new challenge in the e-learning domain. While popular mobile communication devices, such as cell phones, cannot directly accommodate traditional synchronous content due to the major limitation of display size, other constraints also restrict convenient interactions while using mobile devices in a synchronous…

Choosing mental, written, or calculator procedures is important for children to learn. Children should be encouraged to be flexible and consider alternatives when doing mental calculation. Developing mental skills, symbols and rules, and numbers in context are each considered. (MNS)

A simplified model of an industrially relevant fluid-particle flow system is analyzed using linear stability theory. Instabilities of the uniform state of a fluidized bed are investigated in response to small flow perturbations. Students are expected to perform each step of the computational analysis, and physical insight into key mechanistic…

The present study focused on two main goals. One was to test the "representational mapping hypothesis": The greater the transparency of the mapping between physical materials and desired internal representations, the greater the learning of the desired internal representation. The implication of the representational mapping hypothesis in the…

Everyday, people face situations that call for adding, subtracting, multiplying, or dividing, and at least half of the time, these calculations are accomplished without the use of pen, paper, or calculators. Because figuring "in your head" is such an important life skill, it should have a regular role in classroom math teaching. This article…

Two mental algorithms, one for addition and one for subtraction, are described. It is felt such algorithms should be taught explicitly. The usual process taught for paper and pencil is seen to inhibit mental arithmetic, and a need to include mental algorithms in the regular mathematics curriculum is promoted. (MP)

Included in this section are brief articles outlining an approach to teaching mental computation, an inductive approach to algebra, and using football to teach probability. (MNS)

Focuses on mental strategies for computing in the middle grades. Describes what they are and why they are important. Refers to relevant research and presents some teaching ideas for developing these strategies beyond the primary grades. Includes a discussion of the role of mental calculation in everyday life both past and future. Contains 27…

The aim of this study is to evaluate the benefit of chess in mathematics lessons for children with learning disabilities based on lower intelligence (IQ 70-85). School classes of four German schools for children with learning disabilities were randomly assigned to receive one hour of chess lesson instead of one hour of regular mathematics lessons…

This experiment, designed for a general chemistry laboratory, illustrates the use of Dalton's law of partial pressures to determine the vapor pressure of a volatile liquid. A predetermined volume of air is injected into a calibrated tube filled with a liquid whose vapor pressure is to be measured. The volume of the liquid displaced is greater than…