As part of the discussion about Newton's work in a history of mathematics course, one of the presentations calculated the amount of energy necessary to send a projectile into deep space. Afterwards, the students asked for a recalculation with two changes: First the launch under study consisted of a single stage, but the students desired to…

In the present study, the authors investigated the initial development of the Early Expository Comprehension Assessment (EECA) by examining its reliability. The EECA consists of a compare/contrast passage, manipulatives to represent the information in the paragraph, and three response tasks ("Retelling, Mapping, and Comparing"). The authors…

Campbell's rule for estimating entropy changes is discussed in relation to an earlier article by Norman Craig, where it was proposed that the approximate value of the entropy of reaction was related to net moles of gas consumed or generated. It was seen that the average for Campbell's data set was lower than that for Craig's data set and…

The preliminary findings resulting when invented algorithm is used with entry-level students while introducing linear equations is described. As calculations are accessible, the algorithm is preferable to more rigorous statistical procedures in entry-level classrooms.

Range-based estimation is used when working with young children in two distinct mathematical environments, which are the Family Math environment and the classroom setting. The types of estimation activities discussed help students of different ages develop a sense of number, size, and quantity.

Before primitive man had grasped the concept of number, the written word or even speech, he was able to count. This was important for keeping track of food supplies, sending messages, trading between villages and even keeping track of how many animals were in their herd. Counting was done in various ways, but in all cases, the underlying principle…

Investigating the relationship between fractions and their equivalent decimal representations helps clarify to students that both representations stand for a single (rational) number on the number line. Since students are taught to perform computations with fractions and also to compute with decimals, performing these computations side-by-side…

Sample size recommendations in confirmatory factor analysis (CFA) have recently shifted away from observations per variable or per parameter toward consideration of model quality. Extending research by Marsh, Hau, Balla, and Grayson (1998), simulations were conducted to determine the extent to which CFA model convergence and parameter estimation…

In this article, I survey the integrated connectionist/symbolic (ICS) cognitive architecture in which higher cognition must be formally characterized on two levels of description. At the microlevel, parallel distributed processing (PDP) characterizes mental processing; this PDP system has special organization in virtue of which it can be…

If the point of suspension of a multiple pendulum is suitably oscillated then the pendulum can remain in motion in an upside-down position. Since such pendulums can model flexible materials, this inverted motion is sometimes referred to as an 'Indian rope trick'. Despite the complexity of the governing differential equations, this rope trick can…

The telescoping sum constitutes a powerful technique for summing series. In this note, this technique is illustrated by a series of problems starting off with some simple ones in arithmetic, then some in trigonometry, famous families of numbers, Apery-like formulas, and finally ending with a class of problems that are solved by computer.

Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.

In this note the well-known Lagrange identity is extended to matrices. The resulting generalized Lagrange identity is used to give characterizations of symmetry, commutativity of projectors and normality.

The mean and variance of the number of turning points in random permutations of two kinds of distinct elements are evaluated. These results are applied to a Wald-Wolfowitz run test.

Research indicates that children do not typically understand the connection between counting and cardinality for several months after learning to count, yet parents speak to 3-year-olds as though they already understood the significance of counting. The present research was designed to investigate mothers' awareness of the discrepancy between…