The paper discusses an elementary spring model representing the motion of a magnet suspended from the ceiling at one end of a vertical spring which is held directly above a second magnet fixed on the floor. There are two cases depending upon the north-south pole orientation of the two magnets. The attraction or repelling force induced by the…

The inability to develop, strengthen, and access associations in memory that allow for the rapid and accurate retrieval of answers to basic addition problems is a distinguishing characteristic of a mathematics learning difficulty. The "two-factor theory of math fact learning" (Robinson, Menchetti, & Torgesen, 2002) proposes that a weakness in…

A structural equation modeling approach to scale reliability evaluation can be employed to estimate generalizability theory indexes in settings where sampling of subjects and conditions is carried out. In one- and two-facet crossed designs, it is demonstrated how this method can be used to obtain estimates of relative generalizability…

The sequence 1, 1, 2, 3, 5, 8, 13, 21, ..., known as Fibonacci sequence, has a long history and special importance in mathematics. This sequence came about as a solution to the famous rabbits' problem posed by Fibonacci in his landmark book, "Liber abaci" (1202). If the "n"th term of Fibonacci sequence is denoted by [f][subscript n], then it may…

For 137 years Markovnikov's rule has been extensively used in organic chemical education and research to describe the regioselectivity in electrophilic addition reactions to alkenes and alkynes. When the structures of the final reaction products are used as reference, the rule requests that certain polar addition reactions be termed…

In the nineteenth century many people tried to seek a value for the most famous irrational number, [pi], by means of an experiment known as Buffon's needle, consisting of throwing randomly a needle onto a surface ruled with straight parallel lines. Here we propose to extend this experiment in order to evaluate other irrational numbers, such as…

An analytical approach was employed to compare sensitivity of causal effect estimates with different assumptions on treatment noncompliance and non-response behaviors. The core of this approach is to fully clarify bias mechanisms of considered models and to connect these models based on common parameters. Focusing on intention-to-treat analysis,…

A study examined 60 adult students' informal knowledge of percent and its relationship to their formal computational skills. The students studying in adult education programs were interviewed to ascertain the following: (1) their ideas of the meanings of three benchmark percentages--100, 50, and 25 percent--as they appear in advertising and media…

This paper presents research conducted as part of the field test of the University of Chicago School Mathematics Project's (UCSMP) curriculum, Fifth Grade Everyday Mathematics. The UCSMP curriculum is one of the current reform programs funded by the National Science Foundation to implement the Standards of the National Council of Teachers of…

This activity guide is a supplement to the November 1996 issue of the National Council of Teachers of Mathematics Student Math Notes. It contains a series of problems based on one main story problem. Using this problem and the other problems contained in the guide based on it, students explore different mathematical concepts such as graph theory,…

This study examined adult students' informal knowledge of percent and its relationship to their computational skills. Sixty adults studying in urban and suburban adult education programs were interviewed to ascertain: (1) their ideas of the meanings of benchmark percents, 100%, 50%, and 25%, as they appear in advertising and media contexts; (2)…

Multi-line-multi-operation calculators such as the TI-80 provide eighth-grade prealgebra and algebra students with significantly better computational tools for basic order-of-operation problems involving integers and signed rational numbers than do calculators offering only last-entry-or-result displays. Effects are more apparent for weaker…

This paper presents a detailed derivation of method of moments estimates used in computer programs for the four-parameter beta compound binomial strong true score model. A procedure is presented to deal with the case in which the usual method of moments estimates do not exist or result in invalid parameter estimates. The results presented…

This generic science education study demonstrates the contrast of findings obtained through analyzing all the raw data as opposed to removing various combinations of identified potential outliers provided through the application of six diagnostic procedures. Outliers are defined as extreme data points with large residuals. It is argued that an…

Though cognitive science has given psychology a new, more detailed and specific way of expressing models of cognition, correspondingly detailed and precise arguments analyzing and supporting those models have not been forthcoming. Consequently, the new models often fail to meet the traditional criteria of scientific theories. Tools are available…