The study of student error, important across many fields of educational research, has begun to attract interest in the field of e-learning, particularly in relation to usability. However, it remains unclear when errors should be avoided (as usability failures) or embraced (as learning opportunities). Many domains have benefited from taxonomies of…

Vieta's famous product using factors that are nested radicals is the oldest infinite product as well as the first non-iterative method for finding [pi]. In this paper a simple geometric construction intimately related to this product is described. The construction provides the same approximations to [pi] as are given by partial products from…

Three-year-olds were given a search task with conflicting cues about the target's location. A ball rolled behind a transparent screen and stopped behind one of four opaque doors mounted into the screen. A wall that protruded above one door provided a visible cue of blockage in the ball's path, while the transparent screen allowed visual tracking…

Students are often told to use representations to solve mathematics problems, yet it may be a hindrance for many. This article contains an approach, the Graphic Representational Analysis Process, that teachers can use to analyze representations and focus future instruction. (Contains 7 figures.)

I report on the findings from research and literature on (a) use of symbols in mathematics, (b) algebraic/trigonometric expressions, (c) solving equations, and (d) functions and calculus. From these, some insights and implications for teaching and learning are derived.

Many students, with and without disabilities, experience difficulty reaching an appropriate level of reading fluency even though they may attain an appropriate level of reading accuracy. The National Reading Panel (2000) found that students who lack reading fluency often lack reading comprehension also. Other students lack the necessary strategies…

Errors made by language learners in learning a language are regarded as failure of competence. Linguists believe that errors are committed when the learner makes use of the learning strategies. By analyzing the learner's errors, we can better understand his inter-language and his learning process. It's necessary to understand the roots of errors…

Mathematical software packages such as Polymath, MATLAB, and Mathcad are currently widely used for engineering problem solving. Applications of several of these packages to typical chemical engineering problems have been demonstrated by Cutlip, et al. The main characteristic of these packages is that they provide a "problem-solving environment…

In this essay, the author tries to look forward into the 21st century to divine three things: (i) What skills will researchers in the future need to solve the most pressing problems? (ii) What are some of the most likely candidates to be those problems? and (iii) What are some current areas of research that seem mined out and should not distract…

Narrow Window theory, suggested by Y. Kareev ten years ago, has so far focused on one central implication of the limited capacity of working memory on intuitive correlation estimation, namely, overestimation of the distal population correlation. This paper points to additional and perhaps more dramatic implications due to the large dispersion of…

The extensive computational and formatting capabilities of today's spreadsheets enable users to create sophisticated analytical models with professionally formatted outputs. But good-looking reports can mask a host of input errors, formula mistakes, and computational problems. This article examines the subject of spreadsheet error detection in…

Addresses general performance errors in weight training, also discussing each category of error separately. The paper focuses on frequency and intensity, incorrect training velocities, full range of motion, and symmetrical training. It also examines specific errors related to the bench press, squat, military press, and bent- over and seated row…

When the errors in an ordinary least squares (OLS) regression model are heteroscedastic, hypothesis tests involving the regression coefficients can have Type I error rates that are far from the nominal significance level. Asymptotically, this problem can be rectified with the use of a heteroscedasticity-consistent covariance matrix (HCCM)…

Graduate students and new faculty in counselor education are often required to contribute scholarly works. However, graduate schools do not always provide appropriate preparation in scholarly writing. This article outlines the basic components of a scholarly manuscript or paper, identifies prevalent writing errors, and offers suggestions for how…

In this paper, we show the potential of webcams as precision measuring instruments in a physics laboratory. Various sources of error appearing in 2D coordinate measurements using low-cost commercial webcams are discussed, quantifying their impact on accuracy and precision, and simple procedures to control these sources of error are presented.…