Solving mathematical problems is cognitively complex, involving strategy formulation, solution development, and the application of learned concepts. However, gaps in students' knowledge or weakly grasped concepts can lead to errors. Teachers play a crucial role in predicting and addressing these difficulties, which directly influence learning…

In the current study, it is aimed to determine the activities that need to be done to eliminate the mistakes made by primary school fourth grade students in multiplication and division operations and to present solution suggestions for eliminating these mistakes. The study employed action research, one of the qualitative research methods. The…

The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…

The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…

Although finding the limits of the difference quotients in the definitions of the derivative is troubling for many students, a difficulty that preceded this confusion was observed: students were not able to correctly set up the difference quotients as required in the definitions. The purpose of this study is to uncover student errors in setting up…

Although the use of simulation to teach the sampling distribution of the mean is meant to provide students with sound conceptual understanding, it may lead them astray. We discuss a misunderstanding that can be introduced or reinforced when students who intuitively understand that "bigger samples are better" conduct a simulation to…

Student errors are springboards for analyzing, reasoning, and justifying. The mathematics education community recognizes the value of student errors, noting that "mistakes are seen not as dead ends but rather as potential avenues for learning." To induce specific errors and help students learn, choose tasks that might produce mistakes.…

Several schemes use modular arithmetic to append a check digit to product identification numbers for error detection. Some schemes are discussed, including ones for money orders and library books. Then a foolproof method is presented. (MNS)

A listing of the program is available from the author at Northwestern University. (MB)

Gas flow patterns at a sampling nozzle are described in this presentation for the 12th Conference on Methods in Air Pollution and Industrial Hygiene Studies, University of Southern California, April, 1971. Three situations for sampling velocity are illustrated and analyzed, where the flow upstream of a sampling probe is: (1) equal to free stream…

Four methods of finding the range of values of the solution of a problem when the data are known to lie within given bounds are illustrated. (MS)

Discussed are the mathematical methods for detecting a variety of common error patterns within the bar-coded identification numbers utilized in conjunction with scanning devices. Schemes for the use of check digits are examined that ensure conditions for detecting errors of specific types, including single digit error, transposition error, twin…

First purpose of this study was to investigate empirically the accuracy of prediction using regression weights selected through the use of variance-reduction procedures. (Author)

Students make errors in mathematics for a variety of reasons. It is the job of the educator to identify the source of these errors and to assist students in correcting them. The purpose of this monograph is to help identify, analyze, and evaluate students' computational proficiency. This monograph is divided into four sections: "Whole Numbers";…