Graduate Research Papers


Open Access Graduate Research Paper


Division i s considered by many teachers to be one of the most difficult skills in an elementary school mathematics curriculum (Holland, 1942). This study explored the first step of diagnostic teaching in division; identifying errors made by students. The study was specifically tailored to fourth grade students and their use of the division algorithm on the set of whole numbers. Research has shown that in the case of systematic errors, the child will continue to use the algorithm incorrectly if not corrected (Cox , 1974). Grossnickle (1936) concluded "Almost 60% of the total number of errors which will impede pupil progress in long division with a one-figure divisor were systemtic." (p. 368) Therefore, research on the detection and analysis of systematic errors is of educational importance. It is useful to distinguish a careless error pattern from a systematic error pattern because the remedial procedures will be quite different. Yhen dealing with systematic errors, no matter how many times the child works the problem, he/she will probably make the same mistake. Using a sample of 25 randomly selected test papers from a population of 57 fourth grade students, errors from a thirty-item test were classified as random , careless, or systematic. iv Systematic errors comprised 39% of the total errors and these were further categorized into six error groups. Faulty or incomplete procedures; 30%, and regrouping; 25%, were the most common systematic errors. These were followed by zero/identity concept; 18%, place value; 16%, and remainder; 11%. No basic fact errors were found in the tests analyzed in this study.

Year of Submission


Degree Name

Master of Arts in Education


Department of Curriculum and Instruction

First Advisor

Greg P. Stefanich


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