We tested human performance on the Euclidean Traveling Salesman Problem using problems with 6-50 cities. Results confirmed our earlier findings that: (a) the time of solving a problem is proportional to the number of cities, and (b) the solution error grows very slowly with the number of cities. We formulated a new version of a pyramid model. The…

Cognitive load theorists have frequently used subjective measures of cognitive load to test the effectiveness of instructional procedures. This study sought to broaden the applications of subjective measures by testing their ability to detect variations in intrinsic cognitive load within tasks. In two experiments students were asked to complete…

Algebra word problems were analyzed in terms of the information integration tasks that are required to solve the problems. These tasks were classified into three levels: value assignment, value derivation, and equation construction. Novices (35 first year algebra students) and experts (13 analytic geometry students) were compared on the proportion…

Children's mental performance was studied in the context of arithmetic word problem solution. Response latency and error data indicated subtraction was more difficult than addition. Understanding children's problem solutions in terms of flexible strategy use and the fact that many errors have a systematic basis are important in studying children's…

Managerial problem-sensing includes the macroprocesses of noticing, interpreting, and incorporating stimuli. Each process is composed of micro-social-cognition processes. Analysis using three social cognition theories (social perception, information processing, and social motivation) illustrates how managerial problem-sensing errors can occur and…

A distinction is made between estimation and checking, and an analysis of standard errors made on calculators when pupils are checking answers is given. (MP)

This study focused on analyzing children's difficulties with two-step mathematical word problems. Seventy-one fifth-grade children in Puerto Rico were individually observed solving five problems. Two of these were two-step problems; the remaining three were one-step problems with the same mathematical structures as the components of the two-step…

This paper reports the results of a study in which interviews were conducted with each of 35 sixth graders who made errors that might have been due to reading on the word problem portion of the Metropolitan Achievement Test. To discover evidence of poor reading affecting word problem success, the investigators asked each child to read aloud those…

An experiment with 67 Australian junior high school students demonstrates that presentation of goal-free 2-move mathematics problems, reducing the use of means-ends analysis, prevents the stage effect (increase in errors at the subgoal stage) from occurring. Implications for enhancing learning are discussed. (SLD)

The past several decades have seen numerous approaches toward automated diagnosis and instructional support of students engaged in mathematics problem-solving. These approaches typically involve detailed analysis of potential solution paths for problems, formal representations of correct and incorrect answers, and support in the form of feedback…

Results indicate that for the task of generating counterexamples to invalid syllogisms, a primary source of difficulty is the first step of forming the negation of the conclusion, especially if the conclusion is a "Some are not" statement. When this step is done for the subject, most of the errors disappear. (Author/BJG)

Sixth graders wrote solutions to the word problems in the Metropolitan Achievement Test. Errors were analyzed and classified. At least 52 percent of errors were computational or clerical and could not be attributed to reading difficulties. (SD)

This study introduces the individual consistency index (ICI), which measures the extent to which patterns of responses to parallel sets of items remain consistent over time. ICI is used as an error diagnostic tool to detect aberrant response patterns resulting from the consistent application of erroneous rules of operation. (Author/PN)