In this study, we developed a classification system of programming errors based on the historical data of 680,540 programming records collected on the Online Judge platform. The classification system described six types of programming errors (i.e., syntax, logical, type, writing, misunderstanding, and runtime errors) and their connections with…

Self-diagnosis activities require students to self-diagnose their solutions to problems they solved on their own by detecting and explaining their errors. Worked examples, a step-by-step demonstration of how to solve a problem, are often used to support students in self-diagnosis activities. However, studies indicate that students often fail to…

Recent works on Intelligent Tutoring Systems have focused on more complicated knowledge domains, which pose challenges in automated assessment of student performance. In particular, while the system can log every user action and keep track of the student's solution state, it is unable to determine the hidden intermediate steps leading to such…

Online educational technologies offer opportunities for providing individualized feedback and detailed profiles of students' skills. Yet many technologies for mathematics education assess students based only on the correctness of either their final answers or responses to individual steps. In contrast, examining the choices students make for how…

The aim of this study is to examine the mistakes made by students in the use of logical connectives while simplifying algebraic equations and inequalities, and the extent to which teachers are aware of these mistakes and how they assess them. The study was conducted among 50 ninth grade students and 63 practicing teachers of mathematics. The data…

We examined the type of errors on multiplication and division computation problems of 326 rising fifth graders enrolled in four elementary schools in Northern Portugal. We further examined whether there was a difference in the number of errors across age and whether there was an association between students' performance on number knowledge and…

Background: Erroneous answers in multiple-answer problems not only make the correct answer harder to determine but also indicate why the correct choice is suitable and the erroneous one a mistake when compared to the correct answer. However, it is insufficient to simply create erroneous answers for this purpose: explanations of these answers are…

Although error avoidance during learning appears to be the rule in American classrooms, laboratory studies suggest that it may be a counterproductive strategy, at least for neurologically typical students. Experimental investigations indicate that errorful learning followed by corrective feedback is beneficial to learning. Interestingly, the…

Problems faced by engineering students involve multiple pathways to solution. Students rarely receive effective formative feedback on handwritten homework. This paper examines the potential for computer-based formative assessment of student solutions to multipath engineering problems. In particular, an intelligent tutor approach is adopted and…

Tabular presentations of student data often hide information about the switches in responses by individual students over the course of a semester. We extend unpublished work by Kanim on "escalator diagrams," which show changes in student responses from correct to incorrect (and vice versa) while representing pre- and postinstruction…

Students taking introductory physics are rarely exposed to computational modeling. In a one-semester large lecture introductory calculus-based mechanics course at Georgia Tech, students learned to solve physics problems using the VPython programming environment. During the term, 1357 students in this course solved a suite of 14 computational…

Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

To find out whether the education community shares a collective understanding about how students should be evaluated, we surveyed 202 educators (from all grade levels) and scientists attending assessment workshops (Pennsylvania, California, and Massachusetts) or judging a national student competition (Washington, DC). The educators and scientists…

Number Concepts; Measurement; Geometry; Probability; Statistics; and Patterns, Functions and Algebra. Procedural Errors were further categorized into the following content categories: Computation; Measurement; Statistics; and Patterns, Functions, and Algebra. The results of the analysis showed the main sources of error for 6th, 7th, and 8th…

This article describes activities that promote students' understanding of equation solving through analyzing and correcting student work. (Contains 5 figures.)