In this paper, we introduce logic programming as a domain that exhibits some characteristics of being ill-defined. In order to diagnose student errors in such a domain, we need a means to hypothesise the student's intention, that is the strategy underlying her solution. This is achieved by weighting constraints, so that hypotheses about solution…

This paper presents a "didactic triangulation" strategy to cope with the problem of reliability of NLP applications for computer-assisted language learning (CALL) systems. It is based on the implementation of basic but well mastered NLP techniques and puts the emphasis on an adapted gearing between computable linguistic clues and didactic features…

In this article, the author offers her experience of modeling mistakes and writing spontaneously in the computer classroom to get students' attention and elicit their editorial response. She describes how she taught her class about major sentence errors--comma splices, run-ons, and fragments--through her Sentence Meditation exercise, a rendition…

Researchers often compare the relationship between an outcome and covariate for two or more groups by evaluating whether the fitted regression curves differ significantly. When they do, researchers need to determine the "significance region," or the values of the covariate where the curves significantly differ. In analysis of covariance (ANCOVA),…

The fact that students have difficulties in constructing proofs is well documented. However, some of these difficulties may be lessened if instructors and students have access to a common evaluation framework. Operating in the theoretical tradition of heuristic inquiry, a proof error evaluation tool (PEET) is constructed that may be used by…

The subject of uncertainties (sometimes called errors) is traditionally taught (to first-year science undergraduates) towards the end of a course on statistics that defines probability as the limit of many trials, and discusses probability distribution functions and the Gaussian distribution. We show how to introduce students to the concepts of…

Spelling error corpora can be collected from students' written essays, homework, dictations, translations, tests and lecture notes. Spelling errors can be classified into whole word errors, faulty graphemes and faulty phonemes in which graphemes are deleted, added, reversed or substituted. They can be used for identifying phonological and…

The 2011 edition of the "Digest of Education Statistics" is the 47th in a series of publications initiated in 1962. The "Digest" has been issued annually except for combined editions for the years 1977-78, 1983-84, and 1985-86. Its primary purpose is to provide a compilation of statistical information covering the broad field…

Within the Response-to-Intervention framework, students who fail to profit from high-quality general education instruction, accommodations, and supplemental instruction progress to a more intensive intervention program, sometimes referred to as "Tier III." This article describes a problem-solving approach to designing such intensive, data-based,…

In this article, we present a theory of test translation whose intent is to provide the conceptual foundation for effective, systematic work in the process of test translation and test translation review. According to the theory, translation error is multidimensional; it is not simply the consequence of defective translation but an inevitable fact…

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.