Errors bear the potential to improve knowledge acquisition, provided that learners are able to deal with them in an adaptive and reflexive manner. However, learners experience a host of different--often impeding or maladaptive--emotional and motivational states in the face of academic errors. Research has made few attempts to develop a theory that…

"Specific Mathematics Assessment that Reveal Thinking" (abbreviated as "smart tests") provide an on-line formative assessment of middle years students. They aim to put information from research on students' understanding directly into the hands of teachers, by providing quick automated diagnosis of learning for all students in…

The methods and models for categorical data analysis cover considerable ground, ranging from regression-type models for binary and binomial data, count data, to ordered and unordered polytomous variables, as well as regression models that mix qualitative and continuous data. This article focuses on methods for binary or binomial data, which are…

The 2012 edition of the "Digest of Education Statistics" is the 48th 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…

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…

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…

When the errors in an ordinary least squares (OLS) regression model are heteroscedastic, hypothesis tests involving the regression coefficients can have Type I error rates that are far from the nominal significance level. Asymptotically, this problem can be rectified with the use of a heteroscedasticity-consistent covariance matrix (HCCM)…

Studies that examine the impacts of education interventions on key student, teacher, and school outcomes typically collect data on large samples and on many outcomes. In analyzing these data, researchers typically conduct multiple hypothesis tests to address key impact evaluation questions. Tests are conducted to assess intervention effects for…

This paper focuses on the identification of some conceptual factors underlying the initial learning of algebra. It describes a study which uncovered three predominant notions existing in a sample of ten 12- and 13-year olds prior to formal instruction in algebra, and the ways in which a particular approach to the teaching of algebra affected both…

The authors offer research studies and other documented evidence that teaching grammar without a meaningful context does not improve student writing, largely because that approach does not address the root causes of errors. Several resources that support this position and offer more productive strategies are summarized, including the authors'…

Analysis of errors children make is modeled both with and without computers. Patterns of thinking are traced for a fifth grader, with the discussion focused on getting clues for remedial instruction by analyzing the dialog. (MNS)