In numerous studies, intelligent tutoring systems (ITSs) have proven effective in helping students learn mathematics. Prior work posits that their effectiveness derives from efficiently providing eventually-correct practice opportunities. Yet, there is little empirical evidence on how learning processes with ITSs compare to other forms of…

This study was designed to examine the use of mistakes to promote students' performance in undergraduate Algebra classes by developing a growth mindset. Participants were seventy-four students from three Algebra classes and received one of the three interventions along with regular instruction: (a) growth mindset feedback on mistakes…

The role of mathematical modelling pertains several disciplines, both STEM and non-STEM, and various fields: education, academy, work, everyday and social life. Despite its importance, it is not uncommon to see university students facing difficulties with the use of Mathematics to create models, even when mathematical entities that play a role in…

Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic…

The results of educational research studies are only as accurate as the data used to produce them. Drawing on experiences conducting large-scale efficacy studies of classroom-based algebra interventions for community college and middle school students, I am developing practice-based data cleaning procedures to support scholars in conducting…

Participation in society is increasingly dependent on educational achievement. Accordingly, society as a whole is committing more resources to education to prevent the adverse outcome of students moving through the school system only to emerge without the knowledge and skills that they might be expected to attain. In this paper, we explore the…

This study compared errors made while solving equations using literals (letters) with errors made while solving the same equations using numerals. The subjects were 54 Navy students enrolled in a remedial mathematics course. Error data were analyzed by means of coding all errors into ten major categories, each containing subcategories. Students…

Nonroutine problem-solving, too, involves elements of routine. Often, elementary routines such as solving for a variable are not carried out without error. In this paper, we use new findings from neuroscientific research to explain why even excellent students make mistakes in elementary routines. [For complete proceedings, see ED489597.]

This document contains 15 research papers presented at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics. The papers are organized into four sections. In part I, four position papers by Romberg, Engelhardt, Ashlock, and Heddens reflect research ideas which underlie the Council. Part II…

Verbal protocols were collected from math-anxious and math-comfortable college students while they solved algebra problems. These protocols were then examined for differences in problem-solving processes. Differences occurred in the use of two basic strategies: generating values and symbolic transformations. Math-anxious students generated more…

This paper reports on the first stage of a research project still in progress aiming at identifying undergraduate students' difficulties and errors in solving linear algebra problems. Some students' difficulties related to very basic notions of vector space theory are shown and discussed with respect to both Balacheff's theory of conceptions and…

Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…

This document contains 14 papers selected from those presented at the Seventh Annual Conference of the Research Council for Diagnostic and Prescriptive Mathematics. Categorized as interdisciplinary studies are reports on "Mathematics as an Activity of Our Intelligence" by Skemp and a study on "The Brain Basis of Developing…

This paper, presented at the 1979 meeting of the American Educational Research Association (AERA), investigates student errors in high school mathematics. A conceptual framework of hypothetical information-handling processes such as procedures, frames, retrieval from memory, visually-moderated sequences (VMS sequences), the integrated sequence,…

Advances the idea that performance errors should contribute positively to the process of learning. Argues that errors do not occur randomly and that instructional theory should not condemn errors, but seek them. (PK)