International comparative studies of education have shown that the increase in mathematical attainment differs significantly among students in relation to the different school types in which their mathematical foundations were acquired. In tertiary education, the same differences are observed with respect to simple tasks that relate to the subject…

There is growing concern in Europe that some students are not well-equipped to start a Bachelor's or Master's programme, especially when the programme has a strong mathematical focus. In particular, attention is drawn to problems with mathematics in the transition from secondary to higher education. Higher education expects a certain level of…

Presents an approach to task sequencing that is based on a component-skills view of intelligence and learning. Related research in cognitive psychology and in computer based instruction is reviewed, and a cognitive model of human task sequencing is developed and then applied to an intelligent tutoring system for algebra. (39 references)…

Techniques are suggested for preparing practice exercises in algebra and trigonometry. (JP)

The intention of this investigation was to diagnose the retention of some basic skills in some topics in algebra and geometry and to reveal difficult steps in the learning processes in these topics. (MP)

Describes a laboratory-type activity, liquid assets, used to illustrate, develop, or reinforce central concepts in first-year algebra. These include linear function, slope, intercept, and dependent and independent variables. Presents a group activity for collecting data, transition from group to individual activity in plotting data points, and…

Describes the habits of mind that would be most desirable for students to develop. In high school for example, content-specific habits would include geometric habits of mind that support the mathematical approaches, and algebraic ways of thinking that complement the geometric approaches. (AIM)

The purpose of this document is to survey at least some of the important research literature on solving linear equations in order to identify information that might suggest ways to improve teaching effectiveness. The studies that are examined employ a wide range of research techniques, are based often on quite different perspectives, and span over…

This book introduces journal-writing prompts in mathematics for Algebra I. Content prompts, attitudinal or affective prompts, and process prompts are presented. Each of the content prompts relates or connects topics within and outside of mathematics, targeting important or meaningful concepts and skills. The content prompts also provide situations…

The author defines and discusses the cognitive theory of constructivism as it relates to teaching mathematics. It is suggested that the philosophical and theoretical view of knowledge and learning embodied in constructivism offers hope that educational processes will be discovered enabling students to acquire deep understanding rather than…

Discusses the application of the theory of contingent tutoring to the design of a computer-based system for algebra. Considers help seeking and analyzes interactions between secondary school students and the computer-based tutoring system to explore the relations between individual differences in learner-tutor interaction, learner's prior…

Discusses the need to consider the cognitive models of students and their learning processes when designing computer tutorials, and describes a tutorial designed to teach students how to generate algebraic equations for story problems. Testing and revisions of the tutorial, with both college and high school students are described. (14 references)…

This paper deals with the question of how teacher attitudes emerge as teacher behaviors and the relationships between teacher attitudes toward mathematics, teaching, and students, and teacher behaviors as measured by external observers and pupils. Forty-nine ninth-grade mathematics teachers were the subject of this research. It was observed that…

THE QUESTION OF PRIMARY CONCERN IN FOUR STUDIES WAS IMMEDIATE FEEDBACK IN ADJUNCT AUTOINSTRUCTIONAL EXERCISES (LEARNING EXERCISES DEFINED AS THOSE DESIGNED TO TAKE ADVANTAGE OF THE STRUCTURE INHERENT IN SUBJECT MATTER). IN A CONTROLLED SITUATION, DIFFERENT FEEDBACK DELAYS (IMMEDIATE, 1-HOUR DELAY, 2-DAY DELAY, AND 1-WEEK DELAY) WERE TESTED. OTHER…

This paper presents a critical review of computer assisted instruction (CAI); an overview of recent intelligent tutoring systems (ITSs), including current perceived shortcomings; major activities of the field, i.e., analysis of teaching/learning processes, and extending and developing artificial intelligence techniques for use in intelligent…