Calculus, perhaps more than other areas of mathematics, has a reputation for being steeped with procedures. In fact, through the years, it has been noticed of many students getting caught in the trap of trying to memorize algorithms and rules without developing associated concept knowledge. Specifically, students often struggle with the…

The research has shown a model of learning activities that can be used to stimulate reflective abstraction in students. Reflective abstraction as a method of constructing knowledge in the Action-Process-Object-Schema theory, and is expected to occur when students are in learning activities, will be able to encourage students to make the process of…

Computer simulations and animations for developing statistical concepts are often not understood by beginners. Hands-on physical simulations that morph into computer simulations are teaching approaches that can build students' concepts. In this paper we review the literature on visual and verbal cognitive processing and on the efficacy of…

Undergraduate students (N = 97) used an introductory text and a computer simulation to learn fundamental concepts about statistical analyses (e.g., analysis of variance, regression analysis and General Linear Model). Each learner was randomly assigned to one cell of a 2 (with or without instructional advice) x 2 (with or without time advice) x 2…

This project was designed to test Mayer's multimedia theory in an elementary school to improve students' mathematics learning for low-income children. The study designed and developed two multimedia mathematics experiments in 3rd grade: 9's multiplication experiment and geometric solids experiment. The two experimental lessons were implemented in…

One of the most useful ways to enhance collaboration is to create scenarios where learners are able to interact more effectively. Nevertheless, the design of pedagogically sound and well-thought-out collaborative learning scenarios is a complex issue. This is due to the context of group learning where the synergy among learners' interactions…

In this article the manifold aims and theorised benefits of Learning by Design are explored and evaluated through the practices and experiences of an early years mathematics teacher. The article examines and elaborates the ways in which this teacher took up and embraced Learning by Design as both a professional meta-language and as a design…

Developing a software environment to enhance 3D geometric proficiency demands the consideration of theoretical views of the learning process. Simultaneously, this effort requires taking into account the range of tools that technology offers, as well as their limitations. In this paper, we report on the design of Virtual Spaces 1.0 software, a…

Seventy-nine college students were taught laws of logarithms via the TICCIT CAI system. Most of the students were assigned to learner control or yoked treatment groups. Students assigned to learner control groups were able to choose how many instances to study. Students assigned to yoked groups were randomly yoked to students in the learner…

Discussion of the use of virtual reality (VR) to help students learn highlights the use of VR with elementary algebra. Learning theory is examined, including knowledge construction; knowledge representation is discussed, including the symbol systems of algebra; and spatial algebra is described and illustrated. (34 references) (LRW)

This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

Research on structural learning theory is reviewed as a base for designing computer-assisted instruction programs. An intelligent "Rule Tutor" emphasizing diagnosis and remediation for whole number concepts is described. (MNS)

The second in a series of three articles, some themes of an undercurrent of educational objectives that move beyond the evident content goals are outlined. The themes relate the computer software materials analyzed in Part I to the cognitive experiences that students should have in learning about subject matter. (MDH)

Fifteen research reports related to mathematics education are abstracted and analyzed. Six of the reports deal with aspects of learning theory, four with areas in mathematics instruction (calculus, elementary mathematics for students of economics, and planning for topics for kindergarten children), and two with assessment or prediction of…

A study was developed to evaluate the effectiveness of a preinstruction retention index (designed to maximize recall of mathematical concepts by predicting the idiosyncratic number of examples per mathematical concept required by each student). Subjects, 27 female and 26 male eighth grade students, were administered a retention measure through…