MathCheck is a relatively new online tool that gives students feedback on their solutions to elementary university mathematics and theoretical computer science exercises. MathCheck was designed with constructivism learning theory in mind and it differs from other online tools as it checks the solutions step by step and shows a counter-example if…

In a series of two "in vivo" experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly…

This study examined the influence of virtual manipulatives on different achievement groups during a teaching experiment in four fifth-grade classrooms. During a two-week unit focusing on two rational number concepts (fraction equivalence and fraction addition with unlike denominators) one low achieving, two average achieving, and one high…

Assigning difficulty level indicators to the knowledge units helps the learners plan their learning activities more efficiently. This paper focuses on how to use the topology of a knowledge map to compute and rank the difficulty levels of knowledge units. Firstly, the authors present the hierarchical structure and properties of the knowledge map.…

This experiment illustrates how the effective use of a technology treatment integrated into pre-algebra curricula can help students achieve on the New Jersey Standardized Grade 8 Proficiency Assessment (GEPA). The researcher obtained data by comparing a treatment group to a control group; the first group was given a weekly 44-minute-long…

Current cognitive multimedia design theories provide several guidelines on how to integrate verbal and pictorial information. However, the recommendations for the design of auditory texts (narrations) are still fragmentary, especially with regard to the characteristics of the voices used. In the current paper, a fundamental question is addressed,…

This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…

Geometry theorem proving involves skills that are difficult to learn. Instead of working with abstract and complicated representations, students might start with concrete, graphical representations. A proof tree is a graphical representation of a formal proof, with each node representing a proposition or given conditions. A computer-assisted…

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…

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…

An increasing number of K-12 school teachers have been using handheld, or palmtop, computers in the classroom as an integral means of facilitating education due to the flexibility, mobility, interactive learning capability, and comparatively inexpensive cost. This study involved two experiments in handheld computers: (a) a comparison of the…

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 paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…

This research demonstrates the design of a Joyful Classroom Learning System (JCLS) with flexible, mobile and joyful features. The theoretical foundations of this research include the experiential learning theory, constructivist learning theory and joyful learning. The developed JCLS consists of the robot learning companion (RLC), sensing input…

This paper reports on a case-study design experiment in the domain of fraction as number-measure. We designed and implemented a set of exploratory tasks concerning comparison and ordering of fractions as well as operations with fractions. Two groups of 12-year-old students worked collaboratively using paper and pencil as well as a specially…