This study employed the design-based research (DBR) methodology to explore how to design instructional prompts integrated into a computer-based cognitive tool, GeoGebra, for gifted mathematics education. This study was divided into two iterative research phases lasting for 3 semesters, in which differentiating the instructional prompts for gifted…

This paper discusses two "GeoGebra" applets, "Radical" and "Parabola," that are designed to strengthen the conceptual understanding of specific topics in algebra. The design and pedagogical basis of the applets are presented. The integration of the applets in teaching Grade 9 mathematics in a partner high school in…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

In this paper we describe the design and implementation of a technology-active introductory first year university mathematics course. The design principles underpinning the course are presented. The results of the implementation show some areas where the technology-active approach has proven of value, as well as improvements that can be made for…

Historically, what people can learn is co-determined by the "representational infrastructure" for knowledge building. When Latin was the required medium of knowledge building, few could engage in scholarly activities; without the change to the vernacular, nearly universal access to higher education would not be possible. The highly…

The purpose of this study is to determine students' learning levels in derivative subjects and their misconceptions. In addition, this study aims to compared to the effects of the computer based instruction and traditional instruction in resolving these misconceptions. For this purpose, 70 12th grade students were chosen from high schools in Agri…

We share results from a quasi-experimental study in which we compared achievement between traditional face-to-face and computer-based sections of Intermediate Algebra on a common multiple choice exam as well as performance on open-response tasks. Students in the computer-based group performed better on the final exam and were also more likely to…

The purpose of this study is to determine students' learning levels in derivative subjects and their misconceptions. In addition, this study aims to compared to the effects of the computer based instruction and traditional instruction in resolving these misconceptions. For this purpose, 12th grade 70 students were chosen from high schools in Agri…

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…

Technology permeates our daily lives; education has not been untouched. Liaw (2002) points out that "teachers, trainers, and instructional designers of computer-based or Web-based instruction would benefit by being more attentive to learners' perceptions toward Web-based environments." Reviewing the earlier research into student perceptions toward…

In an attempt to study the emerging questions about design of mathematical tasks that could support the solving of challenging problems, we designed two settings of interactive diagrams that share an example represented as an animation of multi-process motion but differ in their organizational functions. The interactive settings, each comprising…

Tablets such as the iPad represent the next iteration of technologies that hold promise to facilitate learning, particularly in mathematics. In the case of algebra, tablets have the potential to bring the curriculum to life by easily linking to supporting materials and they allow an interactive experience whereby manipulation of one type of…

This research study assessed the effectiveness of a three-dimensional mathematics game, DimensionM, through a pretest-posttest control group quasi-experimental design. Participants consisted of 437 eighth graders. The classrooms were randomly assigned either to the treatment group that utilized DimensionM as a supplement to regular classroom…

This study examined the instances of a representational toolkit (RT) in one reform-oriented algebra textbook developed in the United States. The majority of RT uses were active (66%) as opposed to passive and connected (63%) in that the technology results were used in some other manner by either the textbook authors or students as they solved…

This paper shows the basic concept of Functional Modelling in mathematics education which has become more and more important in recent years. Hence it is necessary to think about suitable graphical methods to explain the fundamental idea of a function and its influence on values and other functions. PROGRAPH diagrams are a potentially good way to…