The translation principle allows students to solve problems in different branches of mathematics and thus to develop connectedness in their mathematical knowledge. Successful application of the translation principle depends on the classroom mathematical norms for the development of discussions and the comparison of different solutions to one…

The aim of this study was to examine if there is a difference in the performance on non-linear problems regarding age, gender, and solving situation, and whether the multiple-choice answer format influences students' thinking. A total of 112 students, aged 15-16 and 18-19, were asked to solve problems for which solutions based on proportionality…

The main purpose of the work is to present a successful implementation of CLIL method in Mathematics lessons in elementary schools. Nowadays at all types of schools (elementary schools, high schools and universities) all over the world every school subject tends to be taught in a foreign language. In 2003, a document called Action plan for…

In 1999, Richard Lee Colvin published an article in "The School Administrator" titled "Math Wars: Tradition vs. Real-World Applications" that described the pendulum swing of mathematics education reform. On one side are those who advocate for computational fluency, with a step-by-step emphasis on numbers and skills and the…

Communicating on the mathematical language, problem solving, and reasoning are competencies tested on international test. The aim of this research is to study how secondary school pupils do geometrical constructions, how they give mathematical argumentation and use geometrical notions in their explanations.

Introduction: The present paper shows the importance of a joint use of pencil and paper activities and of technology so that students may develop a complete understanding of ratio and proportion. A previous experience with strategy use when solving ratio and proportion problems provided background. Prompted by a recognition of the cognitive…

For the forty-third time, the Association for Educational Communications and Technology (AECT) is sponsoring the publication of these Proceedings. Papers published in this volume were presented online during the annual AECT Convention. Volume 1 contains 37 papers dealing primarily with research and development topics. Papers dealing with the…

A stopper is called "universal" if it can be used to plug pipes whose cross-sections are a circle, a square, and an isosceles triangle, with the diameter of the circle, the side of the square, and the base and altitude of the triangle all equal. Echoing the well-known result for equal cubes that is attributed to Prince Rupert, we show that it is…

Consider a circular segment (the smaller portion of a circle cut off by one of its chords) with chord length c and height h (the greatest distance from a point on the arc of the circle to the chord). Is there a simple formula involving c and h that can be used to closely approximate the area of this circular segment? Ancient Chinese and Egyptian…

The Mathematics Performance Expectations (MPE) define the content and level of achievement students must reach to be academically prepared for success in entry-level, credit-bearing mathematics courses in college or career training. They were developed through a process that involved faculty from Virginia's two- and four-year colleges and…

This study compared the effects of worked example and problem-solving approaches in individual or group work settings on learning to solve geometry problems. One hundred and one seventh graders from Indonesia were randomly allocated to four experimental groups using a 2 (problem-solving vs. worked examples) x 2 (individual vs. group study) design.…

In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the "What If Not?" (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs'…

This paper examines how mathematical understandings might emerge through student-centred inquiry. Data is drawn from a research project on student-centred curriculum integration (CI) that situated mathematics within authentic problem-solving contexts and involved students in collaboratively constructed curriculum. Participatory action research…

The researchers examined the use of video modeling by means of a handheld computer as an alternative instructional delivery system for learning basic geometry skills. Three high school students with learning disabilities participated in this study. Through video modeling, teacher-developed video clips showing step-by-step problem solving processes…