Taiwanese students consistently rank near the top on international exams on mathematics and science. In 2007, Taiwan recorded the highest TIMSS math score for eighth grade. The central education agency in Taiwan publishes detailed mathematics curriculum guidelines, which textbooks and national exams follow closely. In May each year, all ninth…

In 1992, Klamkin and Liu proved a very general result in the Extended Euclidean Plane that contains the theorems of Ceva and Menelaus as special cases. In this article, we extend the Klamkin and Liu result to projective planes "PG"(2, F) where F is a field. (Contains 2 figures.)

If you take a circle with a horizontal diameter and mark off any two points on the circumference above the diameter, then these two points together with the end points of the diameter form the vertices of a cyclic quadrilateral with the diameter as one of the sides. We refer to the quadrilaterals in question as diametric. In this note we consider…

In this article, the classic problem of finding three ways to determine the probability that the pieces of a stick randomly broken in two places will form a triangle is analyzed anew. To be useful in the classroom, an application must be incorporated into an often-crowded curriculum. What is nice about this triangle problem is that it fits in…

Any individual's response intended to be random should be as probable as any other. However, 3 experiments show that many people's independent responses depart from the expected chance distribution. Participants responding to instructions of chance and related concepts favor the available options unequally in a similar way. Consequently, in…

Four- to 10-year-old children (n = 50) participated in a 2D search task that included geometry (with- and without lines) and feature conditions. During each of 27 trials, participants watched as a cartoon character hid behind one of three landmarks arranged in a triangle on a computer screen. During feature condition trials, participants could use…

The purpose of this study is to investigate the effect of using the Geometer's Sketchpad software in the teaching and learning of graph functions among Form Six (Grade 12) students in a Malaysian secondary school. This study utilized a quasi-experimental design using intact group of students from two classes in an urban secondary school. Two…

Using a unique dataset, this dissertation analyzes the relationship between observable teacher characteristics and teacher effectiveness. Effectiveness is measured as a teacher's ability to improve student achievement on a standardized test. This analysis focuses on teachers of math and science at the elementary and middle school levels, as well…

A series of observations in math classrooms revealed a pervasive problem of "re-teaching". It matters little the subject; before the teacher can begin teaching new material, basic skills often have to be re-taught before the lesson can move forward. Perhaps some methods are more effective than others in the classroom. Consequently, this study…

This submission contains the Proceedings of the 2015 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the Université de Moncton in Moncton, New Brunswick. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of…

Last year the United States unveiled the Common Core State Standards (CCSS) in English and Mathematics for grades K-12. In particular, the authors included two possible sequences of 8-12 mathematics courses that would fulfill the standards. Most notably, the courses titled "3a" and "3b" in these two sequences have become…

Multiple-choice testing is an educational reality. Rather than complain about the negative impact these tests may have on teaching and learning, why not use them to better understand your students' true mathematical knowledge and comprehension? Maryann Wickett and Eunice Hendrix-Martin show teachers how to move beyond the student's answer--right…

This article describes the process of development of assessment instruments for a three-year longitudinal comparative study that focused on evaluating American high school students' mathematics learning from two distinct approaches to content organization: curriculum built around a sequence of three full-year courses (Algebra 1, Geometry, and…

Despite being known as the land of opportunity, the United States is far from equitable when it comes to the mathematics that students have the opportunity to learn. In this article, the authors explore the extent to which students in different schools and districts have an equal opportunity to learn mathematics. Specifically, they discuss…

The Carnegie Learning Cognitive Tutor curricula are based on cognitive models, which include a representation of the learner's thinking, strategies, and misconceptions. The Cognitive Tutor curricula typically speed up learning and yield greater learning as compared to traditional math curricula (Morgan & Ritter, 2002; Sarkis, 2004; Koedinger,…