This study was guided by the question, how do we understand the multiplicative reasoning of upper high school students and use that to give insight to their performance on a standardized test? After administering a partial ACT assessment to a class of high school students, we identified students to make comparisons between low and high scoring…

This research aimed to examine the difficulties and failures of eleventh-grade students regarding probability concepts. With this aim, ten different open-ended probability problems were asked to the 142 eleventh-grade students. Each of these problems requires using different basic probability concepts. It is qualitative research, and the data…

Identifying and expressing relations between quantities is a key aspect of understanding and using functions. We are aiming to understand the development of functions understanding throughout school years in Israel. A survey instrument was developed with teachers and given to 20 high and average achieving students from each of years 7-11 and to 10…

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…

This paper is a descriptive and preliminary report on recent efforts to address two questions: 1) Can school mathematics be used to enhance our students' ability to understand their changing world? and 2) What role might computer technology play in this regard? After recounting some of the mathematical tools that led to a better understanding of…

This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

I identify and discuss ways in which different types of connections are described in the South African mathematics National Curriculum Statement and its related documents, particularly at the Further Education and Training (FET) level. I argue that connections are central to the way the discipline of mathematics, its learning outcomes, and…

This paper provides a pragmatic view of efficient use of graphics calculators. Efficiency is described in terms of quick and easy calculation, as debated and evidenced in a Year 12 calculus class. Students' methods of calculation are analysed in terms of the algebraic understanding and technical skills that underpinned them. Patterns in students'…

In the international community of mathematics and science educators the intuitive rules theory developed by the Israeli researchers Tirosh and Stavy receives much attention. According to this theory, students' responses to a variety of mathematical and scientific tasks can be explained in terms of their application of some common intuitive rules.…

Introduction: The Maui Hawaii Educational consortium (the Maui School District and Maui Community College) sought scientifically based evidence for the effectiveness of the Cognitive Tutor (CT) Algebra I Curriculum to inform adoption decisions. Decision makers were particularly interested in whether the use of the CT program affects achievement of…