The learning process for a user becomes seriously restrictive in trying to discover the relationships between concepts and in searching for a part of concept (called an object) such as a solved example illustrating the concept or the application of the concept. This article presents the theory for building a relational graph that depicts how…

The purpose of this study was to examine students' understanding of and ability to interpret line graphs, using four tasks: two where students constructed a graph and two where students interpreted a given graph. The tasks were unique in that they did not simply involve the explanation of given data but included a language component that looked at…

A sample of 134 sixth-grade students who were using the Connected Mathematics curriculum were administered an open-ended item entitled, Vet Club (Balanced Assessment, 2000). This paper explores the role of misconceptions and naive conceptions in the acquisition of statistical thinking for middle grades students. Students exhibited misconceptions…

Since 1995, astronomers have discovered over 100 known exoplanets--planets outside of the solar system--and determined their properties such as mass, orbital distance, size, and density. By using simple algebraic equations of physics, students can determine these properties as well. In this article, the author discusses an activity titled…

The students need not compute dependent values required in making line graphs but to teach the students the usage of graphing calculator to plot, calculating and graph linear equations, which are best suited to real world data. In this initial learning process, the teacher should give minimum support to the students in arriving at a solution as…

This study uses the context of the weather to explore the development of students' intuitive ideas of variation from pre-Grade 1 to Grade 9. Three aspects of understanding these intuitions associated with variation are explored in individual videotaped interviews with 73 students: explanations, suggestions of data, and graphing. The development of…

A variety of applications of logarithms are presented along with suggestions about how this topic might be made more interesting and relevant in a secondary classroom. In most cases, the treatment is multi-modal using numerical, graphical and algebraic approaches.

The notions of "abstract" and "concrete" are central to the conceptualization of mathematical knowing and learning. Much of the literature takes a dualist approach, leading to the privileging of the former term at the expense of the latter. In this article, we provide a concrete analysis of a scientist interpreting an unfamiliar graph to show how…

A simple and readily understandable visual display of quantitative measures of academic efficiency and productivity is demonstrated in this article. This graphical construction facilitates annual comparisons of unit efficiency and productivity as well as an analysis of temporal changes in unit activity. By establishing a common framework upon…

This article describes an activity for secondary school students that may constitute an appropriate opportunity to discuss with them the idea of proof, particularly in an algebraic context. During the activity the students may experience and understand some of the roles played by proof in mathematics in addition to verification of truth:…

The mathematics students are given a task to understand the fundamentals of liner functions by analyzing the height of the football stadium bleachers, as studying mathematical relationships in real-world contexts can enhance a student's knowledge of mathematics. The study of the stadium seating problem helps students to understand quadratic,…

This study examines the practical work of a pair of students and an instructor using probeware in a mechanics lab. The aim of the study is to describe and discuss a type of interactional sequence that we refer to as "dark matter", the ordinary backdrop to the extraordinary sequences that are easily recognizable as clear-cut instances of learning.…

The objective of the research presented here was to study the influence of two types of instruction for using an argumentation diagram during pedagogical debates over the Internet. In particular, we studied how using an argumentation diagram as a medium of debate compared to using an argumentation diagram as a way of representing a debate. Two…

This paper suggests that mathematics teacher educators should listen carefully to what their students are saying. More specifically, it demonstrates how from one pre-teacher's non-traditional geometric representation of a unit fraction, a variety of learning environments that lead to the enrichment of mathematics for teaching can be developed. The…

The first step in documenting children's progress toward important goals, such as developing strong oral language and early literacy skills, requires measurable outcomes. Measurable outcomes contribute to teachers' understanding of whether the gains they observe in children are meaningful by adding quantitative evaluation of a child's progress…