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…

In November 1996, the voters of Montgomery County (Maryland) approved by referendum an amendment to the County Charter that changed the County Council's review and approval cycle of the six-year Capital Improvements Program (CIP) from an annual to biennial cycle. The referendum specified that in odd-numbered fiscal years (on-years) the County…

This paper analyses technology-based instruction on data-analysis with box plots. Examples of instruction taken from the research literature inform a study of two classes of 17 year-old students (upper secondary) in which the mathematical relationships that their teachers targeted are distinguished as being, or not being, relevant to statistical…

This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in…

This case study investigated the impact of a spreadsheet (EXCEL) exploration on the understanding of statistical graphs among twenty Singapore secondary school students of average ability. Four EXCEL templates were constructed to allow students to explore four aspects of statistical graphs: zero in scale, effect of different scales, size…

The purpose of this study was to determine whether there were significant differences in students' performances amongst conceptual, algorithmic and graphical questions tests. Seventy-one eleventh-grade students were involved in this study. In order to assess students' performance, conceptual, graphical and algorithmic questions tests were…

The Test of Written English (TWE), administered with certain designated examinations of the Test of English as a Foreign Language (TOEFL), consists of a single essay prompt to which examinees have 30 minutes to respond. Questions have been raised about the comparability of different TWE prompts. This study was designed to elicit essays for prompts…

This activity guide is a supplement to the November 1996 issue of the National Council of Teachers of Mathematics Student Math Notes. It contains a series of problems based on one main story problem. Using this problem and the other problems contained in the guide based on it, students explore different mathematical concepts such as graph theory,…

Graphs without a time axis, such as velocity-versus-position graphs, offer interesting possibilities for exploring graphing and motion. Relations depicted by these graphs are not limited to functions. Interviews with a high school student named Olivia, who uses a motion detector to create such graphs, indicate that she uses thought experiments as…

This generic science education study demonstrates the contrast of findings obtained through analyzing all the raw data as opposed to removing various combinations of identified potential outliers provided through the application of six diagnostic procedures. Outliers are defined as extreme data points with large residuals. It is argued that an…