The purpose of this article is to demonstrate how exponential functions and patterns can be taught by well-structured lessons composed of classroom activities, mathematical questions, discussions, and solving problems. Sawyer (1943) used a rope-and-post system to introduce the concept of logarithms and to calculate a product by adding the…

Based on a teaching intervention with modelling activities involving experimental work in 9th grade classes, the goal of this study is to find out how students estimate the credibility a modelling task setting when it integrates a hands-on experimental approach. The theoretical background is based on the concept of authenticity and its long…

This article documents the classroom mathematical practices observed in a collegiate level teacher education course related to the circle topic. The course, which was prepared as design research, utilized a dynamic geometry environment which influenced the type and nature of the evolved mathematical practices. The study uses emergent perspective…

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…

Many studies have shown the difficulties of learning and teaching the decimal number system for whole numbers. In the case of numbers bigger than one hundred, complexity is partly due to the multitude of possible relationships between units. This study was aimed to develop conditions of a resource which can help teachers to enhance their teaching…

This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…

This article presents an example of skimming and skipping stone motion in mathematical terms available to students studying A-level mathematics. The theory developed in the article postulates a possible mathematical model that is verified by experimental results.

Discusses ways to simulate a probability problem of interest to middle school students in which students calculate the average number of packets of trading cards purchased to obtain a complete set of cards. Simulations utilize a spinner, a table of random numbers, and a computer. Includes the BASIC program utilized in the simulation. (MDH)

A simple, guided-inquiry investigation using stacked sandwich cookies is employed to develop a simple linear mathematical model and to explore measurement error by incorporating errors as part of the investigation. Both random and systematic errors are presented. The model and errors are then investigated further by engaging with an interactive…

A major cause of the difficulty undergraduate mathematics majors have with the transition from elementary to advanced mathematics courses is that advanced courses require students to understand how mathematics is created. Describes a course whose main purpose is to introduce students to the creative process in mathematics. The course consists of…

Japanese lesson study, in various adapted forms, is becoming increasingly significant in professional development of mathematics teachers in the USA. Our goal in the research reported in this paper was to investigate, in a three-tiered teaching experiment, the cycles of learning of two researchers, six teachers, and the students in three grade 4…

This guide is support material for geometry teachers in middle schools or high schools in South Carolina. The guide describes the content of each program in the television series and suggests further learning activities for the students. The geometry that underlies the world around us is presented through applications. Contents of the series…

This article examines students' ability to use the balance model to solve for unknowns. A teaching experiment was conducted in four Year 3 classrooms. This experiment focused on exploring the application of the balance model as an analogue for representing equations and solving for unknowns. The teaching experiment promoted a shift by students…

This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr…