The ability to solve geometric construction problems is justly regarded as an essential component of mathematical culture. The dynamic, general nature of objects provided by dynamic geometry systems allows the development of intuitive methods for solving construction problems. The core mathematical concept underlying this approach is the loci…

The goal of this paper is to promote computational thinking among mathematics, engineering, science and technology students, through hands-on computer experiments. These activities have the potential to empower students to learn, create and invent with technology, and they engage computational thinking through simulations, visualizations and data…

The present study evaluated the utility of brief experimental analysis (BEA) in predicting effective interventions for increasing the math fluency of 3 elementary students identified as having math skill deficits. Baseline data were collected followed by implementation of a BEA consisting of the following interventions: cover, copy, and compare,…

This article describes a unit of work that was designed for a Year 9 class of mixed ability and which involved the definition and measurement of angles, as well as the practical application of angle properties--such as complimentary angles and the relationships in a transversal. The unit considered the numeracy skills required to interpret a…

To promote student learning in a relearning situation in university-level mathematics, we developed the learning method TAU ("Think Ask Understand"). TAU provides support (i.e. a role script) for students' interaction during a collaborative problem-solving phase at the beginning of the learning process, while content-related instruction is delayed…

In this article, the authors discuss how acknowledging and embracing that the sample space is one of many ways to partition the set of all possible outcomes impacts the teaching and learning of sample space and probability. After recounting an exchange surrounding two viable answers to a probability question, the authors detail how developments…

In this article, I will extend the falling ball method to measure the viscosity of liquids regardless of the degree of their viscosity. For this, I will show that one can obtain a measurement of the terminal velocity of a falling spherical ball in a viscous liquid by solving numerically the equation of motion which describes the dynamics of the…

Comparing and contrasting examples is a core cognitive process that supports learning in children and adults across a variety of topics. In this experimental study, we evaluated the benefits of supporting comparison in a classroom context for children learning about computational estimation. Fifth- and sixth-grade students (N = 157) learned about…

This article presents a hands-on experiment that covers many areas of high school mathematics. Included are the notions of patterns, proof, triangular numbers and various aspects of problem solving. The problem involves the arrangements of a school of fish using split peas or buttons to represent the fish. (Contains 4 figures.)

In the late seventies, Guy Brousseau set himself the goal of verifying experimentally a theory he had been building up for a number of years. The theory, consistent with what was later named (non-radical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment,…

During one school year, data were collected for vocational education students while they worked collaboratively on open-ended mathematics problems. In collaboration with participating teachers, instructional activities were designed with a twofold goal of modelling the process of problem solving and improving collaboration. Instructional…

This article features NASA's FlyBy Math, a series of six standards-based distance-rate-time investigations in air traffic control. Sixth-grade students--acting as pilots, air traffic controllers, and NASA scientists--conduct an experiment and then use multiple mathematical representations to analyze and solve a problem involving two planes flying…

The purpose of this paper is to present problems (and solutions) from the areas of marketing, population planning, system reliability, and mathematics to show how a computer simulation can be used as a problem-solving strategy in probability. Examples using BASIC and two methods of generating random numbers are given. (Author/MP)

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)

Experimental studies conducted since 1980 were reviewed. Each of the 34 studies concerning problem solving is briefly summarized, followed by comments, criticisms, and/or concerns. A summary indicates that experimental research of the 1980s seems to focus on: (1) children's processes, understanding, functioning, difficulties, and representations;…