The purpose of the study is to identify the classroom mathematical practices developed within a learning environment designed by Realistic Mathematics Education for teaching cone and pyramid to preservice teachers. A teaching experiment including five-week instructional sequence by a hypothetical learning trajectory about the solids of cone and…

This study examines middle school mathematics teachers' concept definitions of five geometric objects (prism, pyramid, cone, cylinder, and sphere). The study included 99 middle-grade mathematics teachers in three provinces and districts. The data were gathered through six open-ended questions determined to reveal the participants' Concept…

Learning is not limited to a certain age group or a formal study environment. However, the first eight years, and particularly the first three years, are the most important because the effects of the care and attention provided to the child during this period will continue throughout his/her life. A child's early learning processes develop his/her…

The aim of the present study is to determine the elementary pre-service mathematics teachers' understanding on solids. For this purpose, pre-service teachers' definitions and drawings of these objects were examined. Qualitative research method was used. A written questionnaire consisting of sixteen open-ended and multiple-choice questions was…

This study investigates early-years prospective teachers' definitions, examples, and non-examples of cylinder and prism. The data were collected from 72 early-years prospective teachers via written tasks and classroom discussions. In written tasks, they were requested to define and then to give different examples and non-examples of cylinder and…

Rats were trained in a triangular-shaped pool to find a hidden platform, whose location was defined in terms of two sources of information, a landmark outside the pool and a particular corner of the pool. Subsequent test trials without the platform pitted these two sources of information against one another. In Experiment 1 this test revealed a…

The most common question the author's students ask is, "When will I ever use this in real life?" To address this question in her geometry classes, the author sought to create a project that would incorporate a real-world business situation with their lesson series on the surface area and volume of three-dimensional objects--specifically, prisms,…

From a young age children feel the need to identify two-dimensional geometric figures (shapes) and three-dimensional geometric figures (solids). The National Council of Teachers of Mathematics indicates the importance of being able to identify and name various geometric figures by kindergarten age. One of the objectives of this study was to learn…

This paper raises serious questions about the reliability of the learning pyramid as a guide to retention among students. The pyramid suggests that certain teaching methods are connected with a corresponding hierarchy of student retention. No specific credible research was uncovered to support the pyramid, which is loosely associated with the…

Spatial reasoning is a skill that needs to be developed in students as it is important in geometry for determining total surface areas and volumes of 3-dimensional shapes (Liedtke, 1995). Simply teaching children the formulae, in this case for finding total surface areas, can limit them in understanding mathematics conceptually (Bonotto, 2003).…

The purpose of this paper is to present a summary of selected facets of geometry and measurement in elementary school programs and to describe curricula content options designed to demonstrate the feasibility of seeking high level outcomes and meanings for students with learning disabilities. While there are a multitude of published papers…

The wealth of assessment options that exists offers teachers and students a "menu" of selections. Just as matching appetite needs with appropriate food selection is fundamental to a successful dining experience, matching assessment options to targeted achievement needs is crucial to an effective assessment experience. The author uses a…

Ritzville Pyramids are cone-shaped piles of wheat found near the community of Ritzville, Washington. Presents the practical problem of determining the volume and surface area of a Ritzville pyramid to help farmers solve cost-effectiveness questions related to selling the wheat. (MDH)

An art activity introduces intermediate grade and middle school students to optical illusions. Students practice drawing geometric shapes such as cubes, cylinders, cones, and pyramids, then combine these shapes to create the illusion of their choice. Graphic outlines for each shape are provided. This document is one of a collection of materials…

THIS BOOKLET, ONE OF A SERIES, HAS BEEN DEVELOPED FOR THE PROJECT, A PROGRAM FOR MATHEMATICALLY UNDERDEVELOPED PUPILS. A PROJECT TEAM, INCLUDING INSERVICE TEACHERS, IS BEING USED TO WRITE AND DEVELOP THE MATERIALS FOR THIS PROGRAM. THE MATERIALS DEVELOPED IN THIS BOOKLET INCLUDE (1) MEASURING VOLUMES OF RECTANGULAR SOLIDS, RIGHT RECTANGULAR…