The resources in this professional development collection were assembled to help you enhance your understanding of geometric concepts via theory, research, and activities that can be adapted for classroom use. If the question “Why Geometry?” is the place to begin, the New Zealand article “Geometry Information” provides key arguments in favor of introducing geometric concepts in the elementary grades.
What Topics are Appropriate?
Some research has investigated how students learn geometric concepts and when they are capable of achieving a deep understanding. The van Hieles worked with individual students and developed their five levels of geometric thought. The IMAGES website details those levels and contains other pages of teaching suggestions and activities to implement them. Jenni Way provides examples of instruction and student work in the van Hiele model. Doug Clements has written extensively on the geometric learning of young children and two of his articles are included.
How Should We Plan to Teach these Topics?
The Annenberg Foundation’s Learner Online has two excellent teacher labs. This collection provides a sampling of topics from the Mathematics Developmental Continuum of the State of Victoria, Australia. In these documents, you will find examples, teaching strategies, activities and progress indicators.
You’ll find sample units of instruction from NCTM Illuminations. One unit introduces young students to motion along a path and some elementary programming. Units for older students include investigating geometric solids and building with triangles. The Educational Development Center has many good resources for teacher professional development. Their article “Right Angle” is one example of how geometric topics can connect with other school subjects.
This narrative document describes the progression of Geometry across the K-6 grade band. It is informed both by research on children's cognitive development and by the logical structure of mathematics. The document discusses the most important goals for elementary geometry in three categories, namely, geometric shapes and their categories, composing and decomposing geometric shapes, and spatial relations and spatial structuring.
This article from New Zealand maths contains justifications for teaching geometry in the elementary grades and thoughts on how children learn geometry, including ideas from Piaget and the van Hieles. The article concludes with an example of how adults in a non-school setting would apply the van Hiele stages in an unfamiliar space.
This article helps educators answer questions about geometric thinking and the activities that develop it. It outlines the 3 levels of thinking about shape and space and the 5 phases of activities known as the van Hiele model. The tangram puzzle provides a vehicle for describing these phases and the types of thinking students achieve in each one. The article concludes with a suggestion about followup activity.
This article outlines the five levels of the van Hiele model for learning geometry and gives instructional suggestions relating to each one. In the model the levels are sequential and not age dependent, and a heavy emphasis is placed on experiential learning. Improving Measurement and Geometry in Elementary Schools (IMAGES) is an initiative of the Pennsylvania State Team of the Mid-Atlantic Eisenhower Consortium for Mathematics and Science Education at Research for Better Schools (RBS).
This article gives suggestions for instructors to help children develop geometric and measurement concepts. Strategies include using concrete models, computer software, examples and non-examples, and context and prior knowledge. Improving Measurement and Geometry in Elementary Schools (IMAGES) is an initiative of the Pennsylvania State Team of the Mid-Atlantic Eisenhower Consortium for Mathematics and Science Education at Research for Better Schools (RBS).
This article provides information from research on the benefits and cautions associated with using manipulatives to teach children. The authors urge that much care be used in assessing whether the learner regards the activity with concrete objects in the same context as was intended by the instructor. The article looks at the comparative advantages of computer manipulatives and gives advice on the selection and use of both physical and computer manipulatives. An extensive reference list is included.
This set of three interactive challenges from the Annenberg Teachers' Lab has learners investigate properties of squares and groups of squares. In Quilts learners construct quilt blocks exhibiting four types of symmetry. In Taxicab Treasure Hunt, they work with distance and direction on a grid of city streets. Finally, in From Corner to Corner learners measure the sides and diagonals of squares looking for an approximate relationship between the two measures. Background discussion and NCTM standards information is included.
This set of three interactive challenges from the Annenberg Teachers' Lab has learners develop spatial visualization skills. In "I Took a Trip on a Train," in "Plot Plans and Silhouettes" and in "Shadows" learners solve problems involving visual perspective. Background discussion and NCTM standards information is included.
This article gives teachers background information on right angles. It provides geometric and practical examples, a paper folding construction method, and some history of the usage of the term 'right.'
The activities in this four-lesson unit enable students to use their knowledge of number, measurement, and geometry to solve interesting problems. Planning and visualizing, estimating and measuring, and testing and revising are components of the ladybug activities. Students design "virtual paths" that enable a ladybug to either hide under a leaf or go through a maze. They develop navigational skills by testing their path and revising it. Two interactive Java applets (Ladybug Mazes and Hiding Ladybug, cataloged separately) support student solutions.
This is a listing of over 60 activities or activity categories that assist in the teaching of geometric and measurement concepts. Many are hands on, some use literature connections, and some involve puzzles. Improving Measurement and Geometry in Elementary Schools (IMAGES) is an initiative of the Pennsylvania State Team of the Mid-Atlantic Eisenhower Consortium for Mathematics and Science Education at Research for Better Schools (RBS).
These 4 activities, part of the Mathematics Developmental Continuum of the State of Victoria, Australia, are intended to introduce young learners to line and rotational symmetry. Supporting documents, materials, and progress indicators are included.
These 5 activities, part of the Mathematics Developmental Continuum of the State of Victoria, Australia, are intended to introduce young learners to compasses, the cardinal directions, left and right turns, and the use of map coordinates. Supporting documents and materials, teaching strategies, and progress indicators are included. Note that in Australia the noontime Sun is to the north.
This 3 lesson instructional unit helps students investigate many different aspects of triangles including basic properties of triangles, building other shapes from triangles, the dependence of the third side length on the other two (Triangle Inequality Theorem), and the Sierpinski Triangle fractal. The lesson includes student activity sheets and links to interactive applets.
These 3 activities, part of the Mathematics Developmental Continuum of the State of Victoria, Australia, are intended to introduce learners to demonstrating congruence and line and rotational symmetry through the use of transformations. Hands on activities and computer software are employed. Supporting documents, materials, and progress indicators are included.
Explore geometric solids and their properties with these interactive tools, beginning with an introduction to the faces of basic polyhedra; counting the number of faces, edges, and corners (vertices) in various solids; discovering Euler's Formula; constructing physical models of geometric solids; and identifying which geometric solids can be made from given nets.
This tool lets learners explore various geometric solids and their properties. Learners can manipulate and color each shape to explore the faces, edges, and vertices, and they can use this tool to investigate the relationship among the number of faces, vertices, and edges. This tool supports the 5-lesson unit "Geometric Solids and Their Properties" (cataloged separately).
This article from Teaching Children Mathematics by Pierre van Hiele asserts that for children, geometry begins with play. Rich and stimulating instruction in geometry can be provided through playful activities with mosaics. Activities with mosaics and others using paper folding, drawing, and pattern blocks can enrich children's store of visual structures. They also develop a knowledge of shapes and their properties.
Important geometric concepts are embedded in the shape and design of natural and manufactured objects. In this article from Teaching Children Mathematics, the authors, David and Phyllis Whitin, first describe fourth graders exploring why manhole covers are circles. They then offer a range of activities to demonstrate how inquiring about shape in botany, geology, biology, and industry can effectively integrate science and mathematics and foster a life-long spirit of inquiry.
This article from Teaching Children Mathematics, describes a four-part lesson used in a study of 3rd and 4th graders. The authors, Valerie Munier, Claude Devichi, and Hélène Merle describe an experimental sequence to teach the concept of angle in elementary school. It shows how children abstract this concept from a real-life physical situation to connect physical and geometrical knowledge. The article has photos and pictures of student work.