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Steven J. Heilig – Mathematics Teacher: Learning and Teaching PK-12, 2024
Geometry students often wonder about the importance of construction techniques. Are they the only way to create geometric figures? What purpose do they serve? How do these techniques relate to other parts of geometry? This article introduces a project used at the high school level that gets all students in a class engaged with construction, gets…
Descriptors: High School Students, High School Teachers, Geometry, Geometric Concepts
Meagher, Michael S.; Özgün-Koca, S. Asli; Edwards, M. Todd – Journal of Mathematics Education at Teachers College, 2020
Generating mathematical conjectures is an important mathematical habit of mind for preservice teachers to develop so that they can, in turn, help their students to develop this skill. In this paper we present a classroom episode in which preservice mathematics teachers experience conjecturing in the context of a rich, open-ended task. They also…
Descriptors: Preservice Teachers, Mathematics Instruction, Mathematical Logic, Reflection
Developing Mathematical Knowledge and Skills through the Awareness Approach of Teaching and Learning
Cherif, Abour H.; Gialamas, Stefanos; Stamati, Angeliki – Journal of Education and Practice, 2017
Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…
Descriptors: Mathematics Education, Mathematics Skills, Skill Development, Mathematics Instruction
Keener-Chavis, Paula; Goodwin, Mel – Science Activities: Classroom Projects and Curriculum Ideas, 2009
The implications of Earth's ocean being little explored may not be immediately evident to individuals who are not ocean literate. For this reason, initiatives to improve ocean literacy must articulate compelling reasons for ocean exploration. A lesson plan that addresses this issue has been developed as part of the education and outreach program…
Descriptors: Oceanography, Geometric Concepts, Hands on Science, Inquiry
Madden, Sean P. – Mathematics Teacher, 2009
The author and his first-year algebra students explored the quadratic behavior behind the parabolic shape of fountains at the local family splash park. This hands-on discovery project has three main parts: (1) gathering data by experimenting with and photographing the fountains; (2) analyzing the photographs to obtain numerical data; and (3)…
Descriptors: Graphing Calculators, Algebra, Mathematics Instruction, Experiential Learning
Evans, Tyler J. – PRIMUS, 2008
We describe exercises in which students use PascGaloisJE to formulate conjectures about certain binomial identities which hold when the binomial coefficients are interpreted as elements in the cyclic group Z[subscript p] of integers modulo a prime integer "p". In addition to having an appealing visual component, these exercises are open-ended and…
Descriptors: Discovery Learning, Mathematics Instruction, Mathematical Concepts, Algebra
Smart, Julie; Marshall, Jeff – Science and Children, 2007
Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…
Descriptors: Grade 3, Geometric Concepts, Educational Games, Elementary School Mathematics
Fielker, David S. – Mathematics Teaching, 1981
The process of investigating some of the properties of diagonals and other geometric concepts with a group of 11-year-old girls is presented. Possible changes that could have been made in the lesson are discussed, and examples of individual student work are provided. (MP)
Descriptors: Discovery Learning, Elementary Secondary Education, Geometric Concepts, Geometry

Srinivasan, P. K. – Mathematics Teacher, 1981
A method for approaching the value of pi using a transparent sheet of parallel lines is discussed. (MP)
Descriptors: Discovery Learning, Geometric Concepts, Manipulative Materials, Mathematical Concepts
Evans, Patricia – Mathematics Teaching, 1981
Details of pupil exploration as to the largest number of sides that a polygon could have on a geoboard are presented. The problem is not seen as open-ended, but many different avenues of pursuit stem from it. (MP)
Descriptors: Discovery Learning, Elementary Secondary Education, Geometric Concepts, Learning Activities
Maida, Paula; Maida, Michael – Mathematics Teaching in the Middle School, 2006
This article describes an activity in measurement and geometry in which sixth-grade students explore the volume and surface area of a donut. Through calculation, creative thinking, and discovery, the students enhanced their geometric vocabulary and reasoning. (Contains 9 figures.)
Descriptors: Geometric Concepts, Creative Thinking, Geometry, Measurement
Hirst, Keith – Mathematics Teaching, 1981
Details of a class exploration of graphs that drew upon knowledge about the behavior of particular kinds of functions and applied them in a new context are provided. (MP)
Descriptors: College Mathematics, Discovery Learning, Geometric Concepts, Geometry

Ryden, Robert – Mathematics Teacher, 1983
The nature of an investigation into numbers termed Nearly Isosceles Pythagorean Triples (NIPTs) is detailed. The exploration, even though it is stated to have no practical value, is defended as helping pupils see the beauty of patterns in mathematics. Two questions regarding the pattern of generating NIPTs are noted. (MP)
Descriptors: Discovery Learning, Geometric Concepts, Mathematical Enrichment, Mathematics Instruction

Griffiths, H. B. – Mathematics in School, 1981
A lesson involving moebius strips and geometric properties is reviewed. Specific activities are suggested. (MP)
Descriptors: Discovery Learning, Elementary School Mathematics, Elementary Secondary Education, Geometric Concepts

Vincent, Peter – Mathematics in School, 1981
Student exploration at a secondary school level of fraction relationships using special graphs is described. (MP)
Descriptors: Discovery Learning, Elementary Secondary Education, Fractions, Geometric Concepts
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