The Art of Teaching: Teaching Solid Geometry

1943 ◽  
Vol 36 (3) ◽  
pp. 126-128
Author(s):  
Nancy C. Wylie
Keyword(s):  
Mathematics Teacher ◽  
Euclidean Geometry ◽  
Three Dimensional ◽  
Solid Geometry ◽  
Art Of Teaching ◽  
Spatial Imagination

This Article is corroborating and supplementing the timely suggestions made by James V. Bernardo in the January 1940 issue of The Mathematics Teacher, on the teaching of solid geometry. I say, timely; first, because of its contribution to the meager body of material on the teaching of these books of Euclidean geometry; second, because most instructors are ready to begin a new semester and desire all additional light on methods of presenting the three-dimensional concepts. Any aids for perfecting technique that will enable the instructor to help the pupil in developing his spatial imagination will, very probably, be received with enthusiasm.

The Art of Teaching: A Helpful Technique in Teaching Solid Geometry

1940 ◽  
Vol 33 (1) ◽  
pp. 39-40
Author(s):  
James V. Bernardo
Keyword(s):  
Three Dimensional ◽  
The Real ◽  
Solid Geometry ◽  
Average Student ◽  
Art Of Teaching

It has been my experience; as it has been undoubtedly that of many who teach solid geometry, to find that the three-dimensional concepts are not easily conceived by the average student. He does not comprehend fully the meaning of the drawings of “solid” figures in one plane. To develop an aptitude for drawing and for interpreting figures is the real job for the teacher who is attempting to expound the propositions of the sixth, seventh, and eighth “Books” of Euclid.

Models in Solid Geometry

1942 ◽  
Vol 35 (1) ◽  
pp. 05-07
Author(s):  
Miles C. Hartley
Keyword(s):  
Three Dimensional ◽  
Joint Commission ◽  
National Committee ◽  
National Council ◽  
Spatial Relationships ◽  
Mathematical Association ◽  
Solid Geometry ◽  
Long Time ◽  
Spatial Imagination ◽  
The Joint Commission

The development of the pupil's ability to visualize spatial relationships has for a long time been recognized as one of the problems confronting the teacher of Solid Geometry. In 1923, the National Committee on Mathematics Requirements wrote: “The aim of the work in Solid Geometry should be to exercise further the spatial imagination of the student and to give him both a knowledge of the fundamental relationships and the power to work with tbem.”1 In 1940, the Joint Commission of the Mathematical Association of America and the National Council of Teachers of Mathematics reported: “Much attention should be given to the visualization of spatial figmes and relations, to the representation of three dimensional figures on paper.…”2

Three Dimensional CT Reconstruction for the Evaluation and Surgical Planning of Facial Fractures

1986 ◽  
Vol 95 (1) ◽  
pp. 10-15 ◽  
Author(s):  
Peter J. Koltai ◽  
Gary W. Wood
Keyword(s):  
Surgical Planning ◽  
Three Dimensional ◽  
Ct Scanning ◽  
Data Systems ◽  
Ct Reconstruction ◽  
Facial Fractures ◽  
Facial Skeleton ◽  
The Face ◽  
Spatial Imagination ◽  
The Relationship

Despite advances in radiology—including CT scanning—the three-dimensional (3D) nature of facial fractures must still be inferred by the spatial imagination of the physician. A computer system (Insight Phoenix Data Systems, Inc., Albany, N.Y.) uses CT studies as substrate for 3D reconstructions. We have used the insight computer for the evaluation and surgical planning of facial fractures of 16 patients with complex injuries. We present five illustrative cases, directly photographed from the computer monitor. Images can also be manipulated in real time by rotating or planar sectioning (functions best appreciated on video). The ability to cybernetically extract the facial skeleton from living subjects provides precise anatomic data previously unobtainable. The images are valuable for an accurate assessment of the relationship between the injured and uninjured sections of the face. We conclude that 3D reconstruction is an important advance in the treatment of facial fractures.

Enhancing Plane Euclidean Geometry with Three-Dimensional Analogs

2008 ◽  
Vol 102 (5) ◽  
pp. 394-398
Author(s):  
Alfred S. Posamentier ◽  
L. Raphael Patton
Keyword(s):  
Euclidean Geometry ◽  
Three Dimensional ◽  
Educational Process ◽  
Human Beings ◽  
The World

Human beings are born with an ability to sense, perceive, and then remember, and as we grow and develop this ability matures through exercise and practice. Most of us can recall learning to see how circles and lines are tangent to one another, how midpoints and perpendiculars partition triangles, and how one might prove conjectures about these. Learning how to see literally, how to make images of the world, and how to perceive the world more completely and accurately is part of that educational process.

The Art of Teaching A New Department

1936 ◽  
Vol 29 (3) ◽  
pp. 145
Author(s):  
Edith Imogene Brown
Keyword(s):  
Solid Geometry ◽  
The Subject ◽  
Art Of Teaching

For Several years the first few weeks of my course in Solid Geometry were very discouraging both to the class and to the teacher. It became evident that a different approach to the subject was necessary. After much thought and research I worked out a method which has proved very satisfactory with my classes.

Accurate Drawings of Three Dimensional Figures

1944 ◽  
Vol 37 (8) ◽  
pp. 350-353
Author(s):  
Margaret Joseph
Keyword(s):  
Three Dimensional ◽  
Regular Tetrahedron ◽  
Solid Geometry

Every teacher of solid geometry has no doubt experienced having a student fail to prove an original exercise just because his drawing of the figure required was so much out of proportion that he failed to establish the proper relationship between lines, angles, triangles, or planes necessary in the proof. If, for example, a student would draw a square for the base of an oblique prism or a circle for the base of a cone, instead of the parallelogram and ellipse as they appear in perspective, then the whole figure is distorted. Just recently I had a student come to me for help in deriving the formula for the altitude of a regular tetrahedron in terms of its edge e. As soon as I saw the rough sketch he was using, where the faces were scalene triangles, I knew why he had two unknowns in the equation that he was trying to solve. The altitude did not meet the base of the figure at its center. I made a better drawing for him and he immediately recognized his error and proceeded with the solution without further help from me.

Equipment workspace analysis in infrastructure projects

2007 ◽  
Vol 34 (10) ◽  
pp. 1247-1256 ◽  
Author(s):  
Amin Hammad ◽  
Cheng Zhang ◽  
Mohamed Al-Hussein ◽  
Germain Cardinal
Keyword(s):  
Three Dimensional ◽  
Construction Equipment ◽  
Prototype System ◽  
Constructive Solid Geometry ◽  
Infrastructure Projects ◽  
Bridge Construction ◽  
Solid Geometry ◽  
Workspace Analysis ◽  
Computational Aspects

Workspace conflicts are one of the important problems that can delay construction activities, reduce productivity, or cause accidents that threaten the safety of workers. Workspace planning is particularly important in the case of large infrastructure projects, such as bridge construction, and rehabilitation projects where equipment with complex workspace requirement is required. This paper aims to extend the previous research on workspace representation and analysis in the case of large infrastructure projects focusing on the following issues: (i) specific representation of equipment workspaces using composite shapes, (ii) semiautomatic generation and analysis of workspaces, and (iii) development of a prototype system that can generate workspaces and detect spatiotemporal conflicts in a three-dimensional environment. The computational aspects of the proposed approach are discussed and demonstrated through the development of a prototype system, which has been applied in a case study of the deck replacement of Jacques Cartier Bridge in Montréal.Key words: workspace analysis, spatiotemporal conflicts, construction equipment, infrastructure projects, bridge redecking, constructive solid geometry.

scholarly journals Norms That Regulate the Theorem Construction Process in an Inquiry Classroom of 3D Geometry: Teacher’s Management to Promote Them

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2296
Author(s):  
Oscar Molina ◽  
Vicenç Font ◽  
Luis Pino-Fan
Keyword(s):  
Mathematics Teacher ◽  
Three Dimensional ◽  
Construction Process ◽  
Mathematical Practices ◽  
3D Geometry ◽  
Semiotic Approach ◽  
Different Types ◽  
Whole Class ◽  
Toulmin’S Model

This paper aims to illustrate how a teacher instilled norms that regulate the theorem construction process in a three-dimensional geometry course. The course was part of a preservice mathematics teacher program, and it was characterized by promoting inquiry and argumentation. We analyze class excerpts in which students address tasks that require formulating conjectures, that emerge as a solution to a problem and proving such conjectures, and the teacher leads whole-class activities where students’ productions are exposed. For this, we used elements of the didactical analysis proposed by the onto-semiotic approach and Toulmin’s model for argumentation. The teacher’s professional actions that promoted reiterative actions in students’ mathematical practices were identified; we illustrate how these professional actions impelled students’ actions to become norms concerning issues about the legitimacy of different types of arguments (e.g., analogical and abductive) in the theorem construction process.

scholarly journals Paris Was Not Built in a Day… Three-Dimensional Puzzles and Architectural Blocks as a Universal Tool Supporting the Process of Aesthetic Education

2021 ◽  
Vol 6 ◽  
pp. 105-123
Author(s):  
Marta Kasprzak
Keyword(s):  
General Education ◽  
Core Curriculum ◽  
Three Dimensional ◽  
Educational Practice ◽  
Cultural Changes ◽  
The Core ◽  
Starting Point ◽  
Manual Skills ◽  
Spatial Imagination ◽  
Use Of Knowledge

This article proposes the use of knowledge of space studies in the school educational practice. It allows for implementation of obligatory content and skills indicated in the core curriculum for general education. Shaping the spatial imagination and aesthetic sensitivity is accompanied by the development of both social and manual skills, while the construction of miniature buildings by students is a convenient starting point for a discussion on social and cultural changes.

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