High School Level — Geometry
Pendleton Heights High School, Pendleton, Indiana
M.Ed., Ball State University
For over 30 years James Noggle
has been letting his students in on a secret at the
high school in Pendleton, Indiana.
He makes geometry feel like a long, cool drink as he guides you through the
mysteries of lines, planes, angles, inductive and deductive reasoning, parallel
lines and planes, triangles, polygons, and more.
In this course taught by award-winning teacher James
Noggle, you develop the ability to read, write, think,
and communicate about the concepts of geometry. As your
comprehension and understanding of the geometrical vocabulary
increase, you will have the ability to explain answers,
justify mathematical reasoning, and describe problem-solving
The language of geometry is beautifully expressed in words, symbols, formulas,
postulates, and theorems. These are the dynamic tools by which you can solve
problems, communicate, and express geometrical ideas and concepts.
Connecting the geometrical concepts includes linking new theorems and ideas
to previous ones. This helps you to see geometry as a unified body of knowledge
whose concepts build upon one another. And you should be able to connect these
concepts to appropriate real-world applications.
Mr. Noggle relies heavily on the blackboard and a flipchart on an easel in
his 30 lectures. Very little use is made of computer-generated graphics, though
several physical models of geometric objects are used throughout the lectures.
Upon completion of
Geometry, you should
be able to:
- State and apply postulates and theorems related to points, lines, planes,
and angles and use symbols to name and draw representations of them.
- State and apply components of deductive reasoning to investigate relationships,
solve problems, and prove statements.
- State and apply postulates and theorems involving parallel lines and convex
polygons to solve related problems and prove statements using deductive reasoning.
- State and apply postulates and theorems related to congruent polygons to
prove triangles and/or their corresponding parts congruent.
- State and apply definitions, properties, and postulates to identify different
quadrilaterals and prove statements about them.
- State and apply components of logic and indirect proof to investigate inequities
- State and apply definitions, properties, postulates, and theorems related
to similar polygons to prove triangles similar using deductive reasoning and
to deduce information about segments or angles.
- State and apply properties, postulates, and theorems related to right triangles
to deduce relationships and solve for missing information in diagrams.
- State and apply definitions, properties, postulates, and theorems about
circles and terms related to circles to solve problems and prove statements
using deductive reasoning.
- Use compass, straight edge, and previously learned relationships to construct
simple geometric figures.
- State and apply formulas for finding area and volume for plane figures.
- State and apply formulas for finding surface area and volume for simple
How We Found the SuperStar Teachers of the
High School Classroom
by Tom Rollins, Founder of The Teaching Company
The dream that got me to quit my job as Chief Counsel to a U. S. Senate Committee,
sell all my possessions, and move into an attic so I could start The Teaching
Company was this: to let every student in America learn from the best teacher
in the country.
How could we find the stars of the high school classroom?
We sent a letter to every teacher listed in
Who among American High School Teachers. (Teachers
are included if they are nominated as outstanding by
a student listed in
Who’s Who among American
High School Students.)
We explained to the teachers that we were looking for the SuperStars of the
American High School classroom, and that the only way we could judge this at
a distance would be for the teachers to send us videotapes of their classroom
In these days of the portable video camera, asking all of these teachers to
send us a sample of their work did not seem unreasonable.
But then all of the tapes arrived. It took me two days just to open all of
them. And it took months in front of the VCR in my office to watch all of the
entries we had received.
Was it tough to watch all of them? Of course. But the reward when a great teacher
came along was worth the wait.
I remember a late Saturday night, marching dutifully
through a big box of videocassettes, when I put in the
tape of James Noggle, a geometry teacher from Pendleton,
Indiana. He was explaining to his class the calculation
of the volumes of pyramids and cones and the ways in
which these were similar.
The lesson was carefully planned: he knew exactly when to use the formulas
on the board, when to use a three-dimensional model, and how to introduce
into the formula.
And I thought to myself, "If I’d had you for high school math,
Mr. Noggle, I would have stayed with my boyhood ambitions in science and medicine
rather than becoming a lawyer."
I had the same reaction when I saw Murray Siegel (named by Kentucky Educational
Television as the Best Math Teacher in America) on quadratic equations, and
Frank Cardulla (recipient of the Presidential Award for Science Teaching) on
Lin Thompson’s lecture on the Vikings was so good that when Lin came
to town to tape the course several people at the company rearranged their work
schedules to be in the studio audience for his lectures. And so on.
These were folks who could explain math, science, and history in a way that
intrigues you, draws you in, and makes the solution-finding as exciting as finishing
a good novel.
And they are the people who can fulfill a dream I had long ago—to make
the best teachers in America available to every student.
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