Hi, I'm Robert!
For my fellow teachers, I've constructed a model of teaching that I've summarized as the puncturing of space with pedagogical objects. . . The term "objects which puncture space" may help solidified one's sense of how pedagogy can be described within its new conceptual framework. Teachers who see the world in this manner should become more fully invested in the enterprise of teaching and learning.
Teaching Methematics
S.T.O.R.E.S.
for teachers
S.T.O.R.E.S.
for students
Handbook
The Euclid Project
Teacher's Manual
The Euclid Project
Student's Manual
An Introduction
to Geometer's Sketchpad
The Euclid Project
Pre-Algebra
Teaching Mathematics
"Teaching Mathematics Puncturing Space: A Developing Pedagogical Tool" uses a diverse
body of research to clearly introduce important ideas related to learning. Theories from
the fields of neurology and cognitive development about how students obtain, synthesize
and retain information are examined and cohesively presented.

With an in-depth discussion of how educators compete with predictable outside stimuli
as well as with the internal life of the student mind, Dr. Mason explains the idea of
using a combination of objects as pedagogical tools to 'puncture' the learning space to
re-engage the student and to re-establish attentive behavior.

This readable book is valuable to educators in all fields not just to those teaching
Mathematics, and not just to those teaching in lower and secondary schools. Educators
will think carefully and differently about how information is delivered and processed
in the classroom, after reading this book.
S.T.O.R.E.S.
(for teachers)
Structured Teaching of Research and Experimentation
Skills (S.T.O.R.E.S.) science curriculum for elementary
school and middle school students is a process oriented
approach, focusing on classical principles of induction
and deduction, evidence gathering, and hypothesis
building, and empirical testing and refinement of
hypotheses that highlights scientific procedures.
S.T.O.R.E.S.
(for students)
Structured Teaching of Research and Experimentation
Skills (S.T.O.R.E.S.) science curriculum for elementary
school and middle school students is a process oriented
approach, focusing on classical principles of induction
and deduction, evidence gathering, and hypothesis
building, and empirical testing and refinement of
hypotheses that highlights scientific procedures.
Sketchpad Basics
Handbook
Sketchpad Basics Handbook is designed to introduce elementary school and middle school students
and teacher to Geometer’s Sketchpad. The Sketchpad, is a construction tablet on which one draws models of geometric shapes, transforms them, colors them, measures them, and animates them. The models invite students to explore, represent, solve problems, construct, discuss, investigate, describe, and predict. Implicit to these functions is the ability to build mathematical models of simple and complex ideas. The Sketchpad allows students to engage in “doing mathematics,” which is emphasized in the National Council of Teachers of Mathematics (NCTM) Standards.

The investigations encourage students to work together in pairs and small groups, and to build on their knowledge by applying their knowledge to new information.

Sketchpad introduced through a series of explorations. All of the explorations are designed specifically to teach how to use the “tool box.” They represent technical exercises. That is, they teach how to use the drawing tools, and how to use the command menus to accomplish specific task. In some investigations students will replicate as set of instructions and then evaluate their findings. In other activities students are free to create their own investigation.
The Euclid Project
Teacher's Manual
The Euclid Project computer-based geometry program uses a scientific-experimentation approach to
providing middle school students with an intuitive un?derstanding of geometry as a precursor to the formal study of geometry later (e.g., in the 10th grade) and as a mediator for application of geometric understanding in a variety of contexts.

This scientific-experimentation approach to teaching geometry involves pre?senting the students with a mathematical hypothesis
(e.g., a line drawn across two sides of a triangle parallel to the third side divides the first two sides proportionally),
then having them use a “construction tablet” (Logo, Geometer Supposer, Geometer’s Sketchpad computer programs) to systematically
generate a series of cases to test the validity of the hypothesis (e.g., create a triangle and line parallel to a side,
then use animation to gener?ate a series of such triangles to see if the hypothesis holds for all of them).
The Euclid Project
Student's Manual
The Euclid Project computer-based geometry program uses a scientific-experimentation approach to
providing middle school students with an intuitive un?derstanding of geometry as a precursor to the formal study of geometry later (e.g., in the 10th grade) and as a mediator for application of geometric understanding in a variety of contexts.

This scientific-experimentation approach to teaching geometry involves pre?senting the students with a mathematical hypothesis
(e.g., a line drawn across two sides of a triangle parallel to the third side divides the first two sides proportionally),
then having them use a “construction tablet” (Logo, Geometer Supposer, Geometer’s Sketchpad computer programs) to systematically
generate a series of cases to test the validity of the hypothesis (e.g., create a triangle and line parallel to a side,
then use animation to gener?ate a series of such triangles to see if the hypothesis holds for all of them).
An Introduction to
Geometer's Sketchpad
This workbook is designed to introduce elementary school and middle school teachers to Geometer’s Sketchpad.

The Sketchpad, is a construction tablet on which one draws models of geometric shapes, transforms them, colors them, measures them, and animates them. The models invite students to explore, represent, solve problems, construct, discuss, investigate, describe, and predict.

Implicit to these functions is the ability to build mathematical models of simple and complex ideas.
The Sketchpad allows students to engage in “doing mathematics,” which is emphasized in the National Council of Teachers of Mathematics (NCTM) Standards.
The Euclid
Pre-Algebra
description

STORES and STEM

A Phase II Sample Question

Working with Carbon Dioxide, Oxygen, and Hydrogen Gases

In Phase II will apply their knowledge of the scientific process skills that you have learned while fixing several of the forty–five mini-proposals in Phase I. Application of what you have learned to actual experiments can be both rewarding and fun. The emphasis of Phase II is to allow you to do creative problem solving within the framework of the scientific method of inquiry. You may work collaboratively in small groups to discover the properties of carbon dioxide, oxygen, and hydrogen.

A Phase II Sample Question

In preparing carbon dioxide (CO2) by the technique described above, would you get more carbon dioxide by using more baking soda or more citric acid? Excellent question to use the controlled experiment design. Can you pour carbon dioxide from one jar into another jar? Be very careful to document your procedures and observations. What will you measure? What are your controls? Remember to collect some data, display the data in a bar chart, or line graph. Remember to complete the experiment summary form below.

His Structured Teaching of Research and Experimentation Skills (S.T.O.R.E.S.) approach is process oriented, focusing on classical principles of induction and deduction, evidence gathering, and hypothesis building, and empirical testing and refinement of hypotheses. He uses a series of critiques of mini-proposals as a first phase, progressing to a more formal set of exercises to develop skills of deriving relationships between evidence and explanations, and communicating scientific arguments in the context of original experiments that illustrate larger concepts. Dr. Kenneth Offit.
Example of a Phase One Mini-proposal #19: Lifting Ability of Magnets

Anthony wanted to know how strong was his magnet? As a result of his research about magnets he discovered how barriers and increased distance can vary the strength of a magnet. Anthony wondered if forces can act from a distance? He convinced himself that he could show that the strength of a magnetic field decreases the farther you move away from the magnet if he tied one end of a thread to a paper clip and taped the other end to the surface of a table. He would the hold a magnet above the paper clip. Anthony noticed that he could hold the clip up in the air (and keep the string taut) as long as the magnet is fairly close to the paper clip. But, if he moved the magnet too far away from the clip, the strength of the magnetic field decreases, and the paper clip fell. Anthony's preliminary investigations made him think about this question even more. How can he quantify the strength of his magnet? How could he measure the strength of a magnet systematically? Anthony designed the following experiment to determine how strong was his magnet.

Procedure

He selected a partner. He then clamped his magnet to the wood clothespin, and taped the clothespin to the bottom of the cup. He pulled out one end of a paperclip to form a hook. He touched the hook to the magnet and noticed that it stuck to one pole of your magnet.
Anthony and his partner took turns adding paper clips to the hook, one by one, and counted the total number of paper clips they could hang onto the hook before the weight becomes too much for the magnet to hold and the paper clips fall. He wrote this number of paper clips on your data sheet on the line for zero pieces of tape. Next, he stuck three pieces of masking tape (labeled #1, #2, and #3) on the bottom of your magnet. He kept adding pieces of tape, three at a time, repeated the experiment, and recorded the outcome.

  • By Michael Sturm

    Robert Mason, affectionately known as Doc by both faculty and students, alike, has taught middle school math at Dalton for the last 20 years. ...

  • Frank A. Moretti, Ph.D

    There are times when a rare person, for mysterious reasons, transcends this set of circumstances and feels the inner necessity to locate practice in the context of theory. Dr. Robert Emmett Mason IV, however, has taken on the challenge of integrating his range of experience in a way ...

  • Kenneth Offit

    The Puncturing of Space: a Developing Pedagogical Tool by Dr. Robert Emmett Mason IV, does not fit an easy description. It is part authoritative teaching handbook, part textbook, and part philosophical discourse from a master pedagogue with thirty years teaching experience ...

  • Victoria Geduld

    Dr Robert E. Mason's Teaching Mathematics might seem far removed from productive pedagogical reading that would be assigned to an incoming Ph.D. teaching assistant in a History department. Indeed, this book should be mandatory for teachers in all disciplines at both the beginning and more advanced levels. ...