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

Michael Sturm

 

 

He evolved from a young teacher to become a believer in the constructivist method.

 

Robert Mason, affectionately known as “Doc” by both faculty and students, alike, has taught middle schoolmath at Dalton for the last 20 years. Dr. Mason’s recent book–for both fellow teachers and lay people– explores this experienced educator’s innovative methods and theory to “unlock” each student’s learning potential.

Michael Sturm, another Dalton math department veteran, provides his perspective:

In his book, Dr. Mason relates how he evolved from a young teacher, using mainly the lecturing

 

method, to become a believer in the constructivist method, whereby the teacher seizes the moments in

which he “wins” the competition for the student’s attention that is influenced by internal stimuli as well

as the external environment.

Through extensive readings and studies of the work of Piaget and Vygotsky, among others,

Dr. Mason became aware of the importance of providing visual stimuli and the

understanding of the Zone of Proximal Development (ZPD). This zone is essentially the

boundary between two stages in the sense of Piaget: what students can achieve on their

own versus the stage at which they need the support of the teacher. Dr. Mason describes

the concept of “boundedness,” which, he explains, is exemplified in a good lesson plan.

This, in turn, culminates in the author’s main thesis: teaching is the “puncturing of

space” with pedagogical objects. While these objects may vary from teacher to teacher,

Dr. Mason maintains that they should maximize the process of conveying content. A

lesson plan is one such object.

As he moves forward in his career, Dr. Mason describes how he changed his teaching

style from a lecture format to maximize the “puncturing of space” method. In my own

teaching of transformational geometry, I can relate to this method as well. The goal there is to teach

students how to literally transform the conditions of a new problem to enable the application of a previously

solved situation.

To make the puncturing process successful, he describes the importance for the teacher to be aware of

the ZPD of the student audience. The younger the audience, the more crucial concrete examples are.

These are called concept proxies and at the early stages are the well-known manipulatives. Later on, as

Dr. Mason describes in detail, the geobard is a useful device for non-trivial insights into geometry.

Not only does Dr. Mason give specific examples of how he constantly tested the major educational theories

in his classroom, but he also provides an analysis in which he compares the dichotomy between the

theories of Piaget and Vygotsky. He sides more readily with the latter, since Vygotsky espouses two key

ideas that support the constructivist approach: i) the child’s intellectual development is continually evolving

without endpoint, and ii) a teacher can influence the levels of thinking in the ZPD.

Dr. Mason provides a concrete example of what it means to work within the ZPD; he cites his

work–supported by a grant–to obtain computers for the Geo Sketchpad software program. For the

author, this project exhibited all phases of the puncturing of space. With minimal teacher guidance, he

leads students in carrying out genuine problem solving.

Dr. Mason concludes that recent research in neuroscience should become the new frontier to expand

upon the theories of Piaget and Vygotsky.

 

 

 

  • 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. ...