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

Kenneth Offit Forward for S.T.O.R.E.S.

Dr. Robert E. Mason IV’s Structured Teaching of Research and Experimentation Skills (S.T.O.R.E.S). addresses a longstanding set of challenges confronting teachers of science and quantitative skills. In 2004 the president of the U.S. National Academy of Sciences formed a Board on Science Education to take on the issue of education reform in science teaching. DCitySmartScholarste a decade of effort, the report card is not good. In 2012, 69 percent of American high-school graduates did not meet college-readiness benchmarks in science, and the U.S. ranked last out of the eight countries studied (including England, South Korea, and Hungary) in math and science readiness. An assessment developed by the Program for International Student Assessment and taken by 15-year-olds in over 70 countries indicated that about 40% of U.S. high school students did not demonstrate “basic” knowledge of science. To address these challenges, encouraged by reports from the National Academies as well as professional societies, 26 state governments have joined with professional educators to develop “Next Generation” science standards for grades K–12. The common threads for these strategies are twofold. First is the de-emphasizing of memorization in favor of the process of thinking about scientific problems. Second is an implicit embrace of multi-disciplinary approaches to science teaching, instead of emphasizing traditional silos and separate curricula, for example, in the biological and physical sciences. A recent report from the University of Washington in Seattle analyzed 225 studies of “active learning” in science, technology, engineering and mathematics (STEM), demonstrating that this type of process oriented approach cut course failure rates by almost a third.

According to Dr Mason, a gifted practitioner as well as thought leader in math and science education, elementary and middle school students offer the ideal “window of opportunity” for teaching using process focused approaches. As stated in the introduction which follows this Preface, Dr. Mason believes that because of their “formative” stage of intellectual, psychological, and emotional development, younger students are receptive to a curriculum that highlights not only scientific procedures but also “the attitudes one must bring to them, rather than solely factual information and details.” 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.

Another theme implicit in all phases of the exercises is their interdisciplinary content. The topic settings for Dr Mason’s first phase of experimental units varies across a wide spectrum of “traditional” science silos, from biology, to chemistry, to physics, without ever making such distinctions. This approach is fully appropriate in an era where such boundaries are being dissolved even at the level of university teaching, where computational techniques in genomics, molecular approaches to biology, and bioengineering are but a few examples of this convergences of the sciences. Likewise, the topics in Dr Mason’s introductory section vary, for example, from the type of sugar hummingbirds prefer, to connections between color and smell of flowers, to the ballistic trajectory of water bottle rockets, to more complex tests of thermal conduction and thermal expansion of liquids. Progressing to the second phase of this program, students address carbon dioxide, oxygen, and hydrogen gases from a historiographic approach that introduces them to the fascinating stories of the discovery of these gasses as well as to a thoroughly modern analysis of their physical properties. In the finale to this teaching compendium, Dr Mason asks his students (and their mentors) to take up the challenge of an independent set of experiments involving as experimental subjects, mealworms, hydra, earthworms, insects, snails and/or other simple organisms. This module allows students to plan independent controlled experiments, and develop statistical and analytic tools to test their hypothesis.

If all of this sounds ambitious, it is. Dr Mason firmly adheres to the dogma of the Soviet psychologist and social constructivist Lev Vygotsky (1896 - 1934), who set out the principle that “a child follows an adult's example and gradually develops the ability to do certain tasks without help.” Dr Mason is a vowed Vygotsky acolyte, having previously tested this model in his influential work, The Puncturing of Space: A Developing Pedagogical Tool. That prior book was part teaching handbook, part textbook, and part philosophical discourse from a master pedagogue. As noted in my Preface to that opus, from his very first teaching job in 1973 at a school for gifted children in New York, Dr. Robert Mason has developed a philosophy of pedagogy in which the teacher moves from instructionalist to constructivist educator, constantly modifying improving didactic approaches according to the skills and interests of the student. Dr Mason is also the creator of Euclid Two, as well as the prior annotation of Geometers’ Sketchpad that has been widely utilized in classrooms for decades. While there remains no substitute for witnessing Dr. Mason’s teaching in the classroom, this new volume provides yet another example of an exciting as well as ambitious pedagogical tool created by a gifted educator. At a time when society is looking to our next generation to take on the technological and scientific challenges that will define our continued existence, and growth, on this planet, we are lucky to have Dr Mason’s creative and guiding spirit.


Kenneth Offit, M.D., M.P.H.
Member, Memorial Sloan Kettering Cancer Center
Professor, Cornell University Medical College
Member, Cell Biology and Genetics Program, Sloan Kettering Institute
Member, National Academy of Medicine of the U.S. National Academies of Sciences, Engineering, and Medicine

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