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One mode of approaching mathematics--that of the largest group of students-- involves viewing mathematics as one of several academic subjects to learn. These students need to know what to learn, and assume that there is a single best method to learn it.

I’ve found that supplementing drill and practice with essay writing is an effective means of teaching math to these students. The writing organizes their thinking, and reveals that problems can be solved by different approaches. Drill and practice produce mastery of specific concepts and procedures.

The second math approach often belongs to students who demonstrate a genuine aptitude for math and enjoy mathematics as an intellectual exercise. Their approach to learning mathematics is to explore mathematical questions. Most are intuitive thinkers. Talking with them, I often feel as though I am conversing with a future philosopher, because their questions relate to abstractions which could not be answered through concrete examples.

I find myself telling stories which help these students understand the historical development of mathematical concepts. For instance, when Albert Einstein demonstrated that two independent observations were congruent through mathematics, he also illustrated how tolerance of intellectual incongruities and human emotion led to the construction of meaning of the natural phenomena. Understanding Einstein’s intellectual process teaches students to tolerate ambiguity.

Students whose approach is more abstract require help refining their knowledge of how to use mathematics to argue why numerical, algebraic, or geometric relationships are valid. Computer technology and software designed for geometrical construction have also helped me anchor philosophical questions in a context that is observable. For example, on Geometer’s Sketchpad, students created quicktime movies which illustrate that a theorem is true for a large set of instances. Their questions are epistemologically based. For example, Ann Brody, a seventh grader asked, “why does proof by mathematical induction work?” “Can I use it to prove a geometric relationships?” And, “when would I need to use it ?” Her questions prompted several class discussions about the concept of infinity. Through our discussions the class concluded that **(x)** and **(x + 1)** collectively symbolized the mathematics of chasing of infinity. Where box **(x)** was the frame which could hold a number, or an equation. And, **(x + 1)** was the structure in which one tests for consistency. They showed when an increment of (+1) preserves completeness of the theorem.

- 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. ...