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At the closing of each academic school year, I ask myself one question. Have I effectively taught mathematics to students with a broad range of learning styles? Up until 1977, my conclusion was, usually not. During the 1977 summer vacation, I was determined to rectify this problem. That summer, I designed a reading program in the fields of learning and teaching. From these readings and through self-reflection, I realized that my perceptions of the learner, and how these perceptions conditioned my approach to teaching. I had usually taught mathematics through lectures and demonstrations. Given few opportunities to think for themselves, my students learned that they would be rewarded if they sat passively listening to my understanding of mathematics. When unlocking the learner's intellectual potential became my objective, and constructivist teaching became the framework in which I taught, the dynamics of my classroom changed significantly.

When I say I seek to “unlock students’ mathematical potential,” I mean that I believe that students come to my class with a store of knowledge--their potential-- and are often unaware that their existing knowledge of mathematics is part of a larger system. Enabling students to both recognize the knowledge that they possess and relate their knowledge to new information is my goal.

My curriculum provides situations in which students experience this recognition and internalize these relationships. For example, if seventh graders are given the problem, "combine 1/a + 1/b," they know, from arithmetic, how to add positive rational numbers with unlike denominators. Therefore, teaching students to recognize that adding 1/a + 1/b involves the addition of positive rational numbers is the first step. The process of unlocking potential, in this case, occurs when students recognize that they can apply some of their knowledge about adding fractions with unlike denominators to combining the algebraic expression problem, and then determine what is needed to bring closure to this problem.** **

By structuring math activities around questions and procedures, my teaching is constructivist. It directs students to survey their knowledge base to locate “chunks” of information that apply to the problem. They figure out what they understand about a problem, use this information to begin problem solving, and then speculate about what is needed to further their progress.

When students fail to identify useful information, we brainstorm about mathematical concepts, procedure, and problem-solving strategies. My role in these brainstorming sessions is to pose questions which initiate general discussions about the next step in their thinking and problem-solving process. For instance, I will ask, “Is there something in the work we did that points us in the direction of the next step?” Through modeling, constructivist teaching trains students to initiate these prompts for themselves. When learning at their own rate and viewing mistakes as learning opportunities, students are put in the role of “makers of meaning.” As a result of my transition to a more encompassing vision of my students, I’ve discovered that students “make meaning” in various ways. I’ve increased the opportunities for learning by developing several teaching approaches to convey the same information to different learners. While learning is individualized, students share in the common search for the particular keys to their potential. All students get a taste of these diverse approaches so that their perspective of math and thinking broadens.

- 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. ...