The Theoretical Learning approach to mathematics learning, as piloted in the Portland Public Schools, is based on a general approach to human development called "Activity Theory" that derives from the work of three 20th-century Russian psychologists, Vygotsky, Luria, and Leontiev. Advocates of Activity Theory believe that it is an alternative to cognitive psychology that overcomes the latter's shortcomings as a theory of learning. Activity theory shifts the focus in human mental development away from the isolated brain and towards human culture and the human activity of creating and using tools, especially (but not only) the tool of language.

Russian origins

The particular approach to mathematics instruction used in the Portland pilot is based directly on the work of Vasily Davydov (1930-1998), an outstanding Russian psychologist from the school of Vygotsky. Inspired by Davydov's theory of learning, several different teams of teachers and textbook authors in Russia have created a series of radically innovative school curricula not only in mathematics but also in literacy, natural science, literature, art, and music. These curricula are currently in use in about 10% of schools in Russia, where the approach is known as the Elkonin-Davydov system or as the "Developmental Learning" curriculum. We are calling our local adaptation of this approach "Theoretical Learning" or "Theoretical Math" just to distinguish it from other "developmental" approaches.

Related programs in the United States and other countries

In the United States, adaptations of Davydov's mathematics curriculum have been used in the Susquehanna School, a private school in Binghamton, New York, and in schools in Hawaii and Delaware. The Portland Public Schools pilot program includes a large number of teachers and schools (22 teachers, 4 schools), although we are restricting ourselves to Grades 1 and 2 (including a transition to traditional approaches in Grade 3). To our knowledge, the Portland pilot is the widest application of this approach in an American public school system.

Besides these Russian and American uses of Davydov-based curricula, Activity Theory is widely used in Scandinavia and Germany, among other countries. In Denmark, for example, it has been used to develop a new history curriculum for use in elementary schools. In Finland, it has been applied not only in schools but also as a new model for workplace learning. Activity Theory is the basis for the Fifth Dimension, an innovative model for after-school learning that originated in the U.S. but which is now used internationally.

What's different

What's "different" about the Theoretical Learning approach in comparison to traditional mathematics curricula? For one thing, the children work with real objects in a way that is completely different from the usual exercises with "manipulatives." The real objects are not just three-dimensional illustrations of "facts" provided by the teacher, but support a genuine inquiry into the meaning of number. Another difference is that learning occurs collectively, by the class as a whole, prior to the mastery of any new knowledge by an individual child. Another striking thing is that number is not introduced until after three months into the school year. This is related to the fact that children are not handed a "ready-made" conception of number. Instead, they are gradually led to discover where numbers came from and how they are used, leading to a genuine mastery of the concept of number.

The Theoretical Learning approach, as used in the Portland Public Schools pilot, is intended to develop a "talented" understanding of mathematics in all children. This is possible because of a special "modeling" approach to concept development, where algebra-like diagrams and formulas make hidden mathematical relationships readily visible to the children. For example, in Grade 1 the children measure lengths, areas, and volumes using unit lengths, areas, or volumes. Then they model the results of their measurements using certain special diagrams. These special diagrams enable the children to obtain a genuine, scientific concept of number at an early age, making it easier for them to master computations and to solve word problems. By the end of second grade, they understand multidigit numbers at a rather sophisticated level, not only in the base 10 (decimal) system, but in base 3, base 4, base 5, and so on. Perhaps the most striking result in the Portland pilot has been the development of children's ability to attack new types of math problems they have never seen before, as well as to explain what they are doing and why.

For more information, please contact us or read the information related to Grade 1, Grade 2, or Grade 3.

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