Curriculum & Instruction

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A New Approach to Algebra

An answer to the question, "What do we need to include in the mathematical education of every middle school student?" frames the Algebra Projcet. In his work with children, Robert Moses began to notice a common and critical difficulty they had with generalizing an arethmetic concept of number, usually associated with the question "how many?", with an algebraic concept of number, that requires an additional question of knowledge about basic operations on numbers, such as addition and subtraction, are fundamental to an understanding of algebra.

How can these generalizations be aquired within a mathematics classroom? Moses began to develop an answer to this question by thinking about how children move from physical experience to symbolic representations of physical experiences. He conceptualized this movement in a five step process that includes.

• Experiencing a Physical Event;
• Drawing a Picture, or modeling the event;
• Discussing and writing descriptions of the event in informal, intuitive language (People Talk);
• Regimenting or formalizing the language used to describe the event (Feature Talk); and,
• Developing Symbolic Representations of the event

These five steps are the underpinnings of a teching and learning process, called the curricular process, through which the Indianapolis Algebra Project moves students from ordinary experiences to abstract mathematical. The curriculum begins with the physical event of taking a ride on a subway or a bus system as the basis for building an understanding of the abstract concepts of the number line, displacements and the use of integers as position coordinates and as displacements.

In general, this learning and teaching process implies that a child's learning must be a constructive and social activity. A child constructs mathematical knowledge in a shared world of informal and formal language. Teachers can most effectively move children through these steps by engaging them in inquiry about their experiences and representation of experiences. In this context, the Indianapolis Algebra Project has a goal toward the development of a mathematical curriculum reflecting a learning and teaching process where children are asked and helped to construct mathematical knowledge.

The Indianapolis Algebra Project also recognizes that the question about what is needed in mathematical education cannot ignore the pervading cultural and social message that learning mathematics requires some type of innate ability, and the message that if you are a person of color that you will probably not be able to learn mathematics. We hold as a goal the creation of a learning and teaching enviornment where children and teachers understand learning as a consequence of motivation and effort, rather than innate ability, regardless of race, gender or creed.

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Purpose

• To change the way teachers teach inner-city youth