Constructing Potential Learning Opportunities in Middle Grades Mathematics
With a renewed emphasis on mathematics curriculum (e.g., National Council of Teachers of Mathematics (NCTM) 1989) in schools causing educators to reexamine what is occurring in classrooms, the multitude of people involved with education are being challenged to consider questions such as, What is mathematics? What does it mean to do mathematics? and What are appropriate experiences for teaching and learning mathematics? In addition, the images individuals hold of mathematics and teaching and learning mathematics are being challenged by research efforts that continue to focus on mathematical learning and how students construct various mathematical concepts (e.g., Cobb et al. 1991; Hiebert and Behr 1988). In particular, research efforts in mathematics specific to middle grades are receiving increased attention ( Hiebert and Behr 1988). The purpose of this chapter is to provide an opportunity for the reader to reflect on what does occur in mathematical learning environments and what could occur if students are provided experiences that are conducive to promoting potential learning opportunities. Potential learning opportunities occur when a person attempts to make sense of an experience and to communicate this experience.
In describing mathematical activities, words such as experiences, activities, or tasks are used instead of classwork or homework. This is done to deemphasize the work notion that appears to accompany such words and to emphasize a learning atmosphere that should characterize classrooms ( Marshall 1988).
As students move into middle level classrooms, certain characteristics of the emerging adolescent have implications for teaching and learning middle grades mathematics. Since these students are at various stages in their mathematical development, the mathematics they are engaged in should continue to be conceptually oriented, with logical and/or abstract reasoning a goal of a mathematics program.
Physically, socially, emotionally, and intellectually, middle level children are going through tremendous upheavals in their lives. These changes