A constructivist instructional approach to arithmetic word problem-solving: Children as authors and collaborators

The National Council of Teachers of Mathematics (1989) has identified problem solving as a major goal of school mathematics. Arithmetic word problem solving is difficult for children. The primary cause of this difficulty is not computational, as once believed, but representational. Children have difficulty understanding and representing the information in the problem. The purpose of this study is to design, implement, and evaluate a constructivist instructional approach to help children be successful arithmetic word problem solvers. It is a three week meaning-based approach to problem writing implemented by the teacher in a third grade classroom in a college laboratory school. The approach has children working collaboratively to author their own word problems. Children write math stories based on their everyday experiences. The children then write different types of math stories, along the lines of the typology similar to that proposed by Riley, Greeno, & Heller (1983). Children next explore how these math stories can be turned into problems by deriving the many questions that can be asked from any one story, making it into several problems. Subsequent instruction introduces the idea of multi-step, multi-type story problems. The instructional approach is guided by the important underpinnings in constructivist theory of the need for discourse, collaboration, and knowledge construction. This dissertation is an empirical study, qualitative and descriptive in nature. My field notes, videotapes, and audiotapes of each day\u27s session, and the children\u27s oral and written work provide the raw data for the study. The schematic knowledge necessary to understand arithmetic word problems and Riley, Greeno, and Heller\u27s word problem typology (1983) serve as the theoretical frameworks for the analysis of the data. The data show that children construct the schematic knowledge necessary to understand word problem structure across problem types, knowledge they did not have at the outset of the study. The stories and problems the children create collaboratively and the questions and discussions the children and the teacher pursue together in the spirit of mathematical discourse demonstrate that this approach holds promise as a basis for robust, meaning-based instruction in arithmetic word problem solving