| There is a widespread agreement that algebra is an important topic for all students to learn. Knowledge of the key ideas of algebra is a prerequisite for higher level mathematics study for many diverse disciplines. Failing to learn algebra limits a students' study in a variety of fields and limits career options. The late Professor Robert B. Davis reported results from several programs in a session of the Fifth International Congress in Mathematics Education that indicated children can learn algebraic concepts and techniques at an early age. He argued that there is impressive evidence of the feasibility of introducing algebra earlier to children. A program developed and implemented by Davis, in which children are expected to build up mental representations of key concepts, such as: variable, truth set, open sentence, substitution, signed numbers, and solving quadratic equations by using patterns, provides a video data base for showing the feasibility for teaching early algebra ideas to 6th grade students. Davis' approach is students' recognizing patterns and discovering relationships and rules, in contrast to showing or telling. It is based on students building meaning of key algebraic concepts.;The qualitative research study conducted, made use of archived videotaped data from the Rutgers-Kennilworth longitudinal study in which Professor Davis facilitated a strand of research sessions with sixth-grade children. This study analyzed Davis' pedagogy and children's learning, for the first session of the algebra reasoning strand that was videotaped for ninety minutes with four camera views.;Analysis of the data showed that the students were able to build mental representations of variable, open sentences, true or false statements, the rule for substitution, truth set notation, adding/subtracting integers, solving linear and quadratic equations, and solving a linear equation written with two variables.;Davis' pedagogy was "setting the stage", revisiting an earlier idea, using "secrets", whispering answers into the microphone, providing positive reinforcement, soliciting agreement, engaging students from their seat to the board, withholding information from the students that they were expected to discover, and asking questions to probe their thinking. In analyzing the students' mathematical behavior, they solved the problems posed and created and solved quadratic equations that they posed; in working together on problems, they modeled Davis' pedagogy by asking each other questions rather than reveal rules, and explained mathematical ideas such as substitution and the pattern for solving quadratic equations. |
