Problem-solving strategies of young children working on a combinatorics task in a computer environment
Kathleen A. Adleman, Rutgers The State University of New Jersey - New Brunswick, United States
Rutgers The State University of New Jersey - New Brunswick . Awarded
A teaching experiment was conducted with twenty-four fourth grade students from two schools, one urban and one suburban. Students participated in two task-based interviews in which they were asked to solve a non-routine combinatorics problem using a computer-modeling environment. The purpose of the experiment was to investigate children’s problem-solving strategies and explanations. The study extends previous work exploring young children's development of problem solving strategies and justifications leading to building proof by cases. The research questions that were investigated are: (1) What heuristics and strategies do young children demonstrate as they work to solve a combinatorics problem in a computer environment? and (2) What justifications do children offer to support their solutions?
Two individual interviews, ranging from 25 to 60 minutes, were given to all students, approximately three to six weeks apart. The same task was given in each interview and flexible interviewing methods were used to examine children’s mathematical thinking. The task (the Garden Problem) was designed to be isomorphic to tasks given in the earlier related work. The software, a garden microworld from the Counters Tool of the Rutgers Mathematics Construction Tools, was created at Rutgers by a team that included the author.
Videotaped records of the interviews and computer printouts of solution screens as well as transcripts of the videotapes, interviewer descriptions, and observer notes comprise the data for this study. Analysis of data indicates the strategies used and the justifications given by the students. The development of strategies and justifications over the two interviews is traced through profiles of six representative students.
Results were consistent with earlier research done in the mode of model building using physical materials. Children working in a computer-modeling environment invented many of the same strategies as observed in previous research to create local organizations. Four of these students moved toward global organizations, including one who created alternate organizations using skipping techniques. Two students reorganized their thinking to consider and justify cases.
Adleman, K.A. Problem-solving strategies of young children working on a combinatorics task in a computer environment. Ph.D. thesis, Rutgers The State University of New Jersey - New Brunswick.
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