Title

Mathematical problem-solving: The effects of tuning students' attention to information on the key idea of a problem on their mathematical performance

Date of Completion

January 1996

Keywords

Education, Mathematics|Education, Technology of|Education, Curriculum and Instruction

Degree

Ph.D.

Abstract

Mathematics should have problem solving as its central focus. Situating instruction in meaningful, real-world, problem-solving contexts is the theoretical basis for the videodisc adventure series known as "The Adventures of Jasper Woodbury." This study asked the question: Does tuning students' attention to information on the key idea of a problem affect their mathematical performance and impact the solution process?^ This was a traditional quasi-experimental research study, using some observation and interviewing techniques. The participants were sixth grade students in a rural/suburban middle school in Connecticut. The experimental group participated in a three-day activity on bald eagles, intended to tune their attention to information on the key idea of the problem. Both groups worked in pairs to solve the Jasper problem, "Rescue at Boone's Meadow," recording their work, and feelings about their work, in Jasper Book Journals. Students individually solved Cloze Procedure Problems and Transfer Problems. Statistical analyses, e.g., means, standard deviations, and analysis of covariance were used to determine the differences on mathematical perfomance between the two groups. Students were interviewed individually and one pair of high-ability mathematics students from each group was videotaped solving the problem. Students' Jasper Book Journals and transcriptions of the videotapes and interviews were analyzed for emerging themes and a thematic analysis was effected.^ Tuning students' attention to information on the key idea of a problem affected their performance on the Cloze Procedure Problems. No significant difference was found between the two groups on the Transfer Problems. Some of the factors impacting the solution process were that more students in the experimental group than in the control group drew diagrams to help them solve the problem, considered alternative ways to solve the problem, and initialiy paid closer attention to the video. They also had greater knowledge about, and were more empathetic toward, eagles. Students in both classes reported confidence in their own ability to solve challenging problems and enjoyment from solving the problem. Some also reported learning that mathematics was meaningful.^ These findings support the Jasper literature and the Standards on problem solving published by the National Council of Teachers of Mathematics. ^