Using metacognitive skills in the mathematical problem solving heuristics among senior high school students

Date of Publication

2009

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Science Education Major in Mathematics

Subject Categories

Counseling Psychology | Science and Mathematics Education

College

Br. Andrew Gonzalez FSC College of Education

Department/Unit

Science Education

Thesis Adviser

John Addy S. Garcia

Defense Panel Member

Roberto M. Mendoza
Leo J. Capeding
Ma. Alicia-Bustos Orosa
Alicia F. Estrellado

Abstract/Summary

Numerous researches from abroad had been investigating the mathematical problem solving process among students, but little is done with regards to a clear and coherent theoretical framework that underpins the mathematical problems solving heuristics among high school students here in the Philippines. An evolved grounded theory was designed to find out the mathematical problem solving heuristics among high school students. Thirty participants representing different problem solving skills ranging from poor to good problem solvers were interviewed over a period of three months. Interviews were analyzed using Pandit’s grounded theory methodology and the constant comparison method. “Using metacognitive skills in the mathematical problem solving heuristics” was the central concern that emerged. Five main processes have been identified and explained that encompass an emerging substantive theory of “Using Metacognitive Skills in the Mathematical Problem Solving Heuristics”. The multi-distinct yet related processes are: 1) understanding the problem through sense-making, organizing and constructing useful information from the problem, 2) planning solution strategies by identifying, conjecturing and selecting strategies, 3) executing the plan, 4) checking the process and strategies undertaken, and 5) reflecting and extending the problem. The study revealed that the multi-distinct yet related processes could serve as a grounded frame of reference in which students do mathematical problem solving. The mathematical problem solving heuristics/process were neither linear nor just cyclical in nature, but is experienced and underwent by problem solvers with varying degree of creativity and flexibility depending on the problem at hand, their metacognitive skills, prior knowledge and some other factors. The theory proposes that students can be classified as dependent, transitional and independent thinkers according to how they solve mathematical problems using their metacognitive skills. One must be careful in trying to quantify or qualify these types of problem solver because it is possible that in the different processes of using metacognitive skills in mathematical problem solving heuristics; more than one type will prevail, as if two or three types of problem solver co-exist in using metacognitive skills in the mathematical problem solving heuristics. These problem solvers can either be successful or not in solving mathematical problems. It also proposes that certain intervening factors such as self-concept, belief, personality, exposure, motivation, attitude, environment, prior knowledge and skills, ability and faith could have influence in the multi-distinct processes of “using metacognitive skills in the mathematical problem solving heuristics”. The success or failure of the students in passing through each heuristics may be determined by these factors. Over-all, the present study gives a clearer picture on the processes students undergo, the heuristics they used during mathematical problem solving, and the role or influence that their metacognitive skills and other intervening factors may play in their success or failures in doing the task.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTG004625

Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Physical Description

1 computer optical disc ; 4 3/4 in.

Keywords

Families--Vietnam; Resilience (Personality trait)

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