Title

Community college students' understanding of fractions: An investigation of the cognitive and metacognitive characteristics of students verbalizations while problem solving

Date of Completion

January 2003

Keywords

Education, Community College|Education, Mathematics|Education, Special

Degree

Ph.D.

Abstract

Students enrolled in noncredit mathematics courses at community colleges strive to learn mathematics topics such as fractions to acquire the content and skills required to qualify for desired degree or professional certification programs. Despite years of research that has explored the developmental sequence of knowledge of fractions among children, related research with adults is scarce. This study examined community college students' understanding of fractions prior to instruction, whether they solve problems presented in different formats with equal accuracy, and the cognitive and metacognitive characteristics of their verbalizations generated while solving problems involving fractions. ^ Twenty-three students from three community colleges solved 15 computational and contextual problems that reflected the eight elements in the developmental sequence of knowledge of fractions (i.e., fraction representation, partitioning or equal sharing, comparison or order, measurement or division, operator or multiplication, proportional reasoning, addition, and subtraction). Results indicate a stronger relationship existed between the percentage of problems solved correctly and students' performance IQ versus verbal IQ, as measured by the Wechsler Abbreviated Scale of Intelligence (The Psychological Corporation, 1999). There was also a stronger relationship between participants' performance in solving problems and the comprehension versus the vocabulary portion of a reading assessment (Gates-MacGinitie Reading Test, Level AR, Form S) (MacGinitie, MacGinitie, Maria, & Dreyer, 2000). ^ Students' performance in solving problems indicates that most only possess a rudimentary understanding of fractions (i.e., fractional representation and proportional reasoning for contextual problems). Results of a paired sample t-test indicate there was no significant difference in students' accuracy in solving computational compared to contextual problems involving fractions. ^ Factorial multivariate analysis of variance results indicate that successful and unsuccessful students employ both cognitive and metacognitive strategies when solving problems that involve fractions. Overall unsuccessful students verbalized a greater frequency of cognitive and metacognitive strategies when solving computational compared to contextual problems. Successful students generated a greater frequency of metacognitive verbalizations when solving computational compared to contextual problems, while unsuccessful students verbalized more metacognitive strategies for contextual compared to computational problems. Students who were successful were more succinct while students who were unsuccessful were verbose in their verbalizations while problem solving. ^