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>Skills and perceptions related to pure utilitarian mathematics among undergraduate students enrolled in courses for mathematics-based majors.
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Skills and perceptions related to pure utilitarian mathematics among undergraduate students enrolled in courses for mathematics-based majors.
Motivated by the attrition rates in mathematics-based majors over the past two decades, the purpose of this study was to investigate the impact that mathematical emphasis and instructional methodology had on students' preference for mathematics. Literature has indicated that at the high school level there is an emphasis on applied mathematics while at the college level there is more emphasis placed on pure mathematics. There have also been indications that high schools, influenced by mathematics reform, have focussed on constructivist (nontraditional) based methods while at the college level drill-and-practice (traditional) methods have dominated. These issues were investigated in a two-part study. First, there was a quantitative portion that investigated the skills of entering college freshmen enrolled in Calculus I on three components of mathematics: Application, Symbolic Constructs, and Logic. A correlational analysis indicated that students' skills in both Application and Symbolic Constructs were correlated with their Logic skills. However, there was no indication of such a relationship between Application and Symbolic Constructs suggesting that students did not acquire equivalent skills in each of these components at the high school level.; The second part of the study investigated students' perception about mathematics and instruction. Upper-classmen in mathematics were administered a survey consisting of open-ended questions and Likert scale response questions to assess their opinions and perceptions on (a) the differences between high school and college mathematics, (b) what they liked and disliked about mathematics, (c) how often they encountered each mathematical emphasis, pure or utilitarian, and instructional approach, traditional or nontraditional at each the high school and college level, and (d) which mathematical emphasis and instructional methods they preferred. The results of this portion of the study indicated that (a) students perceived high school mathematics to be focussed on application while college focused on theory, (b) students liked mathematical application and disliked pure mathematics even though they indicated they liked the definitiveness of mathematics, (c) students experienced primarily traditional instructional techniques at both the high school and college level but with college having the most variation in instructional techniques, and (d) students preferred traditional methods of instruction over nontraditional methods.
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