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Concrete to Abstract Thinking when M...

St.Agathe, Petrina D.

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Concrete to Abstract Thinking when Manipulating Algebraic Fractions.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Concrete to Abstract Thinking when Manipulating Algebraic Fractions./
作者:	St.Agathe, Petrina D.
面頁冊數:	147 p.
附註:	Source: Dissertation Abstracts International, Volume: 76-08(E), Section: A.
Contained By:	Dissertation Abstracts International76-08A(E).
標題:	Mathematics education. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3686145
ISBN:	9781321628418

Concrete to Abstract Thinking when Manipulating Algebraic Fractions.
St.Agathe, Petrina D.

Concrete to Abstract Thinking when Manipulating Algebraic Fractions. - 147 p.

Source: Dissertation Abstracts International, Volume: 76-08(E), Section: A.

Thesis (Ed.D.)--Hofstra University, 2015.

Recent research has revealed that rational expressions (also known as fractions) are the most cognitively challenging topics for students in today's classrooms (NMAP, 2008; Lamon, 2007; Wu, 2001). These findings have prompted further research on students' misconceptions associated with rational expressions, as well as the identification of successful teaching strategies for enhancing students' conceptual understandings. The primary goal of the Common Core State Standards (CCSS) is to develop students' higher-order thinking skills, as well as deepen their understanding of mathematical concepts. It is anticipated that implementing these goals of the CCSS will have a positive impact on students' understanding of rational expressions.

ISBN: 9781321628418Subjects--Topical Terms:

641129
Mathematics education.

Concrete to Abstract Thinking when Manipulating Algebraic Fractions.
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245 1 0 $a Concrete to Abstract Thinking when Manipulating Algebraic Fractions.
300 $a 147 p.
500 $a Source: Dissertation Abstracts International, Volume: 76-08(E), Section: A.
500 $a Adviser: Sharon Whitton.
502 $a Thesis (Ed.D.)--Hofstra University, 2015.
520 $a Recent research has revealed that rational expressions (also known as fractions) are the most cognitively challenging topics for students in today's classrooms (NMAP, 2008; Lamon, 2007; Wu, 2001). These findings have prompted further research on students' misconceptions associated with rational expressions, as well as the identification of successful teaching strategies for enhancing students' conceptual understandings. The primary goal of the Common Core State Standards (CCSS) is to develop students' higher-order thinking skills, as well as deepen their understanding of mathematical concepts. It is anticipated that implementing these goals of the CCSS will have a positive impact on students' understanding of rational expressions.
520 $a The purpose of this study was to determine whether a concrete to abstract teaching approach will positively affect students' conceptual understanding and procedural fluency with rational expressions as well as their attitudes toward mathematics. Students (n = 107) enrolled in Integrated Algebra (i.e., Algebra I) were randomly assigned to a concrete to abstract learning condition or to a control/traditional instructional group. Participants completed a mathematics attitude survey, multiple-choice items on fraction misconceptions, and short-answer items on numeric and algebraic fractions. Results from statistical analyses showed that the control group did better on the short-answer items at the time of the pre-test ( p < .05), but there was no significant difference between the groups at the time of the post-test. Since both groups performed equally at the time of the post-test, this showed that students in the treatment group made greater gains than students in the control group.
520 $a When performance data of participants from low and high performing groups were analyzed separately, there were no significant differences revealed between high performing students in either the control group or the treatment group. However, low performing students assigned to the concrete to abstract learning condition demonstrated significantly (p < .05) greater gains in short-answer total scores and developed significantly (p < .05) more positive attitudes towards mathematics. These data reveal that teaching methods based on a concrete to abstract approach have potential for improving the procedural fluency and conceptual knowledge of low performing students, as well as fostering positive attitudes towards mathematics. The implications of this study may inform curricular decisions, by providing evidence-based instructional design for educators wishing to use a concrete to abstract approach to further students' conceptual understanding of numeric and algebraic fractions, thus improving fraction instruction in mathematics classrooms.
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792 $a 2015
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856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3686145