Exploring the Performance of Decimal Knowledge on Elementary School Students by Using Constructed Response Items

• Main Authors: Pei-Jung Wu, 巫佩蓉
• Other Authors: Jing Chung
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/qp5yq3

碩士 === 國立臺北教育大學 === 數學暨資訊教育學系(含數學教育碩士班) === 102 === This study is investigating the constructed response items application result of elementary students’ performance of decimal knowledge. It is designed for third-graders to sixth-graders, proceeded with paper-and-pencil test and interviews, and analyzed by students’ problem-solving process. As a result, this study surveys students’ problem-solving demonstration and error patterns, and then it announces the conclusion and also makes some suggestions for further researches. Decimal knowledge is composed of three main ideas, including “decimal conception,” “decimal computations,” and “decimal applications.” First of all, we classify “decimal conceptions” into nine sub-concepts, including decimal meaning, decimal place value, decimal place name, decimal conversion, decimal comparison, decimal density, linkage of decimal and fraction, and decimal conversion between different units. Then, there are four categories in “decimal computations,” including addition of decimal, subtraction of decimal, multiplication of decimal, and division of decimal. At last, “decimal applications” are divided into decimal-addition word problems, decimal-subtraction word problems, decimal-multiplication word problems, decimal-division word problems, and estimation. The research objects are 177 students, which are composed of three-graders to sixth-graders educated in researcher’s elementary school. The data are collected by ways of interviews and written tests, which make a student answering six questions of constructed response items. This study makes several conclusions. Frist of all, when students start to learn decimals, they show better performances when learning single content than learning multiple contents. In the second place, it is easier for students to mark correctly on number line divided into decile than to mark on which divided into bisection or five-parts. Third, the ability to process decimal density problems is much better with upper-graders, as the sixth-graders did better than the fourth-graders. Last but not least, it shows relatively better result when solving decimal addition and subtraction questions than multiplication and division questions in that students are prone to make mistakes when marking decimal points. The third-graders can be confused with place value and place name. When they solve addition and subtraction questions, it is common for them to align the last place name of decimals. Similarly, the students can ignore the decimal point when doing multiplication questions and solve them as integers; while doing division questions, they can also make mistakes when marking the decimal point of remainders. To sum up, most students can solve everyday decimal questions with knowledge, while some of them can not totally understand the meanings of the questions so that they are unable to convert the meaning into questions. For math educators, this study suggests that students should understand decimal meanings and formations in order to be proficient in applying the ability in daily life. The third-graders and the fourth-graders can not connect between conceptual knowledge and procedual knowledge, so they should practice to bind the tie from conceptual knowledge to procedual knowledge.