Students’ Conceptions About Decimals And Connection With Fractions

Author(s):

Dilek Girit(presenting / submitting)Didem Akyüz

Conference:

ECER 2013

Network:

24. Mathematics Education Research

Format:

Paper

Session Information

24 SES 01, Knowledge & Understanding of Mathematics

Paper Session

Time:

2013-09-10

13:15-14:45

Room:

D-405

Chair:

Birgit Pepin

Discussant:

Ramazan Avcu

Contribution

Although fractions and decimals are seen as different number sets, they are related to each other and can be used replaceable (Pagni, 2004). According to the curriculum decimals are another representation of fractions. In general, decimals are taught students after fractions. Van de Walle (2010) has indicated that this way can be the best to teach decimals for developing understanding of students. However, Martinie (2003) noted that children have more difficulty learning decimals than fractions. Thus, to provide students better understanding and conceptualization of decimals, the connection between fractions and decimals should be explained and developed at the beginning (Van de Walle, 2010).

In this perspective, relationships between fractions and decimals are investigated. The purpose of this study is to examine how students understand decimals and how they connect them with fractions, and compare and contrast different students’ conceptions about decimals. In this study, the following research questions are framed:

How do students represent a decimal as a fraction?

How do students represent a fraction as a decimal?

Which representation-decimal or fraction- do students prefer first?

In this study, data will be analyzed based on Leinhardt (1988)’s framework about knowledge types that students have. According to Leinhardt (1988) the four different knowledge types are: intuitive, concrete, computational and conceptual. Leinhardt (1988) defined these knowledge types as following intuitive knowledge refers to the applied, real-life, circumstantial knowledge; concrete knowledge means the knowledge of the nonalgorithmic, frequently, pictorial systems portrayed by texts and sometimes by teachers; computational knowledge means the procedural knowledge of mathematics, the algorithms and procedures for operations; and finally conceptual knowledge means the underlying knowledge of mathematics from which the computational procedures and constraints can be deduced.

Method

Participants are three 6 grade students that have been taught decimals in 5th and 6th class. As the aim of the study is to analyze students’ solution ways and their conceptions, the study is a qualitative study. The participants were determined regarding their mathematics teachers’ identification that one of students is average level, one of them is above average level and the other is below average level. Multiple case study is used to compare students’ solutions with each other. According to Creswell (2007), multiple cases are selected to show the issue with different perspective. In this study, five open-ended questions which require representing decimals as fractions or fractions as decimals were adapted from Elementary and Middle School Mathematics by Van de Walle (2010). In the interviews, the students were asked to solve on the paper and while they were solving the problem they were asked to think aloud. The interviews were audio-taped and students’ papers were collected. The data collected will be analyzed based on Leinhardt (1988)’s framework described above.

Expected Outcomes

Students generally think that there is not a connection among fractions, decimals, and percents. (Pagni, 2004; Sweeney & Quinn, 2000, Guiler, 1946). Thus, the findings are expected to show that students may have difficulty with representing fractions as decimals. The results of National Assessment of Educational Progress (NAEP, 1988) examinations also showed that students had difficulty to connect decimals to fractions. The results from sixth NAEP (1997) also showed that students had difficulty to put decimals on a number line which involved fractions. Based on this research, another finding from this study might include that students may prefer fractions to represent the same point on number line rather than decimals. Another expected result is to find out how students represent fractions as decimals or decimals as fractions in their solutions.

References

Creswell, J. W. (2007). Qualitative inquiry & research design: choosing among five approaches (2nd ed.). USA: Sage publications. Guiler, W. S. (1946). Difficulties in Decimals Encountered by Ninth-Grade Pupils, The Elementary School Journal, 46 (7), pp. 384-393. Leinhardt, G. (1988). Getting to know: tracing students’ mathematical knowledge from intuition to competence. Educational Psychologist, 23 (2), 119-144. Martinie, S. L., & Bay-Williams, J. (2003). Investigating students’ conceptual understanding of decimal fractions using multiple representations. Mathematics Teaching in the Middle School, 8(5), 244–247. Pagni, D. (2004). Fractions and decimals. Australian Mathematics Teacher, (60) 4, p28-30. Sweeney,E. S., & Quinn, R. J. (2000). Concentration: Connecting fractions, decimals & percents. Mathematics Teaching in the Middle School , 5, 324–328. Van de Walle J. A., Karp, K., Karp K. S., & Bay-William, J. M. (2010). Elementary and middle school mathematics: teaching developmentally (7th edition). United States of America: Pearson Education, Inc.

Author Information

Dilek Girit (presenting / submitting)

Middle East Technical University

Elementary Education

Ankara

Didem Akyüz

Middle East Technical University, Turkey

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