The Misconceptions of Sixth Grade Secondary School Students on Fractions

Abstract

The purpose of this study is to determine the misconceptions of 6th-grade secondary school students in terms of part-whole relation in fractions, representation of fractions on the number line, comparison of fractions and operations in fractions. The sample of this study is composed of 104 students who are being educated in 6th-grade of five secondary schools in 2017-2018 teaching year in a province which takes place in the north part of Turkey. Fractional information test, which consists of 5 open-ended questions developed by researchers, was used as data collection tool. The data of the study were analyzed using the content analysis method and in this method frequency/percentage tables were used. By examining the explanations that the students have made, the incorrect answers are divided into categories, and the misconceptions in each question are presented separately. As a result of the study, it has been seen that students have misconceptions in terms of parts-whole relation in fractions, representation of fractions on the number line, comparison of fractions and operations in fractions.

University students' misconceptions about rational numbers: Implications for developmental mathematics and instruction of younger students

“…We also noted many unreasonable responses likely stemmed from a misapplication of procedures or mistakes with natural number calculation (Aliustaoğlu et al, 2018; Bentley & Bossé, 2018; Newton, 2008). In many calculation items, students provided a correct denominator response and an incorrect numerator response.…”

“…Aliustaoğlu et al (2018) described students relying on natural number understanding for comparison of fractions. That is, students determined a fraction was lesser if the difference between the numerator and denominator was less (e.g., is less than because 2 [i.e., difference of 3 and 5] is less than 9 [i.e., difference of 1 and 10]).…”

“…For example, when prompted to order three fractions from least to greatest, fourth-grade students ordered fractions from least to greatest but only considered either the value of the numerators or denominators (Malone & Fuchs, 2017). Aliustaoğlu et al (2018) noted the same error at the middle school level. In this way, students demonstrated a lack of understanding of a fraction as one number with a singular value on a number line (Van Hoof et al, 2018) and treated the numerator and denominator as separate natural numbers.…”

“…This error may be a combination of natural number bias and misapplication of procedures. In the middle school grades, students demonstrated confusion on fraction multiplication and division problems by using multiplication procedures on division problems or vice versa (Aliustaoğlu et al, 2018). At high school, students misapplied addition procedures to multiplication problems (Kelly et al, 1990) and misused algorithms among difference operations (Brown & Quinn, 2006).…”

Ontological Misconception in Mathematics Teaching in Elementary Schools

“…Many research have focused on analyzing students' misconceptions in learning mathematics (Aliustaoğlu, Tuna, & Biber, 2018;Gooding & Metz, 2011;Mohyuddin & Khalil, 2016;Sarwadi & Shahrill, 2014). However, the authors have not discussed yet about teacher mistakes in Mathematics learning in school.…”