Common Errors in Fractions and the Thinking Strategies That Accompany Them

Abstract

This study aimed to reveal the common errors in fractions, the associated thinking strategies among 5th graders, and the persistence of these errors. A quantitative method was applied in this study through calculating the percentages of every type of error the students made in the diagnostic test, The qualitative part was performed through individual interviews and analyzing them to probe the thinking strategies used by the students that lie behind their common errors, The test was conducted for 240 students and 30 students were interviewed. The results showed a variety of common mistakes the students made, and that the rates of these mistakes were as follows: the highest was due to dealing with the fractions as integers, followed by errors about the basic concepts of the fractions. The results further showed a diversification in the students' thinking and the associated mistakes. One of the most noticeable mistakes was expressing the fraction without attention to the equal parts. The rates of other common errors were as follows: considering that the fractional number is always higher than the figure A/B, and that figure A/B is always less than one; treating the fractions as integers; misinterpretation of the relation between the numerator and the denominator with the actual value of the fraction, and ignoring the integer in the fractional number. The results also showed that more than 50% of the students made errors associated with solution strategies in the fractions issue.

The Impact of Using a Single Image in a Representation on a Misconception of Fraction Concept

“…Unfortunately, there are still so many students who have difficulty solving these problems related to fractions. This fact is in line with Alkhateeb [6], who stated that more than 50% experienced difficulties and made mistakes related to the application of fractions in a problem. This difficulty was caused by the students' limited understanding of the concept of fractions.…”

“…This importance is because understanding its concept is a basic skill in mathematics that can make mathematics learning more advanced [1,2]. Besides, it has an important role in learning mathematics to a higher level because these materials are the keys to number development theory which they allow students to deepen their knowledge of numbers beyond the levels that arise from the experience of integer and fraction are prerequisite materials for other numbers such as real and complex numbers [3][4][5][6].…”

Correcting Misconceptions in Fractions Using Interactive Technological Learning Activities

“…Students are still suffering from difficulty in learning the fractions and the different mathematical operations on them. For instance, studies of Alkhateeb (2019); Aksoy and Yazlik (2017); Duzenli-Gokalp and Sharma (2010); Hoch, Reinhold, Werner, Richter-Gebert and Reiss (2018); Reinhold, Hoch, Werner, Richter-Gebert and Reiss (2020); Schumacher and Malone (2017); and Trivena, Ningsih and Jupri (2017). Accordingly, the significance of this study is highlighted as an aspired benefit in providing a remedial strategy to the misconceptions in the fraction subject with the students.…”

“…The test consisted of ten questions that measure ten errors, which could be present with the fourth graders in the fractions subject, which were defined as per their existence in the educational literature. The most frequent errors of the students were chosen (Alkhateeb, 2019;Allen, 2007;Aksoy & Yazlik, 2017;Chang, 2013;Cramer, Wyberg, & Leavitt, 2008;Ghani, &, Maat, 2018;Schumacher & Malone, 2017;Siegler, Fazio, Bailey & Zhou, 2013;Trivena, Ningsih & Jupri, 2017). The questions varied throughout the regular fractions, comparison, and the addition and subtraction operations on them.…”

Investigation of fourth-grade students' mental structures about fractions

“…Ancak öğrencilerde kesir kavramının oluşması uzun zaman almakta (Pesen, 2007), bu nedenle kesirler öğrenciler için en zor ve karmaşık konulardan biri haline gelmektedir (Behr ve diğ., 1983;Charalambous ve Pitta-Pantazi, 2007;Lewis, Hayes ve Wysocki, 2012). Araştırmalar öğrencilerin kesirler konusunda zorluklar çektiklerini, bu konuyu anlama düzeylerinin düşük olduğunu göstermektedir (Alacacı, 2010;Alkhateeb, 2019;Bentley ve Bosse, 2018;Braithwaite, Pyke ve Siegler, 2017;Brown ve Quinn, 2006;Ekawati, Lin ve Yang, 2017;Marmur, Yan ve Zazkis, 2020;Purnomo, Widowati ve Ulfah, 2019;Stafylidou ve Vosniadou, 2004). Bu zorluklar öğrencilerin kesirleri sınırlı olarak anlamlandırmalarından kaynaklanmaktadır (Turidho ve diğ., 2020).…”