The research on classification skills of 6th grade students on fractions

The purpose of this study is to examine how the categorization skills of 6th-grade students in fractions range and to determine that students make overgeneralization, undergeneralization, and misconceptualization errors and the correct classification belonging to the concepts of fractions and fraction types. The other aim of the study is to determine the procedural and conceptual errors of students regarding their learning outcomes in fractions. In other words, it aims to determine the quality of learning about fractions. The descriptive survey method among quantitative research methods was preferred since the research targets the description of an existing situation. The study was conducted in the spring semester of the 2021-2022 academic year, and a total of 292 sixth-grade students, 146 boys and 146 girls, from four secondary schools in Hatay's Iskenderun and Arsuz districts, participated in the research. Developed by the researcher, the Fraction Operation Skill Test (FOST), consisting of 20 multiple-choice items, and the Classification Skills Identification Test (CSIT), consisting of 28 multiple-choice items and three stages, were used as data collection tools in the study. The arithmetic mean and standard deviation of the total scores acquired by the students from CSIT and FOST were calculated in the data analysis, and the percentage distribution of the scores obtained from CSIT and FOST was determined. The first sub-problem of the research is to reveal the distribution of students' classification skills for the concepts of fractions, fraction types, and equivalent fractions. Accordingly, to analyze the undergeneralization, overgeneralization, misconceptualization and correct classification scores of the students, the frequencies and percentages of the scores were calculated by coding the answers of the students into the SPSS 25 program. In the second subproblem of the research, the errors made by students in their conceptual and procedural knowledge were determined. The third research sub-problem is to ascertain what kind of relationship there is between CSIT and FOST. Therefore, the normality analysis of the scores obtained from FOST and CSIT was examined. Because the scores did not follow a normal distribution, a nonparametric test called Spearman Correlation Analysis was used to determine the relationship between the two tests. In the findings of the first sub-objective of the research, in CIST, it was detected that the majority of the students made misclassifications in their skills to distinguish the example and feature of the concept of fraction, to show the fraction that is not divided into equal parts on the figure, to determine the features of a proper fraction when its example is given, to define the concept of an improper fraction and distinguish its feature, to distinguish the feature of the concept of a mixed fraction, and to find the equivalent fraction examples of the fraction represented on the figure. Besides, it was discovered that most of the students made correct classifications in their skills to display the fraction given with its reading, to define the concept of a proper fraction,to determine the features of mixed fractions by being given an example, and to define the concept of an equivalent fraction. The misconceptualization error rate in fraction types is higher than the overgeneralization and undergeneralization error rates. It was accepted that the students with misconceptualization errors had misconceptions about the types of fractions, and in-depth research must be conducted to attain a definitive determination of these misconceptions. According to the findings of the second sub-objective of the research, nearly half of the students properly used the rules of addition, subtraction, and division in fractions in the FOST. Furthermore, it was determined that more than half of the students correctly found which natural number the fraction was close to, and around half of them did operations correctly on mixed fractions. In the errors made by the students in the FOST, it was observed that they made mistakes in dividing the two whole numbers' intervals into equal parts on the number line, adding the denominators when adding fractions, subtracting the denominators when subtracting fractions, applying the rule of addition and subtraction in the rule of division for fractions, failing to pay attention to the decimal part when determining which natural number fractions are close to. Aside from that, it was discovered that when dividing a natural number by a fraction, students tended to divide the numbers in the numerator and denominator of the fraction that are directly divisible by the natural number. In mixed fractions, the students found incorrect results by doing operations on the whole parts by the whole parts and on the fractions by the fractions. In the findings of the research's third sub-objective, it was detected that there was a statistically positive and significant relationship between the scores obtained from FOST and CSIT. The results of the research revealed that the students had difficulty in distinguishing the examples and features of fractions and fraction types, and even though they were partially successful in the operations of fractions, students made procedural and conceptual errors. In this respect, it is recommended not to focus only on procedural knowledge in mathematics, but to present procedural knowledge by combining it with conceptual knowledge, and to illustrate the basic features of the concept by comparing instances of the concept with their non-examples.