Teachers’ conceptual understanding of fraction operations: results from a national sample of elementary school teachers

Teachers’ understanding of the concepts they teach affects the quality of instruction and students’ learning. This study used a sample of 303 teachers from across the USA to examine elementary school mathematics teachers’ knowledge of key concepts underlying fraction arithmetic. Teachers’ explanations were coded based on the accuracy of their explanations and the kinds of concepts and representations they used in their responses. The results showed that teachers’ understanding of fraction arithmetic was limited, especially for fraction division, yet a moderate relationship was found between teachers’ understanding of fraction addition and division. Furthermore, more experienced teachers seemed to have a deeper understanding of fraction arithmetic, whereas special education teachers had a substantially limited understanding.

Improving Mathematics Learning Outcomes Using Pipette Media in Students at SDN 17 Kuala Mandor B

This research was a classroom action research conducted in three cycles, each cycle consisting of planning, action, observation, and reflection. The aspects observed in each cycle were the activities of students and teachers, as well as the learning process of the subject matter in fractions using a simple medium named Pipette. The subjects were 15 students. The results of the study of students' abilities in the chapter of fractions, each cycle has increased. Cycle I, the average score of students was 51.93 with a percentage of completeness 13.33%. Students who reached KKM were 2 students. Based on the result of cycle I and cycle II, the average score of 85 students with a percentage of completeness 86.67%. Students who reached KKM were 13 students. From the two cycles applied, there was an increase in the ability of students in the subject matter of fraction addition. Based on the indicators of success in the second cycle, that the applied papita media can improve the ability of students in the chapter of fraction addition in V grade students of SDN 17 Kuala Mandor B, Kubu Raya Regency.

Analysis of Students' Errors on the Fraction Calculation Operations Problem

Students' errors on fraction problems often occur, especially in fraction counting operations. This error shows that the ability of students who do not understand the fraction problems. To overcome these errors, attention from the teacher is needed so that mistakes can be resolved. The purpose of this study is to describe students' errors in the fraction counting operation problem on each indicator, which is related to converting mixed fractions to ordinary fractions, determining fractions of value, and performing fraction addition and subtraction operations. This research is a qualitative descriptive study. The results showed that the majority of students experienced concept errors on each indicator requested in this study. Also, students make other mistakes such as mistakes of principle and carelessness.

How the eyes add fractions: Adult eye movement patterns during fraction addition problems

Recent studies have tracked eye movements to assess the cognitive processes involved in fraction comparison. This study advances that work by assessing eye movements during the more complex task of fraction addition. Adults mentally solved fraction addition problems that were presented on a computer screen. The study included four types of problems. The two fractions in each problem had either like denominators (e.g., 3/7 + 2/7), or unlike denominators exhibiting one of the following relationships: one denominator was a multiple of the other denominator (e.g., 2/3 + 1/9), both denominators were prime numbers (e.g., 2/7 + 3/5), or both denominators had a common divisor larger than one (e.g., 5/6 + 3/8). Self-reports, accuracy, and response times confirmed that participants adapted their strategy use according to problem type. We analysed the number of eye fixations on each fraction component, as well as the number of saccades (rapid eye movements) between fixations on components. We found that participants predominantly processed the fraction components separately rather than processing the overall fraction magnitudes. Alternating between the two denominators appeared to be the dominant process, although in problems with common denominators alternating between numerators was dominant. Participants rarely used diagonal saccades in any of the problems, which would indicate cross-multiplication. Our findings suggest that adults adapt their cognitive processes of fraction addition according to problem type. We discuss the implications of our findings for numerical cognition and mathematics education, as well as the limitations of our current understanding of eye movement patterns.