Content and Problem Analysis in Turkish and Singaporean Mathematics Textbooks: The Case of Multiplying Fractions

In this study, Turkish and Singaporean textbooks were compared in terms of teaching content for multiplying fractions, a subject that most students have difficulty in understanding. The study analyzed the 6th-grade mathematics textbook published by the Turkish Ministry of National Education and its Singaporean counterpart. While the Singaporean textbook covered all meanings of multiplying fractions, the Turkish textbook did not include the operator meaning of multiplying fractions. Compared to the Turkish textbook, the Singaporean textbook included more solution strategies. The number line model was not used in the textbooks of either country, and only one representation format was used to model a fraction multiplication problem. The Singaporean textbook included more fraction multiplication problems than did the Turkish textbook. Many problems in both textbooks were of a one-step fashion and required numerical answers.

Improve Student Learning Outcomes in Multiplication Learning Mixed Fractions Using Teams Games Tournament (TGT) Model

<p><em>The problem in this study was the low student learning outcomes in mathematics learning the subject of multiplication of mixed fractions in class V. The purpose of this study was to see an increase in student learning outcomes in learning mixed fraction multiplication using the TGT learning model in class V SDN 2 Cigembor, Ciamis District, Regency. Ciamis. The population in the study were 30 grade students of SDN 2 Cigembor. The method used in this research is Classroom Action Research Methods (PTK) according to Kemmis and Mc. Taggart which consists of four stages: planning, implementing, observing, reflecting. This research was conducted in two cycles. The instruments used in this study were evaluation instruments, teacher performance instruments, and student activity instruments. Based on the results of the evaluation test data from cycle I to cycle II, it shows that in the first cycle the average student learning outcomes were 74.40 and learning completeness was 57%, while in the second cycle the average student learning outcomes were 79.83 and completeness learn by 87%. Based on the results of the research, it can be concluded that the use of the TGT learning model can improve student learning outcomes in the multiplication of mixed fractions in class V SDN 2 Cigembor, Ciamis District, Ciamis Regency, Academic Year 2019/2020.</em></p>

Demonstrating Conceptual Understanding of Fraction Arithmetic: An Analysis of Pre-Service Special and General Educators’ Visual Representations

To provide effective fractions instruction, teachers need deep understanding of fraction concepts (i.e., content knowledge) and skill in using visual representations of fractions to support student learning (i.e., pedagogical content knowledge); yet, research indicates that many pre- and in-service teachers lack knowledge in both areas. The present study examines the performance of 55 pre-service teachers (PSTs) on tasks assessing their procedural and conceptual knowledge of fractions, including a test of their ability to generate visual representations and story problems to model fraction multiplication and division. PSTs demonstrated high levels of procedural and conceptual knowledge of fraction addition and subtraction, moderate procedural knowledge for fraction multiplication and division, and relatively weak conceptual knowledge of fraction multiplication and division. Weak conceptual knowledge was related to inability to accurately model fraction multiplication and division using visual representations and story problems. Implications for research and practice are presented.