Makbul Muksar

The Thinking Process of Students in Representing Images to Symbols in Fractions

Thinking is the development of ideas and concepts within a person caused by the process of establishing relationships between parts of the information stored in a person. In the early stages, the object of thought is accepted by the senses, processed in the brain into concepts / ideas, and expressed into a representation. Elementary students who are generally in a concrete operational stage desperately need this representation to facilitate their understanding. This research is a qualitative research with the subject of 12 students grouped into 3 groups, namely: (1) group representation in the usual way; (2) representation group with percent; (3) representation group by degrees. This research is intended to describe the thinking process of students in representing images to symbols on fractional materials. The results show that the representations of these three groups are essentially similar. All of them follow the APOS process (action, process, object and schema). The difference only occurs in group 1, where group 1 tends to think procedurally, while groups 2 and 3 think analytically.

Teachers' Representation in Solving Mathematical Word Problem

The use of multiple representations in mathematics learning plays a vital role to help students build conceptual understanding and solve mathematical problems. Therefore, teachers insight and view about the use of multiple representations in teaching mathematics requires more attention. The present study is aimed to investigate how representations used by mathematics teachers in solving the word problems in their teaching. The subjects for this study are junior high school teachers of mathematics. The data analysis indicated that teachers tend to use one form of representations to solve the word problem rather than use all forms in their mathematics instruction. Implications of the study finding on teachers and their practices are to be discussed.

Analysis of the Students’ Argumentation based on the level of Ability: Study on the Process of Mathematical Proof

Argumentation is one important component in building an understanding of mathematics students. Argumentation is concerned with a persons ability to give reasons based on the facts to make a conclusion and is frequently used in mathematical proofs. Argumentation produce arguments that cannot be categorized right or wrong but it is valid or not, so a persons ability does not guarantee the validity of arguments, depending on his thinking process. This research aims to analyze the arguments using the Toulmin argumentation consists of: data, claim, warrant, backing, qualifier and rebuttal. The researchers grouped students based on skill level high and low then analyze the sixth component of argumentation used students and validitasnya in the process of proof. Qualitative Research methods are used to collect data in the form of the results of the work of students, think aloud, field notes, and the results of the interview. The results showed that students with low ability can make valid arguments with true claims whereas students with high ability can also produce a valid argument with wrong claims. Each component of the argument has different characteristics based on the students ability level.