The ability to connect mathematical concepts is one aspect of ability in mathematical reasoning. Brodie [2] states that, "Mathematical reasoning is reasoning about and with the object of mathematics." While Mullis, et al [3] states that reasoning is the highest cognitive domain after knowing and applying. Ball and Bass [1] argue that reasoning is an essential mathematical skill that is indispensable for understanding mathematical concepts, using mathematical ideas and procedures, and constructing a mathematical understanding.

 

Novak and Gowin [4] states that concept map is an educational tool to help students and teachers to know what knowledge has been mastered by students. In addition, Ausubel (in Novak and Gowin [4]) argue that the learner knows is the most important factor influencing learning. This means, by using the concept map, students are encouraged to connect previously learned and to build new concepts.

Real analysis is the fundamental theory of Differential and Integral Calculus which are widely applied to many areas of life. In real analysis course, students are required to understand every concept such as definitions, theorems, and corollaries. The students must also be able to connect between concepts. In the real analysis, a concept is always related to the other concept that have been studied previously.

 

In the paper, the problem is formulated as follow: how is the students' reasoning ability in linking concepts based on the concept map? Thus, the objective of the study is to investigate students' reasoning ability in linking concepts using concept maps.

In this study, the subjects are 4th semester students who take real analysis course in Department of Mathematics Education, Universitas Muhammadiyah Surakarta academic year 2017/2018. After studying the topic of number sequences, the students are given the task to construct the interrelationships between definitions and theorems on the topic of number sequences. Furthermore, six students are interviewed to find out more about students' reasoning ability to the concepts on the number sequences.

The results showed that there are various forms of concept maps arranged by students in explaining the relation between definitions and concepts in the number sequences. The diversity of the concept map shows the difference of students' understanding to the relation between the concepts on the topic being studied. In general, students have been able to determine the position of the definition in the structure of concept map correctly. All of students put the definition as the main idea in the concept map structure. However, the students have difficulties in determining the relation between the theorems, which is the first additional idea, second additional idea, and so on.

Based on the results of the study, it can be concluded the students' reasoning ability in linking the concepts is still weak. It can be seen from the concept map arranged by the students. In other words, concept maps can be used to investigate the students' reasoning abilities in relating the concepts that have been studied. Further research can be done to find out the ability of students in proofing the theorem associated with its ability in constructing the  concept maps.