The use of various mathematical representation forms is important to be considered in mathematics learning.  The various forms of representation usage on the task or problem can be identified students' difficulties in understanding mathematical concepts. The study about this is crucial in order to recognize the strong connection between mathematical concepts and various representational structures. The aim is to see the real difference among each level of students' mathematical understanding dealing with multiple representation tasks. Therefore, this study focuses on knowing the characteristics of students' understanding in solving multiple representation tasks based on SOLO Taxonomy.

 

The explanatory method in qualitative research was used to obtain the students' understanding characteristics in solving multiple representation tasks. Twenty-five students mathematics major in the Islamic State University of Malang participated in solving multiple representation tasks. This task was classified as a non-routine task because mathematics books and mathematics learning rarely ask students to find the composition function value from three different forms of representation. Shortly after the students solving the task, an interview was conducted to investigate/confirm the mathematical understanding which determined their task solving. The questions posed around the understanding of register representation, the mathematical concepts represented by the register and the connection between the mathematical concepts with different representation registers. Data on written work and interviews data characteristics were reduced, coded and described based on the SOLO taxonomy level. The SOLO taxonomy response indicator described in Table 1.

 

This research found some characteristics of students' mathematical understanding in solving multiple representation tasks. Characteristics of students' mathematical understanding namely complete flexible understanding, incomplete flexible understanding, and compartmentalized understanding. SOLO taxonomy level for students who have a complete flexible understanding of relational and students who have an incomplete flexible understanding is in multi-structural level. Students who have a compartmentalization understanding go to the uni-structural level. The findings of this study can be used as a guide to assess the characteristics of students' understanding of learning based on multiple representations.

 

Table 1. Indicators of student understanding in solving multiple representation tasks based on SOLO taxonomy.

 

Level

Indicators

Pre-structural

• Lack of knowledge in representation register terms.
• Having a little information about representation register, nevertheless cannot explain mathematical concept represented by the register itself.
• Trying to get the tasks done, but failed to find out the right answer.

Uni-structural

• Only understand specific representation register (symbolic,table,or graphic).
• Doing composition function concept interpretation only from the registered particular type of representation.
• Understanding compositional function concept from one kind of representation only.

Multi-structural

• Understanding symbolic, table, and graphic representation register.
• Doing interpretation of symbolic, table, and graphic representation register to come across composition function concepts.
• Understanding composition functions concept from various types of representations (graphics, symbolic and tables).

Connecting the concept of composition function to two forms of representations only.

Relational

• Understanding symbolic, table, and graphic representation register.
• Doing interpretation towards symbolic, table, and graphic representation register to discover composition function concept.
• Understanding composition function concept from many kinds of representations (symbolic, table, and graphics).
• Connecting composition function concept to three representation forms.

Extended Abstract

• Understanding the register of all mathematic representations which reflects real function.
• Doing interpretation towards register of all mathematic representations to pursue composition function concept.
• Understanding composition function concept of all mathematic representation varieties.
• Creating flexible connection among mathematic representation and being able to generalize all mathematic concepts.