The most important thing in physics learning is how to help students to understand the basic concepts of physics to use them flexibly in solving daily life problems (Shin & Phang, 2012). Learning is a process with many factors involved. One such factor is using the learning model (Oliver & Oesterreich, 2013; Pritchard, 1998). Conformity with material characteristics becomes one of the keys to the success of applying the learning model (Pritchard, 1998; Sund & Trowbrigdge, 1973)

In studying physics, the magnetic field is an interesting phenomenon and close to everyday life. Several studies have discussed students' difficulties in understanding magnetic fields primarily in the concept of magnetic force (Ambrosis & Onorato, 2013; M Saarelainen, Laaksonen, & Hirvonen, 2007; Scaife & Heckler, 2010). The most common difficulty encountered is the determination of the direction of the magnetic force (Fatmaryanti, Suparmi, Sarwanto, & Ashadi, 2017a). More specifically, students are not used to cross-vector operations and are too abstract to visualize vector directions (Scaife & Heckler, 2010). In the early stages of the study, we observed that a large number of students made "sign errors" when determining the direction of magnetic force. The concept of magnetic force direction perpendicular to the velocity and magnetic field is not followed by the concept of vector multiplication (Fatmaryanti et al., 2017a). Marking errors in direction also occur in understanding the direction of fields, magnetic poles, and cross products (Kustusch, 2016; M Saarelainen et al., 2007). But there is still little research to assess students' understanding of the mathematical rules on which the rules of the hand are based on the concept of magnetic force directions.

All difficulties encountered related to how to describe the problem situation to obtain mathematical equations and represent mathematical answers in physical content or vice versa (Pospiech, 2012). Other studies have not discussed the abilities that students must have to express how mathematical equations are derived and selected relevant equations (Angell, Kind, Henriksen, & Guttersrud, 2008; Başkan, Alev, & Karal, 2010). For these reasons, students' mathematics modeling ability is needed to solve these problems.

Through mathematical modeling, students learn to rediscover concepts or laws that have been discovered by scientists. At first, students can create a simple mathematical model, then gradually do the test, formalize and generalize the model (Pospiech, 2012). Some studies found that student's mathematics modeling ability in Indonesia not as expected (Fatmaryanti, Suparmi, Sarwanto, & Ashadi, 2015a).

To solve the learning problems in magnetic concept and students' mathematics modeling ability, some learning model has been developed. In electric field concept, new learning model has been developing with active learning (Samsudin, Suhandi, Rusdiana, Kaniawati, & Coştu, 2016). As the electric field, the explanation of the concept of magnetism is very close to everyday life. However, the reality is more explanation of magnetism in mathematical explanation (Albe, Venturini, & Lascours, 2001; Fatmaryanti et al., 2015a) than finding the concept of the magnet itself. If we return to how scientists explain the concept of magnets, then all concepts always begin from the invention (inquiry)(Buck, MacIntyre Latta, & Leslie-Pelecky, 2007; Kock, Taconis, & Bolhuis, 2013).

Some representations can be used to make it easier for students to understand unclear concepts. The use of multiple representations in learning can provide many contexts for learners to understand a concept (Cock, 2012). In the Ainsworth ( 2006) study also stated that multiple- representation in learning is necessary to develop the concept and build students' scientific ability. According to (Kohl, Rosengrant, & Finkelstein, 2007) the use of multiple representations when solving problems affect learners' performance in problem-solving and can be used as a way to solve abstract problems.

In this paper, we look in detail at the innovation of learning model with optimizing students' mathematics modeling ability. We focused how to learn the magnetic concept in topic determine the direction of magnetic force by using mathematical modeling and explore student difficulties with hand rules and their understanding of mathematical modeling in solving problems.

Research Questions

The following questions are the frame of this study:

How are the effectiveness of magnetic force learning by using GIMuR model to enhance students' mathematical modeling ability?
How are the activities of teacher and student activities in all step of GIMuR model?
How are the students' ways in making mathematical modeling of magnetic force direction?