The basis for an adaptive learning system is based on individual learning theories, of which Cronbach’s Aptitude-Treatment Interaction Theory [6] is a background theory. Cronbach suggested Aptitude-Treatment Interaction that adapts classroom procedures and strategy to students’ personalized characteristics. Many related theories were derived from the Aptitude-Treatment Interaction Theory [6]. Tobias proposed the Achievement-treatment Interaction Theory [7] as a special form of the Aptitude-Treatment Interaction Theory rather than interaction between aptitude and treatment. According to studies by Tobias and many other researchers, the learner’s current level of knowledge in curriculum content to be learnt acts as a strong variable in determining the learner’s demand for class [7]. Jonassen [8] proposed the Content-treatment Interaction Theory. According to Jonassen, Content-Treatment interaction can provide a more stable and generalized relationship because inquiring into the quality of content is easier than categorizing the learners’ characteristics [9].

Individual difference theory has become the basic theory of adaptive learning system. It has developed into an adaptive learning system based on this theory of individual differences

Adaptive learning systems can provide adaptability in a variety of ways. It provide adaptability includes prior learning, learning style, cognitive style, learner level, learning objectives and learning content. Among various adaptive functions, learning styles have been considered as an important factor for developing adaptive learning systems [9]. There have been several learning style theories proposed by researchers, such as those proposed by Keefe , Kolb and Felder and Silverman [10] [11]. The Felder–Silverman Learning Style Model (FSLSM) developed by Felder and Soloman have been recognized by many researchers as being a highly suitable model for developing adaptive learning systems [12]. Carver, Howard and Lane indicated that FSLSM could be the most appropriate measurement for developing hypermedia courseware by taking into personal factors into account. Kuljis and Lui [24] further compared several learning style models, and suggested that FSLSM is the most appropriate model with respect to the application in e-learning systems [13].

The previous studies described the function of the adaptive learning system. They did not mention them in connection with the educational theories on which they are based.

This study deals with learning style, learner’ knowledge level, and learning content among the adaptive functions proposed in the previous research. It refer to these adaptive functions by matching them with individual difference theories.

Achievement-Treatment interaction theory supports individual difference according to learners' knowledge level. The Achievement-Treatment interaction theory proposed by Tobias [11] interacts with the level of knowledge of learners.

This Achievement-Treatment interaction theory produced adaptive learning system that is provided a leveled learning according to the learner’ knowledge level. This study describes an adaptive learning system applying Brunner’s EIS theory with example [14].

<Table 1> is an example of the adaptability of an adaptive learning system that provides leveled learning according to Brunner's EIS theory. The system divides learners into three knowledge levels: higher, middle, and lower level. And depending on learner’ knowledge level, the learning content is provided differently. The higher level learners are presented the learning contents by the formula. The middle level learners are provided the content by the vertical line and by the formula. The lower level learners are provided contents continuously by concrete material, vertical line, and formula. Finally, the content and method of learning contents are different according to the learner’ knowledge level.

<Figure 1> shows an example of <Table 2>, which shows how low level learners are learning using concrete material as the first stage of learning. After learning by the concrete material in <Figure 1>, the lower level learners complete the learning using vertical line and formula as mentioned in <Table 1>. The middle level learner and the upper level learner do not learn using concrete materials. Only the lower level learner learns by using the concrete material in <Figure 1>. Finally, this adaptive learning system provides differentiated learning according to the learner’ knowledge level.

Aptitude-Treatment interaction theory by Cronbach [11] supports individual differences according to learners' learning styles. Therefore, Aptitude-Treatment interaction theory supports the individual difference according to their learning styles. This is the most typical example of an adaptability support method in an adaptive learning system. The adaptive learning system provides learning contents in a different and effective way to learners, even with the same contents. In this paper, we describe an example of applying adaptability to each learner according to Gardner’s multiple intelligence. The Gardner's multiple intelligence is the theory that each learner has excellent intelligence [15]. The adaptive learning system identifies firstly the superior intelligence of each learner and supports the learning contents considering each learner's superior intelligence.

This study shows an example of an adaptive learning system in which learning contents are applied to learners with excellent spatial intelligence. Spatial intelligence can recognize the temporal spatial world, and abilities to change forms through these perceptions. In this domain, mind mapping as shown <Table 2> takes place with the general knowledge about “Goryeo” that is old and historic Korea’ country name and is a place that conducts learning based on spatial intelligence. For the learning method, prior knowledge learned about “Goryeo” in the basic learning is used to create a mind map about “Goryeo”. First, circle and the branches are transferred to appropriate locations, and titles of major branches are inserted as shown in <Figure 2>. After save the major branches, sub branches are created and title is inserted in the circle. After generating the mind map, learners can print out what they created. The intense supplementary learning screen of spatial intelligence domain is the same.

The example of <Figure 2> shows an example of the content provided with adaptive learning system for learners with high spatial intelligence.

The Content-Treatment interaction theory proposed by Jonasen [13] provides differentiated learning according to the learning contents. The adaptive learning system based on Content-Treatment interaction theory differentiates the learning method according to the learning contents, not the learning style of the learner.

Currently, the adaptive learning system based on Content-Treatment interaction theory has high learning effect, but there are not many examples developed. This study describe an adaptive learning system that differentiates the learning method according to the contents of the task.

<Table 2> shows an example in which learning contents are presented by differentiating the instructional model according to the learning content. As shown in <Table 2>, when the learning content is concept knowledge, the content is presented in order of the advanced organized learning model, in the order of discovery learning model in case of principle knowledge, and in the order of direct instructional model in case of procedural knowledge. Therefore, the adaptability according to the learning contents provides the instructional model differently considering the learning knowledge. Finally, the learning content is provided adaptively by instructional model considering learning content.