An Educational Method for Theoretical Fields Through Dynamic Visualization

An Educational Method for Theoretical Fields Through Dynamic Visualization

Hiroto Namihira (Former Otsuma Women's University, Japan)
DOI: 10.4018/978-1-7998-1400-9.ch006

Abstract

This chapter proposes a new educational methodology for theoretical contents. It aims to effectively transmit theoretical content meanings. Here, the effects of content visualization enhance the transmission of meaning. By processing visual information, the human brain can immediately understand the mutual relationships between elements in addition to the whole meaning. Comprehension becomes increasingly effective when movement is added to static information. The new educational methodology proposed here is based on such visualization. It is called “The Dynamic Visualization Method.” It is designed so students can visually set allowable conditions before processing them. This selective freedom enables students to extract their hidden leaning interests. Mathematical processes were used to verify the effectiveness of this methodology. A variety of items were thus adopted ranging from the elementary-school to university levels. The contents of those items are visualized in this chapter. The educational effects are then discussed.
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Main Focus Of This Chapter

Aiming at the construction of an effective educational methodology for theoretical contents, a system should be designed to examine desirable items.

A theory’s “function” is interpreted and defined as a type of driving force that gradually transforms a given initial state into a final state following its own procedure.

System flow dictates that an initial state will first be visualized. At this point in the system design, it is required that students be allowed to establish an initial state through willful visual operation. This established initial state is then transformed into another state following the function of the theory and the directions indicated by the student. These transformed states are simultaneously visualized until the transformation reaches the final state. Students will obtain the kernel meaning of the theory by observing these continuously visualized images. These processes are shown in Figure 1.

Figure 1.

System flow

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Visualization should be designed based on each character of the treating contents. Detailed points in the system design are clearly mentioned through an explanation of each introduced example.

Mathematics was chosen as representative theoretical field. Here, vast contents range from the elementary to university level. These are designed and programmed for visualization.

The “Visual Basic” computer language was used to construct the “Dynamic Visualization System” (display resolution was set to 1920×1080). This was the main premise; every system detail was prescribed using Visual Basic.

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Solutions And Recommendations

Divided into two blocks, several examples ranging from elementary-school to university level are introduced here. For each example, the requisite conditions and designing procedures will be discussed in accompaniment to solution figures. The general state of application is surveyed after these examples are introduced.

Key Terms in this Chapter

Tailor Expansion: Express f ( x ) as sum of power x i i =0,1,2,3,….

Wiener Process: Continuous random process keeping constant variance per unit time.

A: Length of vector A. When

Convolution: Convolution of two probability density function f and g is defined as follows: This means a distribution of sum of two variables from f and g .

Characteristic Function: Characteristic function of f(x) is defined as follows: . Every information about f(x) can be extracted from this function.

Eigenvalue, Eigenvector: Characteristic of transformation operated by Matrix. Eigenvector is direction of transformation and Eigenvalue is magnitude of transformation.

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