A COMPARISON BETWEEN THE KNOWLEDGE ORGANIZATION OF UNIVERSITY PHYSICS TEACHERS AND THE TEXTBOOKS THEY USE FOR THEIR TEACHING PURPOSES: BIOT-SAVART LAW AND AMPÈRE’S LAW

Abstract

Knowledge is not simply a collection of facts, principles, and formulas; instead, meaningful knowledge is organized around core concepts that guide peoples’ thinking about a subject. Therefore, knowledge organization is recognized as an important component of understanding learning and teaching. In this research, knowledge organization of two physics university textbooks was compared with that of four physics university teachers. The topic studied was magnetostatics with an emphasis on two topics of Biot-Savart law and Ampère’s law. The aim of study was to examine the structural features of the subject matter knowledge of teachers and textbooks. For this reason, concept maps were utilized to picture clearly their knowledge organizations. Concept maps were evaluated by means of a focus on their structural characteristics including hierarchy and clustering. Results indicate that the hierarchical organizations between knowledge of teachers and textbooks vary from one topic to another. The hierarchical organizations of teachers are more comparable to textbooks for the topic of Biot-Savart law. The clustering behaves in a very similar way in the case of patterns between textbooks and teachers for both topics. It was observed that the knowledge arrangements of Ampère’s law were more hierarchical, while the knowledge organizations of Biot-Savart were more clustered. Moreover, structural properties varied from one topic to another, even though topics belong to the same context. The possibility of recognizing such difference in knowledge organization is a first step towards developing more effective teaching and learning solutions.

Appendices

Appendix A

Formulas and Equations of Biot-Savart Law and Ampère’s Law with Details

Appendix B

Example of Calculating the Hierarchy

This picture is taken from John’s structural patterns, Fig. 7.

According to the definition of hierarchy (H), it is calculated as follows:

H = the number of spokes including Biot-Savart law or Ampère’s law/the total number of links

The number of spokes is calculated as follows:

$$ \left({}_r^n\right)=\frac{n!}{r!\left(n-r\right)!} $$

r :

number of links that form a spoke so r  =  2

n :

total number of links in each pattern

( ⁿ _r )::

represents the number of spokes that could be selected from each pattern

from a set of n links when the order of selection in not considered relevant.

So in the given example, number of spokes can be calculated as follows:

$$ \begin{array}{c}\hfill \left({}_2^6\right)=\frac{6!}{2!(4)!}=15;\kern1em \mathrm{then}\hfill \\ {}\hfill H=\frac{\mathrm{number}\;\mathrm{of}\;\mathrm{spokes}}{\mathrm{total}\;\mathrm{number}\;\mathrm{of}\;\mathrm{links}}=\frac{15}{6}=2.5\hfill \end{array} $$

This is an example of a very sophisticated hierarchy because H >> 1 (c.f. Koponen & Pehkonen, 2010)

Example of calculating the clustering:

This picture is taken from PSE structural patterns, Fig. 4.

There are 5 triangles which include Biot-Savart law or Ampère’s law.

The total number of links is 11, so:

$$ C=\frac{\mathrm{number}\ \mathrm{of}\ \mathrm{triangles}}{\mathrm{total}\ \mathrm{number}\ \mathrm{of}\ \mathrm{links}}=\frac{5}{11}=0.45 $$