Exploring the division algorithm with GeoGebra

Division Algorithm is one of the fundamental topics in Number Theory. In Hong Kong, students need to learn division in Mathematics at primary level. In university, when students study Number Theory, they are required to understand the statement of the Division Algorithm and the proof of uniqueness and existence of the Division Algorithm. However, if we ask university students what division is, the first impression in their mind will normally be the symbol of the division”÷”, divisibility or even long division due to the mechanical work on solving division problems by using of long division in primary and secondary schools. Moreover, they may be confused on what the different between division and the Division Algorithm is. Due to the exam-oriented education in Hong Kong, students normally just mechanically compute division questions. They lack a chance to realize that division is based on the concept of multiplication and addition. As a result, when university students learn the Division Algorithm, they usually think of it as something very abstract and is totally different from they have it. Also, it is easy for them to forget the statement of the Division Algorithm since it is not simply just about the divisibility or the symbol of the division. Due to this learning phenomenon in the course of Elementary Number Theory (MTH2016) in Hong Kong Institute of Education (HKIEd) (HKIEd, 2014), we have to made a project that incopoerates designs a suitable e-learning resource, a GeoGebra applet, and guidance worksheets to enhance the teaching and learning of the course in accordance with the Technological Pedagogical Content Knowledge (TPACK) framework. This paper will first explain what HKIEd students need to learn of the Division Algorithm in the course, followed by the reasons of using TPACK framework in teaching and learning. In addition, it will introduce how candidates solve the difficulties in learning the Division Algorithm by using of GeoGebra applet. Afterwards, it will cover analysis on the feedback from students on the effectiveness and benefits of the applets. It will also provide comments on this new teaching and learning steategy.