__Electronic Proceedings
of the 12 ^{th} Asian Technology Conference in Mathematics__

**Abstract for 12746**

*A Mathematical Lesson on the Applications of
Differentiation *

* Principles*

Authors: Hong Eng Ding, Wooi Ping Hew, Mohd Hazhar bin Jamal

Affiliations: University of Malaya

Keywords:

Differentiation is an important topic in the Additional Mathematics

syllabus in the Malaysia upper secondary school curriculum. This

topic is used extensively in Engineering where it can be used to

investigate or predict the natural characteristics of machineries.

The Department of Electrical Engineering in the University of Malaya

has developed an E-Learning package for studying induction motor.

Differentiation principle was used to determine the maximum torque

the motor can generate. This paper presents a lesson on application

of differentiation that utilizes the relevant part of the Electrical

Engineering E-Learning package. The lesson was being taught to a

group of students in an upper secondary school in Malaysia.

The lesson starts with showing pictures of induction motors from the

E-Learning package, so that the students have a clear idea on the

machine where differentiation can be applied. A small actual

induction motor can also be shown in the classroom. The teacher then

shows a PowerPoint slides on the applications of induction motor in

everyday life. The torque-speed equation is given. The students are

required to differentiate the given equation and equal it to zero

(the principle of finding maximum or minimum value). This condition

yields an optimum parameter that generates the maximum torque. The

students can choose different motors with different characteristics

to perform the required differentiation in order to obtain the

maximum torque. They can check their answers and view the

torque-speed curve using the E-Learning package. The teacher then

concludes on the practical implications of different torque-speed

curves. Furthermore, the students are free to explore other aspect

of the E-Learning package to learn more about application of

differentiation in Engineering.

As a result, the students are exposed to the application of

differentiation principles using real examples. Using this

contextual learning approach, Differentiation will no longer be an

abstract topic but actually it could be applied to a real machine

that they can see and touch. This arouses the interest of students

in the topic of Differentiation and Electrical Engineering. It is a

synergy between the tool (Mathematics) and the application

(Engineering).