Page 212 - Jurnal Pendidikan Tingkatan Enam 2019 - Jilid 3

Objective 1: Improve students’ ability to determine the correct method to solve the
first-order linear differential equations
Students are often confused in determining which methods they should use in solving
problems involving differential equations. Figure 5.3 shows an example of a question on
equations.

Find the general solution of cos ( ) = csc , expressing y in terms of x.

2
2

Figure 5.3 Sample differential equation question

Two steps can be used to guide students to choose between the variable isolation method
or factor extraction method.

Step 1: Make the subject to the left of the equation

The first step they need to do is to make the subject to the left of the equation and move

all the other variables left to right including the variables y and x.
2
csc

2
=

cos

Step 2: Factor the expressions to the right of the equation (between variables x and
y)
Next, students are required to factor the expressions on the right of the equation, namely,
two factors that include only the x-variables, and the second factor that only include the y-
variables. If these differential equations can be factored into two factors involving different
variables, then the method of separating the variables should be used.
2

csc
)
2
= ( ) (

cos
Since the differential expression above can be factored into two factors involving only x
2
csc
2
variables in the first factor ( ) and only y variables in the second factor, ( ), then the
Perubahan Paradigma Pemikiran Ke Arah Pendidikan Berkualiti
cos
method of separating the variables can be used.
2
csc
2
= ( ) ( )
cos
cos
2
∫ = ∫
2
csc
∫ sin cos = ∫
2
2
3

sin sin 3 3 = 3 +
3 +
= sin 3 3
3
+
3 3 3 = + 3
=
3
3
sin
3
3
sin = + 3 3
3
3
sin = + 3 1
−1 = sin ( + 3 )3
1 3
−1
= sin ( + 3 )3 1

3
3
−1
= sin ( + 3 )3

Objective 2: Increase students’ ability to demonstrate proper working steps required
Objective 2: Increase students’ ability to demonstrate proper working steps required
Objective 2: Increase students’ ability to demonstrate proper working steps required
Objective 2: Increase students’ ability to demonstrate proper working steps required
for each equation
for each equation
for each equation
for each equation
Students have been found to skip or not show the complete working steps when answering
Students have been found to skip or not show the complete working steps when answering
Students have been found to skip or not show the complete working steps when answering
Students have been found to skip or not show the complete working steps when answering
the questions on differential equations. Figure 5.4 is a second sample of a question on
the questions on differential equations. Figure 5.4 is a second sample of a question on
the questions on differential equations. Figure 5.4 is a second sample of a question on
differential equations.
the questions on differential equations. Figure 5.4 is a second sample of a question on
differential equations.
differential equations.
differential equations.
Find the general solution of ( ) + 3 = 4 + 6 expressing y in terms of x.

Find the general solution of ( ) + 3 = 4 + 6 expressing y in terms of x.

Find the general solution of ( ) + 3 = 4 + 6 expressing y in terms of x.

Figure 5.4 Sample differential equation question (2)
Figure 5.4 Sample differential equation question (2)
Figure 5.4 Sample differential equation question (2)
Figure 5.4 Sample differential equation question (2)

Students must first identify the correct method to solve the question. The method shown in
Students must first identify the correct method to solve the question. The method shown in
Students must first identify the correct method to solve the question. The method shown in
Students must first identify the correct method to solve the question. The method shown in
objective 1 can be used.
objective 1 can be used.
objective 1 can be used.
objective 1 can be used.
( ) = 4 + 6 − 3
( ) = 4 + 6 − 3

( ) = 4 + 6 − 3
6 3

6 = 4 + −
3
= 4 + − 6 3

= 4 + −

After performing the steps of identifying the correct method, it is apparent that the

After performing the steps of identifying the correct method, it is apparent that the differential
differential equation cannot be factored into two factors as the first factor involves only the
After performing the steps of identifying the correct method, it is apparent that the differential
After performing the steps of identifying the correct method, it is apparent that the differential
equation cannot be factored into two factors as the first factor involves only the x variable
x variable and the second factor is only the y variable. Therefore, a second method using
equation cannot be factored into two factors as the first factor involves only the x variable
equation cannot be factored into two factors as the first factor involves only the x variable
an integrating factor should be used.
and the second factor is only the y variable. Therefore, a second method using an
and the second factor is only the y variable. Therefore, a second method using an
and the second factor is only the y variable. Therefore, a second method using an
integrating factor should be used.
integrating factor should be used.
The “KIMCI CERIA” technique was used as intervention in this study. The “KIMCI CERIA”
integrating factor should be used.
technique is an approach where students are exposed to an advanced three step method.

The “KIMCI CERIA” technique was used as intervention in this study. The “KIMCI CERIA”
The “KIMCI CERIA” technique was used as intervention in this study. The “KIMCI CERIA”
i.
Use of FeMCI 5x2 Kit
The “KIMCI CERIA” technique was used as intervention in this study. The “KIMCI CERIA”
technique is an approach where students are exposed to an advanced three step method.
technique is an approach where students are exposed to an advanced three step method.
ii.
Use of FeMCI 5x2 Tables
technique is an approach where students are exposed to an advanced three step method.
Solutions without using kits and tables
i. iii. i. Use of FeMCI 5x2 Kit
Use of FeMCI 5x2 Kit
Use of FeMCI 5x2 Kit
i.
ii.
Use of FeMCI 5x2 Tables
ii. Table 4 shows the elaboration of the acronym FeMCI.
Use of FeMCI 5x2 Tables
Use of FeMCI 5x2 Tables
ii.
iii.
Solutions without using kits and tables
iii. Solutions without using kits and tables
Solutions without using kits and tables
iii.
Table 4 shows the elaboration of the acronym FeMCI.
Table 4 shows the elaboration of the acronym FeMCI.
Table 4 shows the elaboration of the acronym FeMCI. Kementerian Pendidikan Malaysia 211