The use of metacognitive knowledge patterns to compose physics higher order thinking problems

Based on the procedure developed in this research, physics textbook written by Resnick & Halliday was selected to be studied. The book was chosen simply because of it is widely used as a main reference in teaching physics in Indonesian universities and other countries. Besides that, problems provided in this book were arranged systematically based on the level of difficulties.

The next step was studying problems about motion in one dimension at constant velocity. It was found that there is one problem required higher order thinking skill. This problem is related to escalator kinematics as follows.

A person is walking upwards in a rest escalator. She arrives on top of the escalator in 90s. If she just standing and the escalator is moving she arrives on top in 60s. How long does she will take to reach top while walking in a moving escalator? (Source: Resnick & Halliday, 1997)

International Physics Education students. The results showed that 90.77% of students were unable to answer the question correctly. The rest 9.23 % of students answered the question correctly but their answers were not equipped with logical sketch similar to the following sketch provided by the team.

Solution to escalator kinematics problem

It is clear that there are three different motion systems in this problem. The logical sketch and its knowledge pattern can be drawn as follows:

Figure 3.a. Logical sketch and knowledge pattern for the first case

Figure 3.b. Logical sketch and knowledge pattern for the second case

Figure 3.c. Logical sketch and knowledge pattern for the third case

Substituting the first equation into the second equation, it gives:
….. (2)
Then, the second equation is substitute into the third equation, it gives:
…. (3)
From equation (2) and (3) we will have t = 36s. So, the time she need to reach the top of escalator is 36 s.

Based on the analysis results of escalator kinematics problem, triangular type was found in every case. If all triangular patterns is combined and S is used as correlation quantity (the height of escalator is the same for each case), it result in a new pattern as depicted in Fig. 4.

Figure 4. Hexagonal pattern

Figure 5. Rectangular pattern

Based on three design of knowledge pattern mentioned above, each pattern can be defined as follows: (1) triangular pattern is a basic pattern which contain only one procedural knowledge, (2) rectangular pattern is a pattern which contain two types of procedural knowledge, and (3) hexagonal pattern is a pattern which contain three types of procedural knowledge. For rectangular and hexagonal pattern, their procedural knowledge can be similar or different types.

The next problem is how to design problems for higher order thinking exercises by using the aforementioned knowledge pattern. As an example, rectangular pattern with two different procedurals knowledge will be developed. For instance, a problem which connected two different equations, its procedure is as follows.

1. Established procedural knowledge, for example:

2. Create knowledge pattern, such as

Figure 6. Techniques to design problem based on rectangular pattern

3. Determine the quantity or concept to be the statement, hidden or asked. For instance, the problem statement are F, m, and Δt, while a is hidden quantity, and Δv is a quantity to be determined.

4. Draw a logical sketch, such as in Fig. 7

Figure 7. Logical sketch to design problem for student exercise

5. Develop problem, for the above case, the problem can be stated as follows.

A car is moving with constant velocity on a straight road. The driver is suddenly slammed on brakes with a force of 1000N when he sees an accident blocking the road. He noted that it take 20s to stop the car in front of the accident site. Determine the velocity of the car at the time the driver slammed on brakes.

In the process of problems development the use of box like the above examples is not important and teachers can create their own style. They can develop problem modes which appropriate or suitable with their students’ environment such as hole on the road, a cat or a herd of cattle crossing the roads. Similarly, teachers can use examples other than a car and it is not necessary the problem that related to the road.