Developing Students’ Mathematical Critical Thinking Skills Using Open-Ended Questions and Activities Based on Student Learning Preferences

Table 2

Use of open-ended questions in intervention.

Critical thinking subskills	Example of open-ended questions in polynomials session
Interpretation	T: what do the polynomials in each jigsaw mean?
	S: the polynomials represent the length of that side of the field.
Analysis	T: Abang said that “the area and perimeter of each ditch are the same.”
	Do you believe him?
	S: no, I don’t.
	T: why?
	S: the area of the ditch A is , but the area of the ditch B is . Therefore, my friends and I found that the area of the ditch A is different from the ditch B.
Evaluation	T: how do you know that is true, since we don’t even know the value of x?
	S: my friend and I tried to substitute positive integers, the area of ditch B more than the area of ditch A because ditch B has more expression terms.
Inference	T: are both perimeters equal? How do you know that?
	S: if I substituted x by 1 and 2, then the perimeter of the ditch A is less than that of ditch B. However, if I replaced x by 3, the perimeter of the ditch A is greater than that of ditch B. Therefore, the value of x that can equalize the perimeter should be somewhere between 2 and 3.