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

Table 10

Interview results.

Critical thinking subskills	Interview transcripts
(1) First interview at period 5
Evaluation (question 1)	T: “Multiplication between a monomial and a polynomial can be illustrated by finding the area of a rectangle.” Do you agree with this statement?; All were students silent for more than 10 seconds
Interpretation	T: what do you see in the picture?
	H: I see rectangles, variables, and numbers.	F: I see algebra tiles.	L: I see a monomial.
Analysis	T: can you explain more how it is related to our points?
	H: the width is represented by a monomial, and the height is represented by a polynomial.	F: it has a variable x and 1.	L: the picture has an x and a 1.
Evaluation	T: so, do you agree that finding the area of a rectangle can be used to demonstrate multiplication between a monomial and a polynomial? Why?
	H: yes, I do, because the expression of the width is a monomial, and the expression of the height is a polynomial. I think the statement is false because both expressions are monomials.	F: no, I don’t, because we cannot use monomials to find the area of rectangle.	L: no, I don’t. (Silent and smile)
Inference (question 2)	T: do you think your friends would answer this question (question 1) the same as you or different? Why?
	H: I think, the same as me.	F: i think, the same as me.	L: I think they will answer it as monomials and think like me.
2. Second interview at period 11
Evaluation (question 1)	T: “Multiplication between a monomial and a polynomial can be illustrated by finding the area of a rectangle.” Do you agree with this statement?
	H: yes, I do.	F: of course, yes.	L: yes, I do.
Interpretation and analysis	T: why?
	H: it related to some of the formulas.; T: the formula of what?; H: the formula of the area of the rectangle.; T: how it related to our point?; H: i think the rectangle’s width and height, respectively, are represented by a monomial and a polynomial.	F: in order to find the area of the rectangle, I just multiply between a monomial and a polynomial in this picture (Figure 2).	L: (Think more than 10 seconds) it could be x (x + 1).; T: what do you mean by “it could be x (x + 1)”?; L: (Silent); T: what does x represent in the picture?; L: I think it represents the width of the rectangle.
Inference (question 2)	T: do you think your friends would answer this question (question 1) the same as you or different? and why?
	H: yes, I think my friends would answer similarly to me because the length of the rectangle times the width of the rectangle. This is the general formula.	F: yes, I think the answer should be the same way, because my friends should know the formula for finding the area.	L: I think I’m not sure.; T: why are you not sure?; L: because each person has their own way of thinking.