One possible study can focus on the types of verbal questions a

teacher asks in order to promote critical thinking in a problem-solving classroom. The website http://www.criticalthinking.org/resources/k12/socratic-teaching.cfm discusses the importance of Socratic Teaching where teachers challenge students to think critically by asking specific types of questions. The site http://www.engin.umich.edu/~problemsolving/strategy/cthinking.htm lists the six types of questions namely:
a. clarification questions
b. questions that probe assumptions
c. questions that probe reasons and evidence
d. questions that probe viewpoints and perspectives
e. questions that probe implications and consequences
f. questions about the question
This study may be done by conducting classroom observations wherein the researcher will take note of all the questions the teacher asks during the period. These questions will then be coded and classified according to the type of questions asked. A possible way of classifying is through the six types of questions already mentioned earlier. The researcher may also interview the teacher in order to find out his reasons for asking specific questions.
Another way to go about studying the effects of the types of questions a teacher asks in a mathematics classroom, the researcher may conduct a study between an experimental and control classroom settings. Once it has been determined that the classes are comparable in terms of mathematical ability, the researcher may begin the study. In the experimental classroom, the researcher specifies the types of questions a teacher should ask in order to promote critical thinking while the teacher in the control class goes about conducting the class in the normal way. Comparisons between the effects of the treatment may then be studied through the use of an achievement test given to both classes. A survey about the thoughts and feelings of the students (as well as the teacher) as they experienced the ‘treatment’ may also be done.
I believe researching about questions that effectively promote critical thinking will help mathematics teachers choose appropriate questions to ask in class. Based on the result of this research, teachers will be more purposeful in their questioning techniques. Rather than concentrating on questions that have only one correct answer, the teacher may be able to encourage students to think critically so that they can come up with solid justifications for their arguments rather than coming up with poorly-reasoned answers.
Using a blog such as this one can be an effective tool in conducting research since it has the capability of reaching a vast number of people. Surveys can be uploaded and answers from the survey are received instantaneously. Educators, as well as students from all over the world, may share different opinions, ideas and experiences through this medium. However, it is difficult to verify information (about respondents, about the data, etc.) received through the internet or blogs.
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