# Tool 3: Use of Socratic Questioning to Test Mathematical Understanding

It is quite common to hear classroom teachers asking students questions that return yes-no replies, or responses which are closed-ended, leaving no further room for thinking or discussion. To ensure that students understand the concepts, teachers need to use good questions to trigger thinking and inquiry in the students’ minds.

Socratic questioning is a powerful tool for educators to pose questions that provoke deep thinking in learners. It is a process where the teacher ‘poses a carefully constructed sequence of questions to students to help them improve their logical reasoning and critical thinking’ (Tomlinson et al. 2002, p. 55). In a classroom, usage of Socratic questioning technique to create a Socratic dialogue between teacher and students is one way of engagement, where both parties have a chance to clarify and verify concepts and knowledge. In short, Socratic questioning provides students with opportunities to clarify their thinking, challenge assumptions and look for evidence in their argument. It is also a strategy used to seek alternative viewpoints and perspectives from other students in the class and for the students to discover implications and consequences from their understanding of the concepts. Last but not least, good questions actually allow metacognitive development to take place, where students question their own questions and whether they are aware of what they know or not already know.

When Socratic questioning is used often in the classroom, students are not merely absorbing information from the teacher but are constantly processing and finding linkages between the responses and the questions and forming connections with existing knowledge. They also have a better understanding of the conditions and applications of the concepts and are thinking critically. Knowing how to apply the concept then becomes intuitive, and students find more meaning in their learning.

Some examples of Socratic questioning in the mathematics classroom include:

• 1. Why did you apply this formula?
• 2. What assumptions did you make for your formula to work?
• 3. Is there another way to solve the problem?
• 4. What can you generalise from the set of results?
• 5. Why are we considering the different approaches to solving this question?

It is in such a classroom where the teacher and students are engaged in Socratic dialogue that high level of intellectual exchanges can take place. The teacher must be skillful enough to pose questions that are pitched just sufficient to elicit responses from the students without giving away too much of the ‘answers’ and also to be patient to wait for students to think through the questions before they are able to give their response.

Because of the time needed to engage in deep thinking and dialogue, this is often not used in the typical classroom, especially when there is a wide range of abilities in the students in the same classroom, as some students may not be able to understand or grasp the meaning behind the questions, or if the questions are quickly answered by students of higher ability in the classroom, leaving others still figuring out the question. Hence, Socratic questioning is still best done with a small group of students with similar abilities so that they can ‘catch on’ each other’s thoughts to refine and deepen their own understanding. Another concern is the lack of opportunity to engage in Socratic dialogue due to the need to complete the syllabus within a set limited time. Teachers often shorten the time for questioning or resort to getting the higher-ability students to provide quick responses, in hopes that the rest of the class would be able to assimilate the ideas quickly.