Questioning

Van de Walle and Lovin (2006) suggest that teachers “must transform classroom into a mathematical community of learners where student’s learning is enhanced by the reflective thought that social interactions promote.” (p.5) These social interactions, the conversations based on reflective thought, need to be focused on the intended mathematical concepts and it is through questioning that teachers can bring the conversation back on track. Good questions are those that give the teacher access to children’s mathematical thoughts, which will allow for supporting their development. As the teacher in the excerpt realized, the conversations about multiplication was not where s/he wanted it to go. S/he used guiding questions and comments to bring the conversation to a place where students were required to extend their thinking about what multiplication was, to how it could be used in different situations. Students need to be asked questions that lead to good conversations. Without thinking about it, questioning is something teachers do everyday. The reason for doing this may include to assess student thinking or to stimulate it. For this reason, it is important to ask the right types of questions that will allow each child in all classes the same opportunities to access the math and learning. There are particular questions that foster this communication and reasoning, namely open-ended questions, and it is these types of questions that we need to ask more often to open our classroom to allow all students to enter the world of mathematics.
Small (2008) defines an open ended question as a question “that can be approached very differently, but meaningfully, by students at different developmental levels” (p.642). She goes on to suggest that one of the key features of open questions that can allow for this differentiation is the fact that there are many different possible answers and many ways to get these answers. When students are asked open-ended questions, such as “What can you tell me about 13X52?, teachers are able to get insight into how students think about this question and what they know about the mathematics that surround it. When asking such a question, the desired answer is not for students to tell us the exact product, but to see how they go about thinking about what that product may be. Each and every student in this particular class would be able to offer some type of solution, even if it is something like the product will be greater than 100. The beauty of this question is that there is no one right answer or one right way of coming up with the solution, which is what makes it open ended. Teachers may wish to use scaffolding to make it even more accessible to all students as they could use different numbers, such as 1 digit numbers, then 1 and 2-digit number and so on, to help the student finally have some kind of success with the original question. More information about how to make questions more accessible to students will follow.
As teachers verbally ask more open ended questions, they get a chance to listen to students as they develop their own methods of doing. Students are asked to show their thinking and their way of knowing. In a more traditional classroom, where the main form of communication is in writing, students get really good at making teachers believe they understand something, and teachers get really good at believing them. If students were asked to calculate the product of 13 and 52 (a closed–ended question requiring only one correct answer), they may or may not get the answer correct. If they didn’t get it right, teachers would be lead to believe they don’t know how to multiply two two-digit numbers, when in fact they really did. Or, similarly, they may have gotten the product right, which would lead teachers into thinking they understood multiplication and can demonstrate this understanding by getting the product right, which again, could be the furthest from the truth. Through the use of open ended questioning student deception would be a lot more difficult. Therefore, teachers must ensure their questions do not lead to deception, as this is harmful to both teacher and student.