Questioning in the Mathematics Classroom
By Kelli Harris
Questioning is imperative in any classroom, but how it looks in a classroom varies depending on the content area, teacher, and students. Therefore, teachers need to find the appropriate questioning techniques for their classrooms. My questioning strategies are based on Richard Mayer’s research on how students learn. Mayer emphasizes that students must select, organize, and integrate the material. Prior knowledge plays a crucial role in this process. In their respective books, both John Bransford and Mayer explain that students need to construct their own knowledge in order for meaningful learning to occur. Through selection, organization, and integration, students make connections between their prior knowledge and new learning. This process needs to be respected and considered when planning instruction. For students to construct their own knowledge, effective and well-planned questioning strategies are crucial.
Doug Fisher and Nancy Frey’s gradual release model aligns with the goal of helping students construct their own knowledge and make connections to prior learning. For this reason, the gradual release model is evident in my mathematics classroom. Barbara Rogoff explains that guided participation helps bridge prior experiences with new learning. Guided participation is best achieved in a social context when the teacher guides the students through the problem being solved. As the gradual release model implies, the teacher is gradually placing more responsibility on the students. Varying and adjusting the questions asked throughout instruction typically achieves this. Fisher and Frey suggest the use of questions and prompts during the guided instruction phase. Questions and prompts require students to elaborate, discuss misconceptions, and uncover the why behind the concept. Ultimately, questioning and prompts during guided instruction get students thinking.
A favorite questioning strategy in my mathematics classroom pertains to analyzing errors. There are several ways this type of error-analysis strategy can be implemented. In the first method, I show students a math problem that is solved incorrectly. Students then analyze the problem to find where the error occurred. Some students will rework the problem, while other students will scan the hypothetical student’s work until they find the error. Following the think-pair-share approach, students then collaborate with their table partner and discuss where the error occurred. As a class, we then have a discussion about the identified mistake. Another method is to have the problem solved correctly (labeled “Friend 1”) and incorrectly (labeled “Friend 2”). Again, using the think-pair-share approach, students discuss with their table partner to determine which friend is correct and why. As a class, we then analyze the two friends’ thought processes. Example questions to pose at students may include the following:
- Which friend is correct? Why?
- Why may a student make this mistake?
- What misconception(s) do we see here?
- What advice would you give to this student so he can solve the problem correctly next time?
- Is there another way to solve this problem?
- Is there a more efficient way to solve this problem?
- How may the student check his answer to make sure it is solved correctly?
- Do you ever make this mistake? How can you make sure to avoid this mistake in the future?
- In what other situations do mistakes/misconceptions like this appear?
- How has analyzing this mistake helped you become a better mathematician?
All in all, students must critique the work of others, construct their own knowledge, and understand common misconceptions in mathematics. The Standards for Mathematical Practice are imperative for how students learn mathematics. Error-analysis questioning techniques align closely with Mathematical Practice 3, “Construct viable arguments and critique the reasoning of others.” When students can find and communicate the mistake, they are selecting, organizing, and integrating the concepts with prior knowledge and experiences to gain a deeper understanding. For students to experience meaningful learning, the teacher must provide opportunities for students to apply and transfer what they have learned. Error-analysis questioning strategies can provide these needed opportunities.