Use of Student Mathematics Questioning to Promote Active Learning and Metacognition

Abstract

Asking questions is a critical step to advance one's learning. This lecture will cover two specific functions of training students to ask their own questions in order to promote active learning and metacognition. The first function is for students to ask themselves mathematical questions so that they learn to think like mathematicians who often advance knowledge by asking new questions and trying to solve them. This is also called problem posing, an important component of the " look back " step in Polya's problem solving framework. The second function is for students to ask their teachers learning questions during lessons when they do not understand certain parts of the lessons. Students who are hesitant to ask learning questions need to be inducted into the habit of doing so, and a simple tool called Student Question Cards (SQC) will be described to achieve this. Four types of mathematics-related questions are designed to cover meaning, method, reasoning, and applications and these questions are printed on laminated cards given to the students. The teacher will pause at specific parts of a lesson and require the students to select questions to ask to clarify their doubts. This reverses the typical roles of the teacher and the students during classroom interactions. Lessons learnt from a small study that trialed this approach with Grades 4 and 7 students in Singapore will be discussed. These two functions have the potentials to promote active learning of mathematics among school students through strengthening their metacognitive control. Teachers need to pay attention to the science, technology, and art of student questioning. Student questions, problem posing, metacognition, Confucius, Socratic dialogue MAIN THEME Children are naturally curious about themselves and their environment. A natural way with which they try to satisfy their curiosity is to ask questions. The main theme of this regular lecture is to argue that student questioning should be made a stronger part of classroom teaching and learning of mathematics than is currently practiced in many countries. There are many reasons why questioning is important in knowledge construction and its learning. Student questioning can serve two different but related functions. The first function is to help students think like mathematicians by posing their own mathematical questions and trying to solve them. This could lead to " new " knowledge constructed by the students. The second function is to train students to develop the good learning habit of asking their teachers mathematics-related questions about things that they do not understand. This learning function reverses the typical role of the teacher and students: instead of " teacher asks questions and students answer them " , the new role becomes " students ask questions and the teacher answers them " . Examples will be given below to illustrate these two functions. The 1086