The IMPROVE Method and Metacognitive Questioning Techniques

The IMPROVE method was developed by Mevarech and Kramarski (1997) as a method for the development and use of metacognitive skills amongst students to enhance their mathematical thinking. IMPROVE is an acronym that refers to a method of instruction consisting of the following steps: Introducing new concepts; Metacognitive questioning, Practicing; Reviewing and reducing difficulties; Obtaining mastery; Verification; and Enrichment. The IMPROVE method guides and trains students in formulating specific questions when solving mathematical tasks. Through these questions the students determine and plan the structure of the problem; determine and make connections between new and existing knowledge; determine and apply appropriate strategies and principles in solving the new problem; and justify and explain their solution. 

During a lesson in which IMPROVE is implemented, the teacher first introduces the new concepts to the whole class. Students then work in small heterogeneous groups, in which they take turns in asking and answering four kinds of metacognitive questions (These are: comprehension, strategic, connection, and  reflective questions.

Comprehension questions orient the student in articulating the main ideas of the problem (e.g. the student needs to describe the problem in his own words); classify the problem into an appropriate category (e.g. the problem is a rate of change problem or a simplification problem in which one uses factorisation); and elaborate the new concepts (e.g. to elaborate on the definition and meaning of a certain concept or terminology, or recognising and identifying what is given and what is the unknown). Strategic questions refer to strategies appropriate for solving the problem as well as the reasons for using that particular strategy. Students will select a certain strategy, justify their choice of strategy, and describe its application to the given problem as well. Connection questions take into account the similarities and differences between the problem at hand and the problems the students have previously solved and why this is this case .  Reflective questions are used in referring to those concepts in which the student reflects on the process and solution of the problem during and after problem-solving (e.g. asking what went wrong, why did I make certain errors or did I make any errors, and does the solution make sense?).