One reason we learn mathematics is so that we can solve problems. The latest educational research shows that the IMPROVE method of metacognitive questioning, developed in Israel by Mevarech and Kramarski, is very effective. Here are 4 IMPROVE questions to help your Stage 2 and 3 students think about their own thinking. These self-directed questions can be used as a scaffold. They’ll be especially useful when tackling complex, unfamiliar and non-routine problems. Problems like these should be available for all students to solve, not just your low blockage students. Most textbooks are not suitable as they include only routine problems using a known algorism. As Andreas Schleicher (Director for Education and Skills, OECD) says, ” … good mathematics education can … foster the innovative capacities of the entire student population. including creative skills, critical thinking, communication, team work and self-confidence”.
Or view Andreas Schleicher’s TED talk: Use Data to build better Schools http://www.ted.com/talks/andreas_schleicher_use_data_to_build_better_schools?language=en#t-399151