Studying mathematics has been made much easier for young people enrolled on a program called IMPROVE, say researchers in Israel.
Developers Zemira Mevarech and her colleagues at the University of Bar-Ilan claim that making children aware of the processes underlying how they think and learn and giving them some sense of mastery over them, have led to significant improvements in attainment in algebra, numerals, substitution, expression, word problems and mathematical reasoning.
And their findings are borne out by Robert Slavin at the UK Institute for Effective Education whose Best Evidence Encyclopedia (BEE) acknowledges IMPROVE as one of only two programs developed during the last 30 years that have demonstrably improved teenager’s mathematical abilities.
IMPROVE is an acronym of all of the teaching steps involved. The I stands for Introducing the new concepts, the M for Metacognitive questioning, the P for Practising, the R for Reviewing, the O for Obtaining mastery, the V for Verification and the E for Enrichment.
Zemira Mevarech is professor in Education and a former student of Benjamin S. Bloom. Bloom was one of a group of influential psychologists at the University of Chicago who during the last century tried to advance understanding of how individual’s think and learn. His influence on Mevarech is evident in the logic underpinning IMPROVE.
In a series of randomized studies, she and her colleagues found that IMPROVE had significant positive effects on seventh graders compared to their peers in control groups. Benefits were similar among first year college students.
IMPROVE draws on the principles of metacognition, sometimes referred to as “thinking about thinking”. The term is used to encompass knowledge of cognitive processes (such as memory and information processing) and the ability to control and evaluate them (also known as mastery). Developing student’s metacognitive skills can lead to improved problem-solving and reasoning, which in turn make the business of solving mathematical puzzles more straightforward.
For example, an experiment conducted in the 1980s by Ian Schoenfeld showed that students performed better if they asked themselves simple questions such as "What am I doing right now?" and "Why am I doing it?".
At the start of an IMPROVE lesson the teacher demonstrates the self-questioning technique and outlines why it will be beneficial. Students then practice solving mathematical problems using the technique. At the end of the lesson the teacher models the technique again and every two weeks or so he or she reviews students’ progress and provides feedback.
[To read about the only other middle school mathematics program to have passed the Best Evidence Encyclopedia test, see BEE's tough line finds 98 per cent of math programs wanting.]
See: Mevarech Z and Kramarski B (1997) “IMPROVE: A Multidimensional Method for Teaching Mathematics in Heterogenous Classrooms”, American Educational Research Journal, 34, 2, pp 365-394 and> Mevarech Z and Fridkin S (2006) “The effects of IMPROVE on mathematical knowledge, mathematical reasoning and metacognition”, Metacognition Learning, 1, pp 85-97.
