Learning and thought characteristics of "weak" math students

Learning and thought characteristics of "weak" math students

This is a thought provoking research done by Dr. Ronnie Karsenty, Prof. Abraham Arcavi and 

Dr. Nurit Hadas at the Department of Science Teaching, Weizmann Institute of Science.  I've known it in Hebrew but luckily was able to find an English version as well: 

Exploring informal mathematical products of low achievers at the secondary school level.  Ronnie Karsenty, Abraham Arcavi, Nurit Hadas. Journal of Mathematical Behavior 26 (2007) 156–177.

This paper is free for download.

This paper helped us develop the Jerusalem municipality educational psychology service's approach to assessing math and math disabilities.

The point I found the most interesting in this research (among many other interesting points which I will not mention here) is that every child, including a child with poor math skills, has an inner theory or an inner set of basic intuitions or premises according to which he performs in math.  Children invent  informal methods to solve math problems that are based on these inner theories.  Children's math mistakes are not coincidental but are the result of implementing the inner intuitions or theories.  The uncovering, during assessment, of the child's inner theory will help us understand how he thinks, where the problem is and how to assist him.

The process of uncovering the child's inner theory is a dynamic process of inquiry, targeted at encouraging the child to test his premises and consequently  decide  whether  to keep or to change them.  Thus the assessment process becomes one of discovery, during which the child learns about himself (reflects on his thinking process) and also learns the material that is being taught.

I think math teachers should find this research interesting and stimulating, suggesting a fresh 

way to work with low achieving students.

This assessment process – the uncovering of the inner premises that guide children's work, is useful not only for math assessment, but for reading comprehension assessment as well.  A parallel process can be done with a text: uncovering, with the child, his inner premises about the text, that caused him to draw the conclusions he drew.  This way we can understand the sources of his difficulties and design, with the child's collaboration, suitable interventions.