I am doing my thesis and I am looking for some related studies on the levels of conceptual understanding and levels of thinking skills in mathematics.
Arnold, a teacher in the Philippines
I understand you are interested to measure students' levels of understanding in mathematics. There are several frameworks that you may be interested in. Understanding by Design (Wiggins & McTighe) talks about different facets of understanding. There is a Wikipedia entry on this. Richard Skemp (http://www.skemp.org.uk/) has written about instrumental understanding and relational understanding. This is another way to look at different types of understanding that students have in mathematics. These two will be good starting points for you to consider how to investigate students' level of mathematical understanding.
As for levels of thinking, perhaps frameworks that discusses levels of cognition are useful. The good ol' Bloom's taxonomy is one possibility - it has since been updated. Otherwise, you may be interested to read about SOLO taxonomy (Biggs & Collis) - there is a Wikipedia entry on this too. Otherwise see
Marzano's dimensions of thinking may be of interest to you.
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