Levels of Knowing Mathematics
According to Appalachian State University, “The term ‘level’ refers to the order that information presented mathematically is processed and learned. Mahesh C. Sharma, in ‘Learning Problems in Mathematics: Diagnostic and Remedial Perspectives’ states that ‘almost all mathematics teaching activities, in most classrooms, take place at the abstract level. That is where most textbooks are; that is where most of the tests and examinations are.’ For students who have not mastered particular math content, he proposes the following order or ‘Levels of Math’ as effective for teaching mathematics: intuitive, concrete/experiential, pictorial/representational, abstract, applications, and communication.”
Based on Levels of Knowing Mathematics (Mahesh Sharma) and Depth of Knowledge (Norman Webb), this chart is a tool for planning math units, lessons, and/or activities at all levels. It prompts instructors to consider these fundamental questions:
- How can you effectively move your learners through the levels of knowing?
- Which depth of knowledge level is appropriate for each student and/or class?