When planning math lessons it is very important to consider what type of task the students are doing in order to ensure that the students learn as much as possible. It has been known for a long time that there are different levels of inquiry that different lessons and different questions provide. In math there are four distinct levels of cognitive demand have been defined. It is important for teachers to consider what their goal is for their students in regard to these levels. Since I have become aware of these levels this year my teaching has changed. I am much more conscious of what type of task I am doing on a daily basis. I am trying to provide opportunities for my students to “do math” much more than I did before. Here are the levels and some explanations of when they are used.

Low Level –

· Memorization

¨ Committing facts to memory

¨ No procedures

¨ Have no connections to concepts or meaning

· Procedures without connections

¨ Use of procedure is called for or is evident

¨ Limited cognitive demand and what needs to be done is evident

¨ Co connection to the concept or meaning

¨ Focused on getting right answers not on the understanding of the math

¨ Requires no explanation

High Level –

· Procedures with connections

¨ Focus on the use of procedures to develop deeper levels of understanding

¨ Broad general procedures that connect to concepts

¨ Usually are represented many ways (visual diagrams, manipulative, symbols)

¨ Requires some degree of cognitive effort. Any procedures followed may not be done so mindlessly.

· Doing Math Task

¨ Requires complex thinking (there is no predictable well rehearsed approach to solving the task)

¨ Demand self-monitoring or self-regulation of ones own cognitive process.

¨ Requires students to use prior learning to solve the task

¨ Requires students to analyze the task and the task constraint so see if there is a limit to the solutions.

¨ Requires considerable cognitive effort and may involve some anxiety to the students

It is unrealistic to think that every day and every lesson could be at the level of doing math. It is also imperative that some lessons are at the highest levels. Only by having lessons that require higher level thinking skills can a teacher feel secure that she is preparing her students to be successful in math. The math standards and the math assessment for the state of Colorado require students at each grade to have the ability to “do math”.

This information comes out of the book Implementing Standards-Based Mathematics Instruction by Mary Kate Stein, Margaret Schwan Smith, Marjorie A Henningsen, and Edward A. Silver. There are great case studies in the book which are designed to help teachers make important decisions that will greatly affect their lesson planning and implementation.

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