Taking steps with CRA

As we work to be more intentional in our use of CRA instruction, there are some things for us to consider:

++All students should be involved in the concrete level of instruction.  

++After creating a concrete model, students should have the opportunity to explain their model to a partner and discuss what is being represented in their model.

++When students are learning in the concrete, they should still be exposed to the representational and abstract models.

++Some students may be in the concrete longer than others.  That is okay, but teachers should support these students in representing their concrete models on paper.

++When working in the representational level, students should again be given opportunities to explain their drawing with a partner and discuss what is being represented.

++Once students move to the abstract level with a concept, they should still be able to represent their thinking about that concept concretely and pictorially.  If they are unable to, then their basis of conceptual understanding is probably not strong enough.

++Remember--these steps are important to students' strong base for future math concepts that are much more complex.  We want our students to feel comfortable in using concrete materials.  We want our manipulatives to be readily available and the norm in our classrooms for all students.

Math talk is so important for our students to better reason through their work so that they gain a stronger conceptual understanding.  As we work to build our CRA instruction, we don't want to skip opportunities for students to discuss their models with others.

This acronym developed by Witzel, Riccomini and Schneider (2008) is a good place to start as you look at your lessons through a CRA lens.

1. Choose the math topic to be taught.
2. Review procedures to solve the problem.
3. Adjust the steps to eliminate notation or calculation tricks.
4. Match the abstract steps with an appropriate concrete manipulative.
5. Arrange concrete and representational lessons.
6. Teach each concrete, representational and abstract lesson to student mastery.
7. Help students generalize what they learn through word problems.

What are you learning about your students through this method of instruction?  What do you think are the hurdles?