Concrete Models

What are concrete models?

Forms of nonlinguistic representations, concrete models are a kind of learning tool that has important consequences for the development of understanding. They are external supports for learning and should be thought of as amplifiers of thinking. Concrete models can help students accomplish tasks more easily or help students do things they could not do alone without such support.  

Concrete models help students:

• Provide a convenient and permanent record of learning activity
• Provide a way of communicating with others
• Apprehend a concept; making difficult thoughts easier to manage or shaping the manner of thinking in approaching a topic

When using any concrete model, teachers should help students make connections with the abstract symbolism; otherwise, the use for the model could become trivial.

What to consider when differentiating instruction

Concrete models are effective instructional scaffolds, allowing more students access to the content. Teachers provide a concrete model to those students identified as benefiting from the added representation. Students who solve a problem with a concrete model have a level of instructional support, in contrast to those students who do not have the concrete model, thus keeping the rigor at the same standard for all students.

One way to apply concrete models for the purpose of differentiation is in the instructions for a problem students are asked to solve. For example, students are engaged in a problem that includes an illustration of different sized blocks. Some students may be given instructions that include, “Build models of the blocks using cubes…” Those students are given a set of blocks to manipulate thus scaffolding the original problem. Other student groups working the same problem are not given the concrete model, having to rely on their spatial intelligence. They may, however, be provided with other structures to organize their thinking for problem solving.  

Resources

Teaching Math, Grades K-12: Defining Representation
http://www.learner.org/channel/courses/teachingmath/gradesk_2/session_05/section_03_b.html (outside link)
To support the teaching of mathematics, teachers use concrete models, as presented in this webpage from Annenberg Media.

References

Hiebert, J. (1997). Mathematical tools as learning supports. Making sense. Portsmouth, NH: Heinemann.

Van de Walle, J. (2004). Elementary and middle school mathematics. Boston: Allyn and Bacon.