Modeling Mathematics

A constant ponder amongst educations is why so many students have trouble learning mathematics.  At the start of the year, a common teacher practice is taking a student inventory and it is sad to say that there are responses which include “I can’t do math.”  Whether or not this is true is another topic of discussion but one can say that many students make this statement based on the fact that they struggle with learning mathematics. 

One the best tools for struggling students is to provide concrete and visual representations to supplement the abstract concepts which are taught at the middle level.  Concrete representations may include pattern blocks, unit cubes, 3D models, fraction bars, balance scales, colored counters and other items which students can manipulate during the mathematical process.  Visual representations may include area models, graphs, number lines, tables, and diagrams.  And with classrooms being filled with 21^st century tools, the usage of technology cannot be forgotten when looking for resources for visualization in mathematics.

The goal of exposing students to visualization tools is to support them in developing efficient and effective strategies when working with abstract mathematics.  This is not to say that teachers expose students to one tool and quickly revert to the abstract.  Providing students with a multitude of visuals where they are asked to apply, create and prove their mathematical work over and over develops a strong foundation for the learner. This means asking students to take ownership in the visualization of mathematics and creating deep roots of understanding long before moving onto the abstract usage of mathematical symbols.