Multiple Representations & Habit 4 Represent Math Non-linguistically

Habit 4 in Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking is labeled "represent math non-linguistically."  It reminds me immediately of Marzano's highly effective strategies.  But in secondary math it is more than using various graphic organizers to organize content although that is significant.

In 2012 Texas adopted new standards.  They are being applied to high school mathematics this year in our district.  There are seven process standards that are the same K - 12.  In that set of seven, at least 3 relate to this habit:

(D)  communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(E)  create and use representations to organize, record, and communicate mathematical ideas
(F)  analyze mathematical relationships to connect and communicate mathematical ideas

Multiple representations has been a strong emphasis for some time now.  Even popular major textbooks identify clearly the exercises that ask students to look at math from multiple representations:

A popular problem solving organizer asks students to represent the problem using a picture, a table, a graph, and an algebraic model.

In addition to these forms of representation, we use manipulatives even in secondary math. From MTBoS bloggers, some examples include:

• Algebra Tiles and Completing the square from Julie
• Legos and Feasible Regions from Fawn
• Skittles and Exponential Growth and Decay from Sarah

We also use media - pictures, video - to represent mathematics.  A couple of great resources include Estimation 180 and 3-Act Tasks.

When you think of representing math non-linguistically, what tools do you hope to find?