Standard 2: Mathematics as Communication

In grades 5-8, the study of mathematics should include opportunities for communication so that students can:

• Model situations using oral, written, concrete, pictorial, graphical, and algebraic methods

Benchmarks 11B (Common Themes: Models)
Grades 3-5, page 268
Geometric figures, number sequences, graphs, diagrams, sketches, number lines, maps, and stories can be used to represent objects, events, and processes in the real world, although such representations can never be exact in every detail.

Benchmarks 11B (Common Themes: Models)
Grades 3-5, page 268
Seeing how a model works after changes are made to it may suggest how the real thing would work if the same thing were done to it.

Benchmarks 11B (Common Themes: Models)
Grades 6-8, page 269
Models are often used to think about processes that happen too slowly, too quickly, or on too small a scale to observe directly, or that are too vast to be changed deliberately, or that are potentially dangerous.

Benchmarks 11B (Common Themes: Models)
Grades 6-8, page 269
Mathematical models can be displayed on a computer then modified to see what happens.
 

• Reflect on and clarify their own thinking about mathematical ideas and situations

  Benchmarks 11B (Common Themes: Models)
Grades 6-8, page 269
Different models can be used to represent the same thing. What kind of a model to use and how complex it should be depends on its purpose. The usefulness of a model may be limited if it is too simple or if it is needlessly complicated. Choosing a useful model is one of the instances in which intuition and creativity come into play in science, mathematics, and engineering.
 
• Develop common understandings of mathematical ideas, including the role of definitions

Benchmarks 9E (The Mathematical World: Reasoning)
Grades 6-8, page 233
Sometimes people invent a general rule to explain how something works by summarizing observations. But people tend to over generalize, imagining general rules on the basis of only a few observations.
 

• Use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas

Benchmarks 12D (Habits of Mind: Communication Skills)
Grades 6-8, page 297
Locate information in reference books, back issues of newspapers and magazines, compact disks, and computer databases.

Benchmarks 12D (Habits of Mind: Communication Skills)
Grades 6-8, page 297
Understand writing that incorporates circle charts, bar and line graphs, two-way data tables, diagrams, and symbols.

Benchmarks 12D (Habits of Mind: Communication Skills)
Grades 6-8, page 297
Find and describe locations on maps with rectangular and polar coordinates
 

• Discuss mathematical ideas and make conjectures and convincing arguments

Benchmarks 1C (The Nature of Science: The Science Enterprise)
Grades 3-5, page 16
Clear communication is an essential part of doing science. It enables scientists to inform others about their work, expose their ideas to criticism by other scientists, and stay informed about scientific discoveries around the world.

Benchmarks 1B (The Nature of Science: Scientific Inquiry)
Grades 3-5, page 11
Scientists do not pay much attention to claims about how something they know about works unless the claims are backed up with evidence that can be confirmed and with a logical argument.
 

• Appreciate the value of mathematical notation and its role in the development of mathematical ideas

Benchmarks 2C (The Nature of Mathematics: Mathematical Inquiry)
Grades 6-8, page 37
Mathematicians often represent things with abstract ideas, such as numbers or perfectly straight lines, and then work with those ideas alone. The "things" from which they abstract can be ideas themselves (for example, a proposition about "all equal-sided triangles" or all odd numbers").