Communication according to NCTM

Speaking and communicating in a clear and convincing way is essential in life. In mathematics speaking and communicating helps the students share examples and ideas as well as making clear something they have learned. Through communication you are able to accomplish four major tasks: 1) organize the ideas you have, 2) use mathematical thinking, 3) evaluate and analyze what you have shared as well as the ideas of those around you, and 4) you use mathematical language. Many students find that mathematics is pointless and not going to help them in the real world. Teachers need to make the math more relatable to students, and make it important for them to learn not only for a test, but also for the real world.
Organizing mathematical communication is important and needs to be clear for students to understand it. Students have been taught mathematics skills from a very early age and the mathematics that they will learn will become more and more complex, so they need to understand how it needs to be organized. Students need to be taught how to formulate questions and then understand how to support their answers to these difficult questions. Students also need to be given different types of examples that are not just worksheets and one type of problem. A teacher should be able to show the students diagrams and symbols that are used in mathematics. This will allow the students to reflect on what is happening and allow them to use some type of higher order thinking for what is happening in the math problem.
Students should constantly be working on how to analyze and understand data that is presented to them. Not all students are going to be on the same page mathematically when they are learning new skills and forms of working, so students need to work with one another to learn and teach a skill that will be around for a long time. When students are working together they are able to bounce ideas off of one another and see what ideas work and which ones don’t. They are able to discuss what is happening in a situation and are able to communicate it in a mathematical way. Talking with other students about a mathematical idea or problem will allow all the students who are having difficulty understanding, more help to develop the area that is difficult.