Communicating Mathematics It is important for teachers and students to be engaged in communicating mathematics for higher understanding and the building of problem solving skills. Understanding mathematics means to define the measures of quality and quantity that connections have with new ideas and existing ideas. The greater understanding comes from the greater connections of network ideas. The goals of elementary teaching is to teach mathematics in meaningful and understanding ways to enhance problem solving skills and reasoning strategies based on real life. In doing so, students learn to visualize and communicate abstract ideas that creates opportunity for enrichment in reflective thinking.

A problem solving approach to mathematics engages students in inquiry that helps them build and improve current knowledge (Asking Effective Questions, 2011). A teacher who questions effectively can help students to identify thinking processes, see connections between ideas, and build new understanding in solutions that make sense to them. Reasoning skills are fostered by group work creating mathematical communities and the use of manipulatives. This starts with a student's prior knowledge and making connections within their real worlds. Educators become facilitators, or guides, who listen and observe as well as asks questions to enable students to become independent critical thinkers with...

For a student to gain insight, they must learn to value learning mathematics. This requires teachers and students to be engaged in mathematic communications.
The "back to the basics" idea is outdated and no longer falls into the real world. Technology has no room for the "back to the basics" idea. Because technology is driving the real world today, it is more critical for students to learn to problem solve and reason effectively for higher understanding and finding solutions. Group work in the classroom creates positive influences in the way children learn to solve problems and communicate the solutions.

Engaging students in talking, listening, and writing mathematics, they learn to analyze for mathematical solutions and draw understanding from classmates (Communications in the Mathematics Classroom, 2010). Characteristics of mathematical communication include precision about the problem details, relevant choice of method strategy to solve the problem, and accurate calculations. The assumptions and generalizations show how the details are addressed in the problem. Clarity enables a reader's ease of comprehension. Elaborations explain and justify the ideas and strategies. This enables students to learn to use higher thinking skills in analysis and evaluation to improve their conceptual understanding.

Children learn in different…