Mathematical communications are important to enhance problem solving, reasoning, conceptual thinking, and reflective thinking skills. Children should value learning mathematics in real life variations. Teachers that engage students in mathematical communication in the classroom gain insights to instructional decisions and strategies to meet learning goals. Students draw in understanding from each other.
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 the use of mathematics. 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The "back to the basics" idea is outdated and no longer falls into the real world.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 ways that creates a need to differentiate instruction in the classroom that considers the different ways of learning and provides learning and consolidation of tasks with each child's learning capacity (Differentiating Mathematics Instruction, 2008). Mathematic knowledge, skills, and strategies warrant the need for differentiating instruction. A teacher looks for mathematical connections between each student's solutions to recognize instructional decisions and interactions with students in being responsive to their mathematical ideas, strategies, and communication. Each child should have the opportunity to make a meaningful contribution to the classroom discussion. The sharing of solutions should be organized to build collective knowledge related to learning goals. The key is the mapping of the sequence of instruction to meet learning goals. The mapping of the sequence of instruction to meet learning goals enables the process of mathematical communications with students to be easier to understand and build necessary skills in the conceptualization of the problem.
Communicating mathematics is important in today's classroom for children to learn skills by interacting with each other. A teacher asking effective questions enables students to think critically and examine the details of the mathematical problem. Examining the details enables students to learn strategies and methods for conceptual learning and thinking. This enables students to learn to analyze for solutions that make sense to them and draw understanding from others. It creates a positive learning environment as children learn to work together to solve problems and reason out issues involved.
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