# The Processes of Mathematics

Reasoning

• Justify why an answer or approach to a problem is reasonable;
• Make and test generalizations based upon investigation or observation;
• Make predictions or draw conclusions from available information;
• Analyze statements and provide examples which support or refute them;
• Judge the validity of arguments by applying inductive(1) and deductive(2) thinking;
(1) inductive: inference by reasoning from the specific to the general.
(2) deductive: inference by reasoning from the general to the specific.
• Use supporting data to explain why a chosen method used and a solution are mathematically correct.

Connections

• Identify and use the relationships among mathematical concepts as a basis for learning additional concepts;
• Identify the relationships among graphical, numerical, physical, and algebraic mathematical models and concepts;
• Identify mathematical concepts and processes as they apply to other content areas;
• Use mathematical concepts and processes to translate personal experiences into mathematical language.

Communications

• Use multiple representations to express mathematical concepts and solutions;
• Represent problem situations and express their solutions using pictorial, tabular, graphical, and algebraic methods;
• Use mathematical language and symbolism appropriately;
• Describe situations mathematically by providing mathematical ideas and evidence in written form;
• Present results in written form.

Problem Solving

• Use information to identify and define the question(s) within a problem;
• Make a plan and decide what information and steps are needed to solve the problem;
• Choose the appropriate operation(s) for a given problem situation;
• Select and apply appropriate problem-solving strategies to solve a problem from visual (draw a picture, create a graph), numerical (guess and check, look for a pattern), and symbolic (write an equation) perspectives;
• Organize, interpret, and use relevant information;
• Select and use appropriate tools and technology;
• Show that no solution or multiple solutions may exist;
• Identify alternate ways to find a solution;
• Apply what was learned to a new problem.