|"In the middle grades, students should have frequent and diverse experiences with mathematics reasoning as they . . .
- examine patterns and structures to detect regularities
- formulate generalizations and conjectures about observed regularities
- evaluate conjectures
- construct and evaluate mathematical arguments."
(NCTM, 2000, p. 262)
Being able to reason is essential to understanding mathematics. Students who have regular opportunities to develop ideas, explore, and make and justify conjectures are more likely to expect that mathematics should make sense than those who do not have such opportunities. In the beginning of the middle grades, students will rely more on inductive reasoning, but as they continue to work with increasingly sophisticated and abstract concepts, they should begin to use deductive reasoning.
In this part, we look at inductive and deductive reasoning in the context of the middle grades. We also examine how reasoning and proof relate to the other process standards.
Just as with the other process standards, the teacher is critical in setting the classroom environment to encourage reasoning and proof. We must regularly engage students in thinking and reasoning in the classroom. In other words, we should expect that students will go beyond finding the solution to a problem in order to look for more general structures and relationships. Mathematics instruction should be focused around tasks that call for reasoning as part of the process of investigating mathematical relationships. Assessment should include monitoring the development of students' facility with reasoning, and their ability to justify their ideas to themselves and others.
Inductive and deductive reasoning