Mathematical reasoning and proof offer powerful ways of developing and expressing insights about a wide range of phenomena. Ultimately, a mathematical proof is a formal way of expressing particular kinds of reasoning and justification. Being able to reason is essential to understanding mathematics. Building on the considerable reasoning skills that children bring to school, teachers can help students learn what mathematical reasoning entails.
Proof is a very difficult area for undergraduate mathematics students.
Reasoning and proof should be a consistent part of students' mathematical experience in prekindergarten through grade 12. Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts. Recognize reasoning and proof as fundamental aspects of mathematics From children's earliest experiences with mathematics, it is important to help them understand that assertions should always have reasons. These are the first steps toward realizing that mathematical reasoning is based on specific assumptions and rules. Part of the beauty of mathematics is that when interesting things happen, it is usually for good reason.