Being able to understand how and why an answer was formed can help a child understand math in a less frustrating way, but reasoning and proof is also more specific to math problems themselves. This skill, of asking how and why and then finding the proof through patterns, structure and regularities in their real-life surroundings, is beneficial in the classroom and for life. It is often taught in the math classroom because patterns, structures and consistency is a normal occurrence within number lines, multiplication facts and elsewhere. Although in math class, these proofs are logical, the skill of reasoning and proving can lead to more creative answers in other paths of life. It is a skill taught over time through any lesson that it can be tied into. Children will not being able to successfully execute this skill after just one lesson, no matter how in depth. Questions such as “what do you think will happen next” and “Is this consistent no matter what” are questions that trigger thoughts in children. Their thought process or investigation is an informed one, or a mathematical conjecture. When open ended questions are posed to students, they may not even realize they are using “reasoning and proof” when answering, sometimes it will come more naturally then other times when a real “investigation” is taking place. When forming their answers, they can disagree with the information stated, agree with it, relate it to real-life, other math, or other content areas. They also may still question things that are not as measurable in the classroom.
National Council of Teachers of Mathematics (NCTM). Principles and Standards for School Mathematics. Reston, VA: NCTM, 2000.
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