Although intuition can and should be used in math--particularly for estimation--learners still need to reason to make sense of some of the more challenging and counterintuitive concepts in math, such as zero, negative numbers, irrational numbers and infinity, to name a few.
In elementary school, it begins with mathematical reasoning, "an evolving process of conjecturing, generalizing, investigating why, and developing and evaluating arguments" (Lannin, Ellis, Elliot, 2011)
Math is often considered the science of patterns, whether in the form of numbers, shapes, operations, and relationships. Seeking patterns is what children do naturally as they experience the world around them.
Conjecturing and Generalizing
After a pattern is discovered, mathematicians develop hypotheses to test if they are true. Hypotheses in math is called conjectures, basically working theories. Often conjectures lead into generalization, to see if there's a universal pattern. It goes from "it's true to this case" to "it's true in all cases!"
Zager, Tracy Johnston, Becoming the math teacher you wish you'd had, 2017
Lannin, Ellis, Elliot, 2011. Developing Essential understanding of Mathematical Reasoning for Teaching Mathematics in Pre-K-Grade 8.
Daniel H. Lee
This blog will be dedicated to sharing in three areas: happenings in my classroom and school; analysis and distillation of other educators' wealth of knowledge in various texts; insights from other disciplines and areas of expertise that relate and connect with educational practices.