Columbian researcher Dr. Mauro Garcia is a life-long math teacher. His work attracts a large following of researchers who seek the best ways to teach young minds to view math as an intuitive process rather than an overwhelming chore. Many students struggle with understanding mathematical expressions due to cognitive differences in input strategies. Garcia has found that the most successful students embed concepts in context.
His research identifies critical and rational expressions in algebraic conception. When presented with multiple solutions, it is essential that algebra students learn to differentiate between these concepts. Successful students differentiate by grasping information in a functional context that imbibes material in a progression. When tasked with multiple problems, students could discover solutions to complex problems through multiple methods. To understand the ability of students to grasp information, Garcia assessed student ability to use mathematical principles related to number theory.
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Garcia explained that there are two meanings to a math proof, the demonstrative and the plausible reasoning. The latter is used to distinguish between intuitions, some more or less reasonable than the next, and is present through proofs until validity is proved. Conjecture in mathematics refers to an assumed statement that is not demonstrated; only through further proof does it become a proposition.
“When students are excited about learning maths, they perform their best work. It is up to us to teach them the way,” said Garcia, who plans to assess how students discern variation in problem-solving in his future research.