ABSTRACT

Reasoning problems help students to develop mental muscle. Adaptive reasoning is the capacity for logical thought, reflection, explanation, and justification. Reasoning is one of the essential elements of mathematical proficiency. It means that students will "think logically about the relationships among concepts and situations". Students in elementary school should have many opportunities for explanation and justification but also intuitive and inductive reasoning based on pattern, analogy and metaphor. Students need to be able to write the expression and/or equation that matches a problem because it shows that they can reason about the numbers—going from words to numbers. They also need to be able to reason from the numbers and be able to think about which situations match this problem. Table problems help students to organize information, to handle different pieces of information and to look for patterns.