When you hear the word argument, you might think of a heated dispute or a clashing of opposing sides. In the mathematics classroom, however, the practice of argumentation involves making claims, supporting them with evidence, evaluating the reasoning of others, and making sense of mathematical ideas. This mathematical practice is identified by the Common Core Standards as central to the work of K-12 mathematics. It’s the practice through which a mathematical community determines what will be accepted as true.
While students in the upper grades may engage in more formal argumentation and deductive proof, young children can and do engage in supporting their reasoning with evidence, making sense of the arguments of their peers, and making conjectures about mathematical relationships. For example, students might argue that 5+3 is the same thing as 3+5 by modeling both expressions using unifix cubes.
Or students might move toward making more general statements about how and under what conditions a mathematical relationship is true. For young students, this might sound like, “It doesn’t matter what order you add the numbers in, you will always get the same amount.” This is related to, and perhaps builds on the claim above, but implies this relationship will be true for any number.