Mathematically proficient students … justify their conclusions, communicate them to others, and respond to the arguments of others. They … distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.

… Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. … Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. —CCSS

Children love to talk, but *explanation *is very difficult for children, often into middle school. To “construct a viable argument,” let alone understand another’s argument well enough to formulate and articulate a constructive “critique,” depends heavily on a shared context. and a safe environment where their reasoning is valued.

Children learn language, including mathematical language, by *producing* it as well as by hearing it used. When students are given a suitably challenging task and allowed to work on it together, their **natural drive to communicate** helps develop the academic language they will need in order to “construct viable arguments and critique the reasoning of others.

Learning to know *why* you are right, to explain your reasoning, and to disagree with others politely and constructively are skills that develop through **practice**. My hope is that, given an interesting task, students can *show* their method and **narrate** their demonstration. The key is not the concreteness, but the ability to situate their words in context—to show as well as tell.