In the elementary mathematics classroom, the pursuit of meaning may take many forms, including how we communicate with our physical movements. Often, mathematical communication is organized around verbalization. For example, teachers are often encouraged to facilitate productive mathematical discourse among students (CCSSI 2010; Stein et al. 2008). Similarly, the spoken words of the teacher carry great importance as she or he elects to revoice certain strategies as stated and perhaps verbally modify the language of others to enhance their clarity for the entire class. Such verbal interactions are, indeed, quite important regarding the construction of meaning; but we cannot neglect the nonverbal, physical manner in which we communicate with students. As we will see in subsequent examples, such nonverbal communication plays a role in students' construction of mathematical arguments and critiquing the reasoning of others—the third of the Common Core's (CCSSI 2010, pp. 6-7) Standards for Mathematical Practice (SMP 3)—as well as teachers' facilitation of meaningful mathematical discourse—the fourth of NCTM's Mathematics Teaching Practices (NCTM 2014, p. 10). To put it succinctly, it is well worth our while to consider how we, as a learning community, talk with our hands.
Jonathan N. Thomas, email@example.com, is an associate professor of mathematics education at the University of Kentucky and a Kentucky Center for Mathematics faculty associate. As a former intervention specialist, Thomas is interested in the manner in which teachers and students draw meaning from mathematical situations.