Do Teachers' Gestures Facilitate Students' Mathematics Learning? Evidence from Early Algebra

What factors influence whether students comprehend and learn from instructional language? One potential factor is the nonverbal support for language comprehension provided by teachers' use of visual scaffolding, including pointing, representational gestures, diagrams, and other methods of highlighting visual information. Previous studies in both educational and non-educational settings have shown that visual scaffolding can facilitate comprehension of speech, particularly when the verbal message is ambiguous or highly complex. These findings suggest that scaffolding of this sort may be particularly important in instructional settings, in which students' comprehension is often challenged by new concepts and unfamiliar terms. However, little is known about how teachers actually use visual scaffolding in instructional communication or about how such scaffolding influences students' comprehension and learning.

The proposed research is addressed to RFA Goal 2 (Development) and has three aims: (1) to document how teachers use visual scaffolding in naturalistic instructional communication; (2) to investigate whether teachers' visual scaffolding promotes students' comprehension of instructional language, and therefore their learning; and (3) to investigate possible mechanisms by which visual scaffolding may promote learning; namely, by heightening students' attention to the lesson, or by facilitating their encoding of visual information. We will examine these issues in the context of middle school mathematics learning in the domain of early algebra. Participants will be recruited from a public school district in a mid-sized Midwestern city. The district has an ethnically diverse middle school student population (55% Caucasian, 23% African American, 10% Asian American, and 11% of Hispanic ethnicity) with a wide range of SES. Across studies, we will analyze the data using both quantitative and qualitative methods.

To address Aim 1, we will gather two types of data. First, we will videotape one-on-one tutorial sessions in which middle school teachers and students work together on a complex mathematical task (symbolizing configurations of a pan balance using equations). Second, we will videotape middle school mathematics lessons that focus on linking different representations of mathematical information. We hypothesize that teachers will use visual scaffolding to promote students' comprehension of complex instructional material and to highlight links between representations.

To address Aim 2, we will conduct two experiments. In both, teachers will be asked to vary their use of visual scaffolding in the context of a lesson (a tutorial session in Study 3 and a classroom lesson in Study 4). In one lesson, teachers will use visual scaffolding as they ordinarily would. In the other, teachers will increase their use of visual scaffolding to highlight correspondences among different representations of mathematical information. We will examine whether students' learning varies as a function of the teachers' use of visual scaffolding. We hypothesize that students will learn more from the lessons that incorporate more visual scaffolding.

To address Aim 3, we will investigate whether visual scaffolding serves to heighten students' attention to the lesson in general, or to promote students' encoding of visual information. We will construct videotaped lessons in which teachers' use of visual scaffolding varies in systematic ways. Students will be randomly assigned to view one of the lessons, and following the lessons, students' encoding of visually presented information and their learning will be assessed. We hypothesize that students' encoding, and consequently their learning, will vary as a function of teachers' use of visual scaffolding.