How many do you see? The use of nonspoken representations in first-grade mathematics lessons.

Abstract

Not all relevant instructional information comes in the form of spoken words. In the present study, the authors examine multiple modalities of nonspoken forms of representation-specifically gestures, pictures, objects, and writing-used by 3 teachers in 3 years of lst-grade math lessons. Teachers frequently used visually based modalities of representation and tended to produce combinations of representational forms rather than isolated representations. There were individual differences in their preference for representation types. Teachers used representations to accompany important spoken terms and to respond to student confusion. With nonspoken representations, teachers conveyed information critical to the explanation of mathematical concepts. Students must attend to the visual as well as vocal means of expressing information to gain access to all of the information presented in mathematics lessons.

Developing the use of diagrammatic representations in primary mathematics through professional development

“…Sowell 1989) simply using diagrammatic representations in the teaching of mathematics does not necessarily impact on the learning of pupils. This consideration of how diagrammatic representations can be used is in agreement with the issues around the use of various representations highlighted in the review of the literature (BoultonLewis 1998;Cobb, Yackel and Wood 1992;Flevares and Perry 2001;Hall 1998). In terms of teacher knowledge, this progression also emphasises how teacher knowledge can be more integrated; taking Ball, Thames and Phelps' (2008) model for pedagogical content knowledge as an example, the possible connections between knowledge of content and teaching (KCT) in terms of the representations that can be used to explain a concept and knowledge of content and students (KCS) in terms of the potential difficulties faced by students is evident.…”

“…In particular, teachers cannot assume that students recognise representations in the manner expected (Hall 1998); the meaning that particular representations have for the teacher may be quite different from the meaning they have for the student (Cobb, Yackel and Wood 1992). Therefore, if particular representations are to be used in the classroom, then teachers need to support students in learning to interpret representations (Flevares and Perry 2001), through providing "effective transitional experiences" (Boulton-Lewis 1998, 222) to support students' progression onto using these different representations.…”

“…Diagrammatic representations enable children to make connections between their existing experience and mathematical concepts (Post and Cramer 1989), and to gain insight into more abstract mathematical ideas (Duval 1999;Flevares and Perry 2001). Other benefits of external representations include their role as memory aids through the externalisation of calculation processes (Paivio 1969;Perkins and Unger 1994), and also their role in supporting problem solving processes (Lesh, Landau and Hamilton 1983;Webb, Gold and Qi 1990).…”

Middle School Teachers’ Discipline-Specific Use of Gestures and Implications for Disciplinary Literacy Instruction

“…Valenzeno, Alibali, and Klatzky's (2003) research indicated that this latter type of gesture can be especially vital to students' understandings of mathematical concepts by linking verbal speech to visible objects (cf. Flevares & Perry, 2001). In synthesizing the findings across several studies on gestures in mathematics, Sfard (2009) concluded that "gestures are crucial to the effectiveness of mathematical communication .…”

Animation Stimuli System for Research on Instructor Gestures in Education

“…Broad studies have been conducted regarding how instructor gestures influence the learning process. Math and science teachers frequently use their hands to depict information [2], [3], [4], [5]. Gesture in instruction has been shown to increase learning of a wide variety of mathematical concepts, including mathematical equivalence [6], [7], [8].…”