Poster #31 - Exploring Children’s Developing Fraction Concepts Through Speech and Gesture

• In Event: 2-163 - Poster Session 08
  In Poster Session: PS 08 Section - Cognitive Processes

Integrative Statement

Fractions are a foundational area of mathematics that provide serious challenges for children (NMAP, 2008). The goal of this study is to explore children’s developing fraction concepts by drawing from two related areas: metaphorical reasoning and gesture. To do this, we examined children’s explanations and gestures to identify the specific mental models (Gentner & Stevens, 1983) that children express and the metaphors in which their understanding is grounded (Lakoff & Núñez, 2000).

Typically, children are introduced to fractions in third grade using area models (CCSSI, 2015), in which a whole area is partitioned into equal parts. However, curricula that disproportionately focus on the area model may be problematic (IES, 2010): Such practice may encourage children to treat the number of parts as whole numbers instead of fractions (Mack, 1990); entrench children into thinking that the properties and operations of whole numbers apply to fractions (Ni & Zhou, 2005); and discourage children from learning that fractions are continuous magnitudes (Newcombe et al., 2015; Siegler et al., 2011).

Because spontaneous gestures that accompany speech can reflect speakers’ mental representations (Alibali et al., 1999) and metaphorical mappings (Núñez, 2008) of mathematics, we need to explore how children conceive of—and gesture about—fractions. Swart and colleagues (2014) made progress on this by indexing approximately 18 different gestures reflecting children’s knowledge about fractions during different activities (e.g., manipulating objects).

In the current investigation, we analyzed video-recordings of 26 interviews with third- through fifth-graders when prompted to describe their understanding of fractions without any framing or tools (e.g., without manipulatives). The models evident in children’s explanations were coded inductively.

Analyses indicated that children conceived of fractions in three predominant ways: the area model, as a symbol, and as a number located on the number line. Most children (96.2%) relied on the area model, and most of these children (69.2%) conceived of the area as a circle (Figure 1). In tandem with using the area model, several children (38.5%) also referred to fractions’ symbolic notation. Only two children (7.7%) referred to the number line. We also noticed a developmental pattern in the use of single versus multiple models: Both third- and fifth-graders relied more on single models whereas fourth-graders relied more on multiple models (Figure 2).

Findings from this study provide additional evidence that gestures contain—and communicate to others—facets of our mental representations (McNeill, 1992; Núñez, 2008). These findings also highlight the value of attending to children’s gestures in educational settings: The gestures that accompany children’s explanations can provide details of how they make sense of mathematical concepts. And by taking up what children communicate, through their mouths and hands, teachers can establish a common ground in the classroom (Nathan et al., 2017) from which they can bridge to new ideas. Future work will further explore developmental patterns in children’s formation of fraction concepts. Additionally, examining how children’s fraction concepts are grounded in metaphor can provide insight into the variety of ways children think about fractions, and ultimately, guide instruction to support learning.

Authors

• Shereen Oca Beilstein, University of Illinois at Urbana-Champaign
  Presenting Author

• Michelle Perry, University of Illinois
  Non-Presenting Author