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Evaluation of Three Interventions Teaching Area Measurement as Spatial Structuring to Young Children

Thu, March 21, 2:15 to 3:45pm, Baltimore Convention Center, Floor: Level 3, Room 331

Integrative Statement

Hypotheses
A previous study with intermediate students indicated that two interventions promoted growth along the area learning trajectory for children at the Area Unit Relater and Repeater (AURR, see Table 1) and Initial Composite Structurer (ICS) levels. This study built upon the earlier work to address the following research questions:
1. How do the treatment conditions affect *younger* children’s production of accurate numerical measurements?
2. Are there patterns in children’s observable behaviors before and after a level shift?
3. Do children operating at level n-2 who experience the modeling of advanced-level strategies from level n learn these directly, or do they develop through the sequence (n-2, n-1, then n)?
4. How do the conditions affect children’s use of strategies and their development of procedural and conceptual knowledge, including transfer of learning?

Study Population
Children who participated in all sessions were 70 children from 12 classrooms in four elementary schools in a large, suburban school district: 29 Grade 1, 23 Grade 2, and 18 Grade 3.

Methods
In this microgenetic study, children were randomly assigned to one of three interventions: (1) constructing arrays by drawing parallel line segments in both dimensions, subdividing rectangles (S intervention) and (2) building a row of square tiles and iterating to fill a rectangular space (I). The comparison condition (3, C) exposed children to a verbal report of area that reflected the implicit multiplication of length and width. Children were asked, “What is the area of this rectangle?” for three rectangles, then showing a video of someone finding the area of the same rectangle consistent with the intervention. We identified and coded broad, observable behaviors; specific, observable behaviors and strategies; and three general approaches.

Results
RQ1: Children in both the I and S groups increased their correctness scores more than children in the C (Control) group (Fig. 1).
RQ2: Children in the I group, with its emphasis on composite units and iteration, saw a visual representation of a single row but did not use that strategy, but abstracted the row and/or column structure that allowed them to use other strategies (such as skip counting). In contrast, children in the S group more directly and completely adopted that intervention’s subdividing strategy.
RQ3: Almost all children moved through the LT even when the intervention was at a higher level, providing empirical support for our LT for area measurement.
RQ4: The success of both interventions, despite their differences, supports the notion that spatial structuring is an important component of area measurement. Also supported is the notion that a combination of animated gestures (Ayres et al., 2009; Cook, Duffy, & Fenn, 2013; Cook & Goldin-Meadow, 2006; Hu, Ginns, & Bobis, 2015) and linked verbalizations in a dual-modality presentation technique (Mousavi, Low, & Sweller, 1995; Tindall-Ford, Chandler, & Sweller, 1997) is an effective way of developing spatial structuring. Further, the S intervention facilitated conceptual understanding and transferred better than the I intervention, providing additional evidence for the importance of spatial structuring.

Authors