Spatial alignment facilitates visual comparison.

Abstract

Humans have a uniquely sophisticated ability to see past superficial features and to understand the relational structure of the world around us. This ability often requires that we compare structures, finding commonalities and differences across visual depictions that are arranged in space, such as maps, graphs, or diagrams. Although such visual comparison of relational structures is ubiquitous in classrooms, textbooks, and news media, surprisingly little is known about how to facilitate this process. Here we suggest a new principle of spatial alignment, whereby visual comparison is substantially more efficient when visuals are placed perpendicular to their structural axes, such that the matching components of the visuals are in direct alignment. In four experiments, this direct alignment led to faster and more accurate comparison than other placements of the same patterns. We discuss the spatial alignment principle in connection to broader work on relational comparison and describe its implications for design and instruction.

Learning to Solve Trigonometry Problems That Involve Algebraic Transformation Skills via Learning by Analogy and Learning by Comparison

“…Clearly, from the preceding sections, research has supported the use of the juxtaposition of two examples to promote analogical learning. Nonetheless, the efficiency of performing one-to-one mapping activities depends on the orientation of the two images (Kurtz and Gentner, 2013), or the objects in two examples (Matlen et al, 2020). Aligning two examples in the same orientation instead of different orientations, in this case, facilitates direct alignment of the mapping process, which improves the efficiency of analogical reasoning.…”

“…Mapping relational commonalities between the source example and the target problem is another critical analogical task that facilitates analogical transfer. However, successful analogical transfer depends on active comparison process (e.g., joint interpretation plus list specific correspondences) (e.g., Kurtz et al, 2001) and direct alignment of the examples (e.g., Matlen et al, 2020). It is interesting to note though, from our examination of the literature, that constructing a mental representation of the source example in the initial phase of learning by analogy (Holyoak and Koh, 1987) has received minimal attention in terms of research and/or teaching development.…”

“…This section of the article details our fundamental premise, which "equates" a Trigonometry problem that has a pronumeral as a numerator (e.g., sin30 • = x/6) with that of a linear equation with a fraction (e.g., x/4 = 3). Capitalizing on existing research investigations (Holyoak, 1984;Holyoak and Koh, 1987;Kurtz et al, 2001;Ngu and Yeung, 2012;Alfieri et al, 2013;Rittle-Johnson et al, 2017;Matlen et al, 2020), we propose two major stages to facilitate analogical learning for Trigonometry problems that involve algebraic transformation skills. We now discuss each of the stages below in detail.…”

“…2 in terms of the relative position of the pronumeral (i.e., left side vs. right side). Different orientation of the pronumeral would prevent direct alignment of the relational elements (Kurtz and Gentner, 2013;Matlen et al, 2020), and therefore this would adversely affect the efficiency of the analogical comparison. In contrast, displaying Eqs.…”

“…All three variants of source examples are one-step equations that have one operational line and two relational lines ( Ngu and Phan, 2016 , 2017 ). We place the three equations side-by-side to facilitate the mapping process ( Kurtz et al, 2001 ; Rittle-Johnson and Star, 2009 ; Matlen et al, 2020 ). Furthermore, we label the solution steps—for example, Lines 1, 2, and 3 in Eq.…”