spatial alignment
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Cognitive supports for analogical reasoning in rational number understanding
In cognitive development, learning more than the input provides is a central challenge. This challenge is especially evident in learning the meaning of numbers. Integers – and the quantities they denote – are potentially infinite, as are the fractional values between every integer. Yet children’s experiences of numbers are necessarily finite. Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input. However, retrieving proper analogy requires cognitive supports. In this talk, I seek to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning. To examine these hypotheses, I will present a series of educational intervention studies with third-to-fifth graders. Results showed that a short, unsupervised intervention of spatial alignment between integers and fractions on number lines produced broad and durable gains in fractional magnitudes. Additionally, training on conceptual knowledge of fractions – that fractions denote magnitude and can be placed on number lines – facilitates explicit analogical reasoning. Together, these studies indicate that analogies can play an important role in rational number learning with the help of number lines as schemas. These studies shed light on helpful practices in STEM education curricula and instructions.
Spatial alignment supports visual comparisons
Visual comparisons are ubiquitous, and they can also be an important source for learning (e.g., Gentner et al., 2016; Kok et al., 2013). In science, technology, engineering, and math (STEM), key information is often conveyed through figures, graphs, and diagrams (Mayer, 1993). Comparing within and across visuals is critical for gleaning insight into the underlying concepts, structures, and processes that they represent. This talk addresses how people make visual comparisons and how visual comparisons can be best supported to improve learning. In particular, the talk will present a series of studies exploring the Spatial Alignment Principle (Matlen et al., 2020), derived from Structure-Mapping Theory (Gentner, 1983). Structure-mapping theory proposes that comparisons involve a process of finding correspondences between elements based on structured relationships. The Spatial Alignment Principle suggests that spatially arranging compared figures directly – to support correct correspondences and minimize interference from incorrect correspondences – will facilitate visual comparisons. We find that direct placement can facilitate visual comparison in educationally relevant stimuli, and that it may be especially important when figures are less familiar. We also present complementary evidence illustrating the preponderance of visual comparisons in 7th grade science textbooks.
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