Prime the Mind
This is a response for Week 5 in 6411 Cognition and Learning relating to abstract thinking.
Abstraction is defined as “withdrawn or separated from material objects or practical matters” while algebra is defined as a “reunion of broken parts”, a process of “reasoning about quantitative relations by the aid of a compact and highly systematized notation” (Etymology Dictionary). From these definitions, I interpret abstraction to be about relationships. Both in art and algebra, abstraction allows for something to represent something else. There is a relationship between one concept or object to another. In art, it’s line, colour, shape, or texture that is representative or intended as a conceptualization of something. In algebra, letters and numbers are used in combination, to represent known or unknown orders, rules and relationships.
Willingham (2009) suggests that abstract thinking is a way of relating old ideas to new ones, while using concrete examples to make sense of concepts. It’s a process of rearranging and comparing old ideas (Willingham, 2009, pg. 91). The process for acquiring abstract thinking skills, or what Willingham (2009) refers to as deep thinking, includes the use of analogy. This is a key factor in the transference of knowledge, a way of connecting ideas in new ways, such as the example of how Velcro was created from an abstract connection between the clinging power of burrs while removing these objects from a dog after a walk in the woods, that Goldwater and Getner (2015) share.
While I admire the simplicity of an algebraic notation, or the colours and lines of a piece of abstract art, neither one reveals any relationship or rule to my ill-informed mind. It’s the complexity within the representation eludes my thinking and challenges students when they begin learning algebra in school. My understanding of algebraic equations or the abstraction in some art, is shallow and is not connected in any way to my experiences. This is also true for students as they are faced with learning abstract concepts, not connected to concreate examples. As Willingham (2009) posits, it takes lots of examples with explicit expectations for deep thought to make the analogous structures make sense. I have no prior knowledge on which to build analogies and relationships that form a semiotic system (Hoffman, 2007) for deep thinking about algebra or abstract art. Hoffman (2007) posits that shifting cognitive abilities from concrete to abstract knowledge requires an understanding of the mediated relationships within the semiotics, the signs and representations, within the system. I can see this being true for both algebra and abstract art. Without knowing that, in algebra, X is a sign or representation for an unknown variable, I’m not able to solve an equation where X is present. Nor could I decipher an abstract art depiction where a circle is representative of the cycle of life. Applying an analogy can help, but only if, as Willingham (2009) suggests, I’ve had lots of prior experience with signs relating to unknown variables or example representations of the cycles of life. Acquiring abstract thinking also relies on ‘doing’, where concrete examples and experiences shape understanding and memory (Goldwater & Getner, 2015; Hoffman, 2007; Willingham, 2009). Abstraction happens in a “prepared mind” (Goldwater & Getner, 2015, p. 137). So preparing students to explicitly think about ideas using analogies and metaphors can prime the mind for abstraction.
Which brings me to the work of Fullan, Quinn & McEachan (2017) to prepare learners to think deeply, and build the richly interconnected knowledge systems) that allow students to see “not just the parts but also the whole”, to apply information to different contexts, and to understand how the whole can change as parts adapt (Willingham, 2009, p. 95). New pedagogies for deeper learning (Fullan, Quinn & McEachan, 2018) is a research supported, global project that encourages educators to make pedagogical changes in their teaching practices to create rich, interconnected and meaningful learning opportunities. While abstract thinking may not be the explicitly stated goal of this work, it lays the foundation for abstraction thinking by shaping semiotic systems (Hoffman, 2007), establishing causal structures (Goldwater & Getner, 2015) and exposing students to many different version of ideas (Willinham, 2009). For these reasons, it’s an important step to “start students down that road, or continue their progress at a good pace (Willingham, 2009).
References
Abstract. (n.d.) Online Etymology Dictionary. Retrieved from https://www.etymonline.com/word/abstract#etymonline_v_90
Fullan, M., Quinn, J., & McEachern, J. (2017). Deep learning: Engage the world change the world. Corwin Press. Retrieved from http://npdl.global/deep-learning-book/
Goldwater, M. B., & Gentner, D. (2015). On the acquisition of abstract knowledge: Structural alignment and explication in learning causal system categories. Cognition, 137, 137-153. doi:10.1016/j.cognition.2014.12.001
Hoffman, M. G. (2007). Learning from people, things, and signs. Studies in Philosophy & Education, 26(3), 185-204. doi:10.1007/s11217-007-9027-5
Willingham, D. (2009). Why don’t students like school? San Francisco, CA: Jossey Bass.
Image Attribution: Photo by Steve Johnson on Unsplash
