Here’s an interesting thing about abstract thinking or reasoning: it doesn’t seem like looking at an abstract painting and developing abstract reasoning in Math are all that similar, but in fact, they have some useful similarities. This is helpful because it expands the understanding of how to conduct abstract reasoning, and may inform its development in students, and this form of thinking is a goal of most high school curriculum.
It is a process, it takes time, and it takes a basis in facts and information to generate an abstract reason for something. Imagine walking into a museum and looking at an abstract painting that appears, at first glance, to be a collection of colors, swirls, lines, and vague images on a canvas. What is the viewer to do? Well, the viewer does not have to figure out exactly what on earth the artist was thinking, they need to figure out what they see, what ideas and thoughts are evoked, whether it changes or expands thinking. The art is a gift to the viewer, allowing them to draw from one source and abstract out their own relevant ideas.
Likewise, in math, when a student is given a set of quantitative information and asked to make projections using that information, this is a process which will draw out their abstract reasoning. Similarly, this works in a process of discovery in science. A collection of possibilities exist, and the thinker must take their time parsing through them, and develop a new set of firm thoughts, possibilities and models based upon the data they have been given.
One challenge is to consider how to affect this in the classroom, or at home, for students. This may be a case in which assessments are highly useful. Not, however, high-stakes assessments that are measuring proficiency or achievement in a subject. The authentic assessments, projects and portfolios that students have an opportunity to work through are excellent mechanisms to transform students into abstract thinkers.
Because it is a process, having a process-oriented assignment will offer students the framework within which to have this cognitive experience. Similarly, at home, the project that is started, worked through, and discussed can generate ideas, sets of possibilities, and thoughts about what is possible in the future. These experiences are immeasurably important to students. They are touchstone, holistic experiences and usually quite a bit of fun.
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