Math Games

Inspire Your Students to Pursue STEM Careers: Strategy 3

Welcome to post 3 in our series that lays out the strategies in our STEM teacher guidebook (available for download end of Mar. 2014). This guide was written by:

Dr. Candace Walkington, Asst Professor of Mathematics Education, Southern Methodist University and 
Dr. Margaret Lucero, Asst Professor of Science Education, Santa Clara University.

3) Connect Abstract STEM Ideas to Things that are Concrete and Readily-understandable.

Many students begin getting turned off to STEM fields in middle school, when they begin to transition to more abstract thinking about STEM principles. The concepts in these middle and high school courses are often difficult for students to grasp, as they were created by STEM specialists for advanced purposes. In STEM classes, students learn new ideas by connecting them to knowledge they already have. If they are introduced to a new, abstract idea that is not well-connected to anything they currently know, they will have great difficulty learning about and applying that idea. However, teachers can creatively find ways to make abstract concepts concrete and understandable to students. This phenomenon is called grounding (Goldstone & Son, 2005) – grounding is a method where you take an idea that students are struggling to understand, and scaffold their understanding by relating it to their prior knowledge. For example, an abstract idea about calculating a proportion in mathematics may become more meaningful and understandable when it is related to students’ experience with shopping for different numbers of items. In science, and abstract idea about the concentration of liquids may become more understandable when students are asked to physically mix and model the solution.

But what are some strategies that teachers can use to ground students’ understanding of new ideas? First, connecting a new idea to an experience students have in the world, interacting with real people, places, and things, can help them make those connections to prior knowledge (Walkington, Sherman, & Howell, in press). Second, giving students concrete, physical, and kinesthetic experiences with manipulatives and objects that embody a STEM principle can make the idea seem less abstract, and more relatable (Walkington, Nathan, Wolfgram, Alibali, & Srisurichan, in press). One physical activity that can ground ideas is gestures – hand motions that that can show what a phenomena looks like, or how it acts (Alibali et al., 2014). Similarly, giving students powerful visual representations – like diagrams, illustrations, charts, and interactive modeling software – can serve to illustrate abstract ideas in an understandable way (Mayer, 2005; Walkington, Cooper, & Howell, 2013). Online animated or in-person simulations that display how phenomena work are another great way to provide grounding – one well-known online resource for this is the PhET Simulations. Simply giving students a physical metaphor they can use to understand something abstract can also be enormously helpful – for example, when teaching abstract ideas about set unions and intersections in mathematics, teachers can describe a set as being a physical container that holds concrete objects or when learning about cellular structure and organelle function, it may be helpful for students to relate cells to manufacturing factories with specialized equipment.

Overall, research has shown that progressive abstraction or progression formalization approaches can be a highly effective instructional strategy (see Nathan, 2012). In these approaches, students first experience a new idea in a concrete, physical, relatable manner. Over time, the ways in which they interact with the idea become more abstract, and less related to physical and real-world models. In this way, they progressively grasp the abstraction in such a way that it remains connected to their prior knowledge and while still being sensible to them.

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