#### The Child’s Ideas for *4. Mineral Materials*

# The Challenges in Learning about Water Displacement

most children think about what happens when objects are placed in water in *dynamic terms*—the object, because of its heft, pushes down on the water, causing the water to rise

Students are typically taught to use water displacement as a method of determining the volume of an irregularly shaped object, without considering whether students have any real understanding of what they are doing when using this method. What is the volume of an object? And why is putting objects in water relevant?

Answers to these questions are by no means initially obvious to children for two main reasons. First, the vast majority of children do not have a concept of volume (as occupied three-dimensional space) that is differentiated from other measures of spatial extent (length and area) and linked to amount of material. For example, when children are asked to measure how much space two different shaped objects fill up, they overwhelmingly focus on measuring the length or areas of the two objects. Further, when they watch as a clay ball is flattened into a pancake and are asked to compare how much space the ball and pancake fill up, they overwhelmingly say that the pancake fills up more space because it is longer or more spread out, rather than reasoning they both fill up the same amount of space because they have the same amount of material, just arranged in a different shape, or noting the compensation among dimensions (e.g., although the pancake is much longer and wider, it is also much thinner).

Second, most children think about what happens when objects are placed in water in *dynamic terms*—the object, because of its heft, pushes down on the water, causing the water to rise. It follows from this dynamic analysis that they think that weight is the relevant factor for the rise in water: heavier objects should push down with greater force, resulting in a greater rise in water. Thus, almost all children, when shown two equal size (and shape) cylinders of very different weight (e.g., one made of aluminum, one made of brass), confidently predict that the heavier cylinder will make the water rise up higher.

Note that in this dynamic analysis, children are not yet thinking that the water rises because the object has *displaced* the water. Seeing the situation as one of “water displacement” calls for students to construct a deeper model of what happens that “goes beyond the information given perceptually.” More specifically, they must combine the belief that “two things can't occupy the same space at the same time” (a deeply held physical principle since infancy) with their newly developing ability to attend to the volume in this situation (rather than weight) and to think of the volume compositionally (i.e., the volume of the whole system is the sum of the volume of the parts—the liquid and the immersed object). In so doing, they can mentally imagine that when the object is immersed in the water, it must “push away” an amount of water equal to its volume. Hence, if one were to capture the water that was “pushed aside,” it would have a volume exactly equal to the volume of the object.

—Carol L. Smith