This is the new updated edition of the first book in the bestselling Uncovering Student Ideas in Science series. Like the first edition of volume 1, this book helps pinpoint what your students know (or think they know) so you can monitor their learning and adjust your teaching accordingly. Loaded with classroom-friendly features you can use immediately, the book includes 25 “probes”—brief, easily administered formative assessments designed to understand your students’ thinking about 60 core science concepts.

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The purpose of this assessment probe is to elicit students’ ideas about the density of a solid object. The probe is designed to find out whether students recognize that in this phenomenon, air is not displaced, such as when there is a hole in a boat.

P-E-O

Properties of matter, density, mass, volume

The best response is C: It will float the same as it did before the holes were punched in it. The degree to which a solid object will float when placed in water depends on the density of the material. Density is defined as the ratio of the total mass to the total volume of an object. This intensive property is independent of the amount of material. As holes are punched uniformly throughout the solid object, regardless of what the material is, the amount of mass and volume that is removed is proportional, so the remaining material will have the same density because it has the same proportional relationship. Because the density remains the same, the object will continue to float in the same manner.

In contrast, mixed density is a condition in which there is more than one substance making up the object. For example, a hollow plastic ball may contain air in it, which would give it a mixed density that includes the total mass of the plastic and the air and the total volume of the object (including the part filled with air). The example provided in this probe is not one of mixed density because the object is solid and does not contain air. The holes that are drilled go all the way through the material and do not displace air. When a boat has holes punched in its hull, it will sink because the air in the hull is displaced by water, thus adding mass and increasing the boat’s density. Objects float in water when they are less dense than the water and sink when they are more dense.

Elementary Students

At the elementary level, students typically have experiences with floating and sinking objects of different sizes and shapes and are able to describe observable properties of objects. They do things to change the shape of objects to make them float. They also have experiences with floating objects that contain air as well as everyday knowledge about floating objects such as boats. Because of their experiences with objects of mixed density (objects that contain air in addition to solid material) such as floating boats, they may not recognize that it is the displacement of air by water that causes a boat or object to sink. Students are affected by their everyday knowledge that when a boat has a hole in the hull, it sinks.

Middle School Students

In middle school, observational experiences with floating and sinking progress to developing a conceptual understanding of density. The crosscutting concept of scale, proportion, and quantity can be applied to density problems by recognizing the proportional relationship between mass and volume. At this level, students encounter mixed-density phenomena and distinguish mixed density from density of an object made of one substance. They can apply an understanding of density to engineering design problems that involve flotation.

High School Students

Instruction builds on students’ basic understanding of density in middle school. Students apply a conceptual and mathematical understanding of density to living, physical, and designed systems. Students at this level can be expected to use a particle model to explain density-related phenomena and solve engineering problems that involve buoyancy.

This probe is best used with grades 6–12. Consider using visual props for this probe. Place a thin block of wood in a container of water to show students how it floats. Then drill holes that go all the way through the wood, but don’t place the block of wood in the water. Ask students to commit to a prediction and share reasons for their prediction before making observations.

• Some students may use an intuitive rule of “less A, less B” to reason that if you have less material, the ability to float decreases (Stavy and Tirosh 2000).
• Because of their everyday experiences, many children think that holes in objects affect the objects’ ability to float. Even when taught that holes through solid objects do not change the object’s ability to float, students still firmly hold the idea (Driver et al. 1994).
• A study by Grimillini, Gandolfi, and Pecori Balandi (1990) of children’s ideas related to buoyancy, found that children take into account four factors when considering how objects float: (1) the role played by material and weight; (2) the role played by shape, cavities, and holes; (3) the role played by air; and (4) the role played by water.

Gomez-Zwiep, S., and D. Harris. 2007. Sinking and floating: Bringing math to the surface. Science Scope 31 (4): 53–56.

Keeley, P. 2013. Using the P-E-O technique. Science and Children 50 (5): 24–26. Keeley, P. 2014. Using the P-E-O technique. In What are they thinking? Promoting elementary learning through formative assessment, P.

Keeley, 150–160. Arlington, VA: NSTA Press. Konicek-Moran, R. 2013. Dancing popcorn. In Everyday physical science mysteries: Stories for inquiry-based science teaching, R.

Konicek- Moran, 123–124. Arlington, VA: NSTA Press.

Mayer, K., and J. Krajcik. 2017. Core idea PS1: Matter and its interactions. In Disciplinary core ideas: Reshaping teaching and learning, ed. R. G. Duncan, J. Krajcik, and A. E. Rivet, 13–32. Arlington, VA: NSTA Press.

Peterson-Chin, L., and D. Sterling. 2004. Looking at density from different perspectives. Science Scope 27 (7): 16–20.

Shaw, M. 1998. Diving into density. Science Scope 22 (3): 24–26.

Yin, Yew, M. Tomita, and R. Shavelson. 2008. Diagnosing and dealing with student misconceptions: Floating and sinking. Science Scope 31 (8): 34–39.

• This probe can be used with the P-E-O (predict-explain-observe) strategy and the science practice of planning and carrying out investigations. Have students predict, explain, systematically test, and observe how the object floats in water when holes are punched through it. If observations do not match students’ initial predictions, have students revisit and revise their initial explanations. Be aware that some students will not believe their observation and may think there needs to be more holes or the holes need to be larger. If so, allow them to test that as well.
• The probe “Mass, Volume, and Density” in Uncovering Student Ideas in Physical Science, Volume 3 can be used to further uncover student thinking about these concepts (Keeley and Cooper 2019).
• Ask a question about a similar phenomenon using a different object. For example, after observing that an apple floats in water, predict what will happen if a large hole is cut through the core of the apple and the apple is placed back in the water.
• There is a solids-and-holes demonstration on YouTube (www.youtube.com/ watch?v=1llYHPd8GSg) that shows how fruits float in water when holes have been cut through them. Show the video and relate it to this probe.
• Help students distinguish between mixed density and density of a single material. Have them reason why materials like metals can be made to float (such as iron ships), comparing and contrasting a mixed-density object with a pure-density object. For example, a hollow metal container filled with air would float because a large part of the volume of the object is made up of air, which decreases its density, whereas a container of solid metal without air trapped in it would sink because its density is greater than water.
• Once students have grasped the idea targeted by the probe, present them with a new situation. Contrast the “holes all the way through” model with the “cavity” model. Place an object that sinks, such as soap (not Ivory soap, as it is one of the few soaps that floats) in water. Take the soap out and carve or drill many holes uniformly (not all the way through, but rather holes that form cavities) so that much of its volume will be filled with air, causing it to float. Ask students to predict what will happen if you take the soap and continue making the holes so they go all the way through. Listen carefully to their ideas, noting if they base their predictions on the probe example, without considering that the object did not float to begin with. Have them test their predictions and construct an explanation for this counterexample.
• Have students apply their knowledge of mixed density to an engineering design problem, such as designing the hull of a boat to carry a heavy load or explaining why oil tankers are designed with double hulls. • After students have had the opportunity to develop an understanding of this phenomenon, revisit the probe and have them construct a revised scientific explanation using data from their investigation, scientific concepts, and appropriate terminology. Extend the probe to three dimensions by asking students to include the crosscutting concept of cause and effect or proportions in their explanation.