Misconceptions About Density:

Density= Mass/Volume

According to Piaget's development theory, Children at younger ages (around 7) are still very focused on the weight or "heaviness" of an object and density is too abstract an idea for them (Driver, et al, pg78). At about age 10-11 they can start to understand better the differences between type of material, one material being heavier than another. If something is misunderstood a child will often fall back to what they understood when they were younger and feel how "heavy" something is to help them. This will often lead to misconceptions about density as seen below.

"An object will sink because it is bigger or heavier."
"An object will sink because it is smaller."
"If I take an object and cut it in half, the mass and volume will change, so the density changes also."


There are many misconceptions surrounding the idea of density for students. These ideas stem from the observations of the student, what they are told about how mass, density, and volume are related and what they have observed in the world around them. By the time students have reached 7th and 8th grade they have some complete and some incomplete ideas when it comes to density and its properties. The gaps in that knowledge they will try to fill in with what they have observed about materials. They understand that density is a mass over a volume but what it means hasn't really sunk in it and often the predictions made on the "fly" can be very wrong.



As part of the process of investigating these misconceptions, I did some informal interviews with the children in the neighborhood. I surveyed 5 Jr. High students and 4 elementary students. In general, this is what I discovered.

A student will look at two blocks of wood:
IMG_2151.JPG
They say one will sink in water because it is bigger and the other will float because it is smaller and lighter, even if told the blocks are of the same material. Conversely, some said that the smaller one will sink and the bigger one will float because there is more surface area to hold up the big one and less for the small one.

A little trickier, I would show them two pieces of light weight aluminum metal:
IMG_2156[1].JPG

Then I would ask what they thought would happen if they put the bigger one in water. The answer would be that it would sink and they then demonstrated that it did indeed sink. Then I would show them the quite smaller piece that was lighter and ask if they thought it would sink or float. Some would answer float because it was so much lighter. They were quite surprised when it did sink.

Then I would show them a large block of green floral styrofoam:
IMG_2155[1].JPG
I would explain that this block has a mass, volume, and density attributed to it. I asked them if I were to take a knife and cut the block in half so that the resulting blocks were smaller, would the density change? Many struggled with this question saying that because mass and volume were related to density, if they were changed, then the density would change as well. I specifically stated that each quantity changed by exactly half they still thought the density would change as well. With further prodding they were able to see that the density would indeed remain the same.
I then took a smaller piece of the same green styrofoam and crushed it a bit smaller. I asked if the density changed. Some would say no, because there was the same amount of material, the density should be the same where in fact the block had just become denser because the volume became smaller with the same amount of mass.

Here there is a link to some more interviews done at Harvard on this issue:

http://www.cfa.harvard.edu/smg/Website/UCP/causal/causal_students_density.html

Resources:
Driver, R. (1994). Making sense of secondary science. London [u.a.: Routledge.