Piaget's Theory of Conservation: When One Cup of Water is Less Than One Cup of Water

Conservation of Mass Testing

1. Since you will be working with human subjects, you need to get advance permission from the children's parents or guardians (and teachers if you are performing the test while they are in school) to make sure that it is alright for the children to participate in the science fair project. There are special considerations when designing an experiment involving human subjects. Regeneron ISEF-affiliated (International Science and Engineering) fairs often require an Informed Consent Form for every participant who is questioned. Consult the rules and regulations of the science fair that you are entering, prior to performing experiments or surveys. Please refer to the following Science Buddies document for additional important requirements for studies involving human subjects: Scientific Review Committee (SRC).
   1. Write a clear description of your science fair project, what you are studying, and what you hope to learn. Include how long the child will be tested. Include a paragraph where you get a parent's or guardian's, and/or teacher's signature.
   2. Print out as many copies as you need for each child you will be surveying.
   3. Pass them out to the children or to the teachers of the children to give to the parents. You must have permission for each child in order to be able to use them as a test subject.
2. Arrange for a quiet place, such as in your school, where you can easily meet with your test subjects, individually. Because there are so many test subjects, you may want to set up several time slots after school or during recess on several days when the test subjects can participate. Each test subject will need to be available for 20 minutes.
3. Set up the table and chairs at your location. The chairs should be across from each other. You will first test conservation of mass reasoning.
4. Add an attractive shade of food coloring to the jug of water. Set up and fill the glasses, as shown in Figure 2. Use the measuring cup to add equal amounts of water from the jug to both of the same-sized water glasses. Also have your dish towel on the table.
   
   
   Figure 2. Glasses B and C filled.
   
   
   
5. Think about what you want to say to the test subjects. You need to say the same thing to each test subject so that the instructions are clear and concise. Write down a script to help you remember.
6. Invite one of the test subjects to come into the room. Assign him or her a number and record that number, his or her age, and gender in a data table, like the one below, in your lab notebook. Then ask him or her to sit down across from you. Go through your script and explain to the test subject that you are doing a human behavior science fair project and that you would like his or her help. Ask the test subject to look at the glasses in front of him or her. Ask the test subject if he or she thinks that the amount of liquid in the two glasses, glass B and glass C, is the same. Record the test subject's response in your data table.

   Test Subject	Age	Gender	Part 1: Are the glasses filled with the same amount of liquid at the beginning of the experiment?	Part 2: Which glass has more liquid, A or C?	Observations

7. Now say that you are going to pour the liquid from one of the glasses, glass B, into the other glass, glass A, as shown in Figure 3. Carefully pour all of the liquid from the shorter glass into the taller glass, in front of the test subject. Try to avoid spilling any of the liquid and quickly wipe up any drips or spills with the dish towel. Move glass B to the side and place glass A next to glass C.
   
   
   
   

   Figure 3. Second step in the conservation of mass test.

   
   
   
8. Now ask the test subject if he or she thinks that glass A has more liquid, if glass C has more liquid, or if both glasses have the same amount of liquid. Record the test subject's response in your data table. Ask the test subject to explain his or her answer. Your younger test subjects might say "I don't know" and that's ok—record all information in the Observations column of the data table.

Conservation of Number Testing

1. Now set all of the glasses aside and arrange two rows of quarters in front of the test subject, as shown in Figure 4a, two rows of five quarters each. You are now going to test for conservation of number reasoning. Ask the test subject if he or she believes that the first row has more quarters, the second row has more quarters, or if the rows have the same number of quarters. Record the test subject's response in a data table, like the one shown below, in your lab notebook.
   
   
   
   Figure 4. Setup for conservation of numbers testing.
   
   

   Test Subject	Age	Gender	Part 1: Is the number of quarters the same in both rows at the beginning of the experiment?	Part 2: Which row has more quarters?	Observations

   
   
2. Now spread only the second row of quarters out evenly, as shown in Figure 4b, with a couple of inches between each quarter. Once you have spread the quarters out, ask the test subject if the first row has more quarters, if the second row has more quarters, or if the rows have the same number of quarters. Record the test subject's response in the data table in your lab notebook. Ask the test subject to explain his or her decision. Your younger test subjects might say "I don't know" and that's ok—record all answers in the Observations column of the data table.
3. The test subject has completed the tests. Thank the test subject for helping you with your human behavior science fair project.
4. Repeat steps 3–8 of Conservation of Mass Testing and steps 1–3 of Conservation of Number Testing with each of the test subjects. If necessary, get more water for the conservation of mass test. You can also reuse the water from the previous test. Remember to record all of the data in your lab notebook.

Analyzing the Data

1. Now that you have collected all of the data, you can start to organize and analyze it.
   1. Total the number of test subjects in each age group.
   2. Add together the number of subjects who understood that glasses A and C were equal.
   3. Calculate the percent of subjects who understood that glasses A and C were equal.
   4. Add together the number of test subjects that understood that the number of quarters were equal, even after spreading out the second row.
   5. Calculate the percent of subjects who understood that the number of quarters was equal, even after spreading out the second row.
   6. Record all of this data in a data table, like the one shown below.
   
   

   Age Group (years)	Total	Number of test subjects who understood that glasses A and C were equal	Percent of test subjects who understood that glasses A and C were equal	Number of test subjects who understood that the number of quarters were equal, even after spreading out the second row	Percent of test subjects who understood the number of quarters were equal, even after spreading out the second row
   4
   5
   6
   7

   
   
2. Plot the data. You can do your plots by hand on graph paper, or you can do your plot online. If you would like to do the plot online, or would like to learn more about plotting, try the following website: Create a Graph. Label the x-axis Age Group and the y-axis Percent of Subjects that Understood That Glasses A and C Were Equal. Make a second plot where the x-axis is labeled Age Group and the y-axis is Percent of Subjects that Understood the Rows of Quarters Were Equal, Even After Spreading the Second Row. Are there any trends that you see? When do children develop conservation of mass reasoning? When do children develop conservation of numbers reasoning?