For example , he describes the 12 year old boy who said, "The Earth is round, and Columbus was the first to discover this by his trip around the world."

Leaving out the question of historical accuracy but probing the child's beliefs about planet Earth, Nussbaum found that the child actually believed that "The is Earth is fat and round and surrounded by a big ocean. Columbus' boat traveled around the world and finally returned home."

In this example the child's misunderstanding arouse when he combined a newly learned concept ( the Earth is round ) with his previously held, more primitive concept ( the Earth is -- ). Misconceptions can arise, too, when two or more learned concepts get mixed up with one another. Nussbaum gives this example: an 11 year old child whose theory was that "at night the Sun travels below so behind the Earth, and this is how the lava in the Earth is heated."

Perhaps the most common example of misunderstanding arises because of verbal confusion -- for example -- what a word means in the 'real world' -- vs. -- the way it is used in the scientific community. Here's a second grader's comment:

We believe that what teachers dismiss as misconceptions are often the student's attempt to integrate new and old understandings (thatŐs called constructivism, eh?). Though such statements obviously indicate that the child does not correctly understand a concept, they do represent the learner's effort to organize the world meaningfully. We suggest that a more appropriate term for these misunderstandings is "mixed conceptions," since this directs us to discover though how the learner has mixed up concepts in his mind. ( another friend calls them: "intelligent wrong answers." )

As we have noted, mixed conceptions arise from both verbal and conceptual confusion. The distortion of a concept due to misunderstanding of how language is being used (as in the "new" moon example) is obvious, and is not limited to young children: "Conservation of energy" is a term with very different meanings in an environmental context and in physical science; the story of relativity is frequently taken by HS students as meaning that "everything is relative; and the phrase "survival of the fittest" often carries to students such strong suggestions of physical strength and cunning that teachers have a hard time moving the emphasis onto reproductive advantage. Another interesting example of verbal confusion arose in a class which was concluding a unit on states of matter. The teacher first melted ice and boiled the water. Then, trying to include as many examples as possible, she asked the class to tell her the state of matter of the "pot" in which the water had been boiled. According to the children, "The pots not a liquid and it's not a gas, it it's also not a solid .... because it is hollow."

Children usually feel that their own ideas are "not only the most natural but also the only one possible." Thus, the mixing of new knowledge with old ideas should be expected. Before a unit on the systems of the body, a 5th-grade boy was asked, "Why are you thirsty after you exercise?" He replied, "When you exercise your mouth gets dry like the Sahara, and you want a drink." After studying the unit, he was asked the same question. His reply: "Well -- after you exercise, your heart sort of pumps faster ....and it sort of runs out of blood."

When children mix two or more ideas learned in school (as was illustrated by the example in which the child thought that lave was heated when the Sun went behind the Earth), they frequently simply ADD one concept right on to another. This is often obvious on essay tests where students string together "all they know" -- lots of information, but no organization, no synthesis.

Teachers who are sensitive to the likelihood of mixed-conceptions will not blame students for their failure to comprehend concepts but will rather try to analyze the sources of the errors and corrections. This will require that teachers encourage discussion, and really give students a chance to explain their ideas.

Curriculum developers should be aware of the frequency at which children "mix" their concepts. Verbal problems can be avoided in two ways.

(l) curriculum develops can make a concentrated effort to catch potential problems early, for example, by including examples that explain multiple meanings.

(2) they can plan instructional strategies to introduce a concept before employing specialized vocabulary. Problems arising from conceptual confusion are more difficult and will require additional research along the line of Nussbaum's.

Teachers who are making up tests will also have to consider the implication of mixed conceptions. The fact that children can correctly answer multiple choice or fill-in-the-blank testing items cannot be accepted as an indication that they truly understand the materials. Preventing and remedying mixed conceptions should be a key objective in science teaching. Our failure to adequately confront this issue is partly due to our over reliance on forms of testing that vie students little or no chance to express ideas in their own words. The acceptance by science educators of the Piagetian interviewing technique and its application to probing children's science concepts directs attention to this vital issue. We suggest that the addition of the notion of mixed conception to Piagetian interview add a new dimensions to clarifying children's' understanding of science.