The table below lists and describes the developmental trends of the common misunderstandings that children have at different grade levels - from kindergarten to high school.
||Examples of Age-Typical Beliefs
- Undergeneralization of the concept of animal (e.g., using the term only for mammals)
- Belief that natural features (e.g., lakes, mountains) are man-made and that natural objects exist for a particular purpose (e.g., rocks have rough edges so that animals can scratch themselves)
- Belief that the world is flat or that it's both round and flat (i.e., pancake-shaped)
- Belief that features on maps depict physical entities (e.g., lines separating states and countries are painted on the earth)
- Use the word animal in diverse contexts (e.g., use it in reference to fish or insects).
- Describe physical causes of natural phenomena in a simple, concrete manner (e.g., "Lakes form when water from rivers collects in a low part of the ground").
- Use globes to find various countries; talk about the earth as a ball rather than a pancake.
- Provide practice in using maps of the local neighborhood and community, showing how some map features are different from physical reality.
- Belief that space has an absolute "up" and "down", so that people standing at the South Pole will fall off the earth
- Belief that plants "eat" soil and fertilizer in much the same way that people eat meat and vegetables
- Belief that in vision something travels from the eye (rather than light traveling to the eye)
- Belief that the problem of poverty can be easily solved by giving poor people a small amount of money
- Explain that gravity draws people to the center of the earth; show videos of people living in the Southern Hemisphere.
- Explore the process of photosynthesis, contrasting the idea of plants making their own food with that of plants simply absorbing food as people do.
- Ask students to draw a line depicting the direction that light travels when a person sees an object; have them explain why they drew the line in the direction they did.
- Have students explore multiple reasons that some people are poor; brainstorm more enduring solutions to poverty.
- Belief that an astronaut who opened the hatch of a spaceship would be "sucked" into space (the astronaut would actually be blown into space by the air within the spaceship)
- Failure to identify squares as rectangles
- Belief that more digits always indicate a larger number (e.g., 2.34 > 2.8)
- Assumption that in algebraic equations (x + y)2 = x2 + y2 , the square root of a plus b equals the square root of a plus the square root of b, and the like
- Begin to explore such physics concepts as force and vacuum, relating these concepts to students' prior experiences (e.g., with wind and vacuum cleaners)
- Identify hierarchical relationships among geometric figures (e.g., squares are rectangles, rectangles are parallelograms, parallelograms are polygons).
- Provide practice with more-less relationships among decimals and fractions; embed some practice within the context of hands-on problems involving real objects.
- Study the appropriate order of calculations in an algebraic expression; contrast correct results with the results obtained from an inappropriate sequence.
- Belief that any moving object has a force acting on it (force is actually needed only to change the direction or speed of movement)
- Belief that the process of division always leads to a smaller number—for instance, that 5 divided by 0.65 yields an answer less than 5 (actual solution is about 7.69)
- Beliefs that Christopher Columbus was Spanish, was the first person to assert that the world was round, and landed on the mainland of North America
- Introduce the concept of inertia; show how it explains movement of planets and spaceships in outer space; explore explanations for apparent violations of this concept (e.g., friction slows an object's speed as it travels along a surface).
- Provide practice with mathematical problems that yield counterintuitive results; ask students to explain why the solutions are correct.
- When describing historical events, explicitly contrast students' beliefs with more accurate information (e.g., Columbus was Italian and landed on islands in the Caribbean; Aristotle suggested that the world was round more than 1,500 years before Columbus's birth).
aThese strategies provide merely a starting point. Some misconceptions are such an integral part of students' belief systems that they may require multiple strategies over a lengthy period. (See the later section "The Challenge of Conceptual Change.")
Sources: Behr & Harel, 1988; S. Carey, 1985; Delval, 1994; diSessa, 1996; J.F. Eaton, Anderson, & Smith, 1984; Gardner, Torff, & Hatch, 1996; Haskell, 2001; Hynd, 2003; Kelemen, 1999; Liben & Downs, 1989; Piaget, 1929; K.J. Roth & Anderson, 1988; Sneider & Pulos, 1983; Tirosh & Graeber, 1990; Vosniadou, 1994; P. S. Wilson, 1988.
Excerpt from Educational Psychology Developing Learners, by J.E. Ormrod, 2008 edition, p. 246.
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