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.
| Grade Level |
Examples of Age-Typical Beliefs |
Suggested Strategiesa |
| K-2 |
- 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.
|
| 3-5 |
- 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.
|
| 6-8 |
- 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.
|
| 9-12 |
- 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.
© ______ 2008, Merrill, an imprint of Pearson Education Inc. Used by permission. All rights reserved. The reproduction, duplication, or distribution of this material by any means including but not limited to email and blogs is strictly prohibited without the explicit permission of the publisher.
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