Preconception

Prior Knowledge: Preconceptions / Misconceptions / Alternative Conceptions / Naive Ideas / Commonsense Ideas in Mathematics and Science (2010)
;What Are They?: ‘Prior knowledge’, ‘preconception’, ‘misconception’, ‘alternative conception’, ‘naive idea’, and ‘commonsense idea’ are some of the many terms ascribed to individual thinking patterns that create problems with respect to science and mathematics learning and teaching (1). The specific terms reflect various perspectives regarding persistent errors that often interfere with new learning. ‘Prior knowledge’ and ‘preconception’ indicate that students walk into science and mathematics classes with understandings that were acquired earlier in their lives, as a consequence of trying try to make sense of their worlds from the time they are born. Individuals sometimes develop their own personal explanations about how things work and other times hear explanations from friends and family. They tend to become quite attached to their explanations when those explanations seem sufficient to help them understand, explain and anticipate events. The terms ‘misconception’ and ‘alternative conception’ designate individuals’ personal theories that are at odds with corresponding scientific and mathematical ideas and therefore are considered incorrect. The term ‘naive idea’ brings to mind the fact that many naive ideas seen in today’s students parallel those of early scientists and mathematicians, including Galileo and Aristotle. Finally, the term ‘commonsense idea’ indicates that individuals have drawn their own conclusions about how something works, in the absence of relevant scientific knowledge (2).
;Why Are Preconceptions Important?: This is a huge issue for teachers and learners of science and mathematics. The evidence is clear that students’ preconceptions can seriously interfere with their abilities to comprehend and retain claims in science and mathematics (3, 4). Simply put, an individual’s preconceptions are not easily altered or replaced. Lecture teaching, the most common form of instruction, has been found to be a particularly inadequate instructional format for helping students modify their preconceptions and build upon them to develop meaningful understanding of science or mathematics. Well-designed hands-on lessons with peer conversations and a good ‘guide on the side’ (that is, an effective teacher/coordinator) are significantly more successful (4). Simple experiments that reveal the inadequacies of an individual’s preconceptions can often help students appreciate the value of the scientific or mathematical concept being presented.
;Where Do Preconceptions Occur?: Preconceptions occur in young children, middle and high school students, college students, and adults - in other words, in virtually everyone (e.g., 5-10). Preconceptions have been documented by many thousands of studies conducted on many topics and in many countries. Many preconceptions are shared by people in cultures around the world. Preconceptions are often fairly logical (though scientifically or mathematically inaccurate), comprehensible interpretations of events and their assumed causes. The resistance of preconceptions to being ‘taught away’ is similarly observed in all cultures.
;Who Knows About Preconceptions?: Virtually all science and mathematics education researchers and many K-12 teachers are aware of the phenomenon of individual’s prior knowledge and its potential interference with instruction. Fewer are likely aware of research showing how to use prior knowledge as a stepping-stone to scientific understanding. Seemingly few college science and mathematics professors know about students’ preconceptions and the issues they create for learners. US Publishers of science and mathematics texts have not seriously engaged in addressing the problems created by persistent, common preconceptions.
;What Are Some Examples of Preconceptions?: For example, many students who learn about state changes and the periodic table think that liquid water and ice have weight while water vapor is part of the air and therefore weightless. Similarly, while many students memorize the formula for photosynthesis in middle school, high school and again in college, they often fail to understand the amazing nature of the process represented by that formula. They have difficulty accepting that plants extract carbon dioxide from the air, convert it by stages into sugar, then assemble sugars into larger carbohydrates including cellulose, in order to construct a leaf, a daisy, or a huge tree. The significance of photosynthesis to life on earth is generally lost in a maze of minor details to be memorized. To illustrate the tenacity of prior knowledge, consider one study (11) that found that ninety percent of a large class of college biology majors in their junior year at a large university responded incorrectly to this question:
Where does the weight of a dry log come from?
a. water
b. soil
c. air
d. sunshine
Light (sunshine) is necessary for photosynthesis to occur, but it does not provide the weight of the plant. Water is also necessary for photosynthesis to occur, adds to the weight of the plant, but has been removed from a log that is dry. The soil provides a plant with nutrients necessary for growth, but the amounts are small, similar to vitamins taken by humans. Actually, plants construct themselves out of thin air. Specifically, plants withdraw carbon dioxide from the air and use it to assemble the building blocks of their bodies as described above.
;What is the Solution to Mitigating the Negative Effects of Preconceptions on Science and Mathematics Learning?: It is much easier to discover preconceptions than to figure out how to teach them away. A few subject-specific solutions have been developed that are reasonably effective in producing high levels of science and mathematics learning. Some teachers use computer simulations to illustrate the flow of heat or other normally invisible phenomena, for example. Some use interactive teaching strategies with whole classes, examining common preconceptions and explaining why they are inadequate. Many lessons involve carefully designed experiences in which students study a phenomenon, observe the inadequacies of their own theories, and gradually recognize the power of the scientific or mathematical theory in predicting and explaining mechanisms and processes.
Large lecture teaching combined with multiple-choice tests composed of fact-recall questions help to mask the problem entirely because students can memorize answers, perform well on the fact-recall tests, and still leave science or mathematics classes with their preconceptions happily intact. Probably the best strategies for lecture courses and textbooks are two-fold. For a prevalent preconception, it can be effective to talk students through that preconception, describe its inadequacies, and then show how the contrasting scientific idea provides a better explanation. In introductory courses, reducing the overall coverage of topics and focusing on developing student understanding of fundamental or core mechanisms and processes seems desirable.
;Why Are Preconceptions So Resistant to Change?: Individuals come to understand the world through an infinite series of successive approximations modifying their worldviews and personal constructs on the bases of their experiences. Thus, many preconceptions are acquired early in life, frequently reinforced, and well connected to other nodes in each individual’s mental models. As long as our preconceptions “work” for us in making sense of our world, we are reluctant to give them up, especially when we have difficulty comprehending the advantages of the mathematical or scientific construct being presented.
;How Do Preconceptions Differ from Other Types of Errors?: There are many kinds of errors. Some errors occur as the result of incomplete or missing information. An individual may have learned a fact incorrectly. One may experience a ‘slip of the tongue.’ One can make a simple mathematical mistake. An individual might form an incorrect connection between two ideas. These are all simple errors that are relatively easy to correct. The stability and persistence of preconceptions in our mental models are what distinguishes them from other errors.
;What Accounts for the Persistence of Preconceptions?: There are many theories regarding the persistence of prior knowledge. Some argue that preconceptions become intricately woven into the fabric of one’s thinking over the years, with many connections to one’s ideas about how other things work (12). Others argue that preconceptions exist as isolated fragments or ‘pieces of knowledge (13). The latter seems to be especially associated with physics knowledge. Many assume that barriers to understanding mathematical and scientific ideas arise especially where abstract thinking is required and processes or events are invisible to the naked eye. Some claim that the more resistant preconceptions fall into a different ontological categories than less resistant preconceptions (14).

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