What is reported in the article
In science education, a main problem is overcoming false preconceptions and naive beliefs. The educational and cognitive sciences have given intensive consideration to naive beliefs as well as misconceptions in physics (Bao et al. 2002; Kautz et al. 2002, 2004, 2005a,[b]) such as the common misconception speed proportional force rather than acceleration proportional force (Bao et al. 2002; Halloun and Hestenes 1987; McCloskey 1983; Rebello and Zollman 2004).
Misconceptions about everyday life phenomena are common. These misconceptions evolve even with simple problems by neglecting critical thought. For example, most people say wind hits one’s face more during biking than it does the back. Of course, when wind comes from one direction, it comes from the other way when you ride back; thus, the chances for both sides are equal. But, because it takes longer to ride against the wind, people feel that the wind blows in their faces more often.
The educational research about misconceptions has been on the way for quite a time. Misconceptions in the minds of students about movement like this were studied in depth by McCloskey (1983), Halloun and Hestenes (1987) and Rebello and Zollman (2004). Misconceptions in application of mathematics to physics have been studied by Reif (1987) and Resnick (1985).
Psychological viewpoints of students' difficulties in the sciences have been considered, such as concepts (Posner et al. 1982; Reif 1987; Kruger et al. 1990; Licht and Thijs 1990), schemata (Chi et al. 1981; Mestre 1991), representations (Reif 1995; Lorenzo 2005), procedural knowledge (van Heuvelen 1991a,[b]), cognitive anchors (Laws 1997; Hammer 2000), concept change (Abbott et al. 2000; Bao et al. 2002) and scripts (Larkin et al. 1980; Caramazza et al. 1981).
For example, misconceptions of movement can be cued by perceptual attention focussed selectively on one direction of motion alone (Reif 1987). According to Reif, misconceptions can arise from concept interpretation relying on associated knowledge fragments having the advantage of being fast and effortless.
Surveys about overcoming student's misconceptions by using new teaching methods have been undertaken, such as the Introductory University Physics Project (IUPP; Rigden et al. 1993; diStefano 1996a,[b]; Coleman et al. 1998 and Hestenes 1998), the Cognitive Acceleration through Science Education (CASE) study (van Heuvelen 1991a,[b]; Adey 1992), the Overview, Case Study (OCS: Physics; Gautreau and Novemsky 1997) and student feedback by clicker questions (Reay et al. 2005, 2008; Ding et al. 2009; James and Willoughby 2012).
The cognitive background for emergence and overcoming of misconceptions were investigated before by Piaget in the first half of the twentieth century in his famous experiments asking children about movement of toy trains overtaking each other and disappearing in a tunnel for a while (Piaget 1998, 2000; Palmer 2007). Children form a kind of ‘Gestalt’ about the world they live in, these ideas were used to explain novel experiences, and Piaget called this process ‘assimilation’. New experiences, which cannot be explained in this way, are in ‘reconciliation’, which can, however, be misleading into a misconception. The concept change, which is necessary to overcome misconceptions, is difficult for students because it requires a change from the ontological categories matter or things to processes and mental states (Chi et al. 1994). Central concepts are likely to be rejected when they have generated a class of problems which they appear to lack the capability to solve (Posner et al. 1982), such as Newton's first law (force proportional change of velocity). This law is perceived by students realising the presence of frictional forces. They feel a contradiction to everyday life experiences with overwhelming influence of frictional forces (force seems to be proportional to velocity).
Representations of problems in students may be in the form of propositions or images (Posner et al. 1982), which can prevent application of central concepts, such as here in a question about the time needed in a vehicle with the influence of wind.
In the development of knowledge, intellectual norms have to be used according to Piaget's epistemology (Palmer 2007; Piaget 2000), such as autonomy, entailment, inter-subjectivity, objectivity and universality.
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Autonomy - use of own reasoning.
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Entailment (necessary knowledge) - a necessary relation about what has to be.
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Inter-subjectivity - being in line with generally accepted axioms, which are a paradigm case of common ground between different thinkers.
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Objectivity - being justified as a true response in a valid argument.
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Universality - whether or not open to transfer under different causal conditions.
Though autonomy is a condition for reasoning, it can evoke wrong representations following naive conclusions drawn from observations, which lead to misconceptions. According to Piaget, children have a tendency to adapt new observations to old naïve beliefs and misconceptions (called assimilation by Piaget) rather than having a conceptual change to new concepts explaining the phenomenon better (called accommodation by Piaget). This behaviour is explained by the tendency of students to reconcile new observations with old misconceptions (réconciliation; Posner et al. 1982; diSessa 1993).
These Piagetian perspectives on reasoning and cognitive development guide the way to find out which representation presented to the students will avoid emergence of misconceptions. Which representation presented to the students can help to overcome misconceptions is investigated here.
Piaget is undeniably one of the greatest psychologists of the twentieth century; however, recent developments have not always confirmed his findings adding new ideas and concepts such as ecological approach to perceptual learning and development and research on embodied cognition considering for example the perception of movement of objects (Gibson and Gibson 1994; Shapiro 2010).
Misconceptions can be analysed by a model of four cognitive steps, which are based on Posner et al. (1982). This model is an application of Piaget's ideas about assimilation and reconciliation when encountering new phenomena (Posner et al. 1982; Chi et al. 1994):
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Rejection: Rejection of observational theory. (Example: the individual observes a vehicle. The time needed is not directly observable and therefore it is rejected).
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Avoid concern: lack of concern with experimental findings. (Example: careful observation would yield to correct information; the velocity decreases; and thus, the time increases while the vehicle faces the wind. This needs reasoning which is avoided).
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Compartmentalization: A compartmentalization of knowledge to prevent information from conflicting with existing belief. (Example: the false explanation could be tested by careful observation or reasoning; however, as it is difficult, this investigation is neglected and a misconception evolves, the interpretation of speed which is put in compartments like ‘speed from force’).
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Assimilation: Assimilation of new information into existing naïve concepts. (Example: in the absence of critical thought, a false explanation will become a false representation).
These four cognitive features of recognition can explain the misconceptions. Considering these four steps, it seems obvious that different representations given to the students solving a problem can protect more or less from falling into misconceptions.
Reif identifies a procedure specifying a mathematics or science concept (Reif 1987, 1995). For example, the concept ‘acceleration’ consists of the five major steps (which should be illustrated in a figure): (1) identify the velocity; (2) velocity at a slightly later time; (3) find the small velocity change (should be done graphically by drawing); (4) find the ratio dividing by time difference and (5) calculation with the time difference chosen progressively closer to zero, this involves a subtle limiting process. Every step should be pointed out in the teaching process. This procedural concept provides a more detailed and explicit specification of a concept and helps to avoid imprecision, which can easily creep into verbal definition statements (Reif 1987, 1995). Accordingly, drawings can be assumed to be important for the understanding of scientific concepts.
Purpose of this study
The kind of representation used in teaching, which induces or avoids misconceptions of students, is investigated in this study. College students were asked to compare the time needed to complete the round trip riding a bicycle with and without wind blowing within 2 min.
The drawing provided shows vectors representing the velocity of the wind and the velocity of the rider. The velocity of the rider, as evoked through the length of the vector, is the same in both directions. The students had been told that the velocities have to be added to obtain the same velocity relative to the air. This should not easily evoke the idea that the rider is trying to maintain the same velocity to ground in both directions; otherwise, the students should have answered “Problem not clear/fail to answer”.
The purpose of this study was further investigation on misconceptions by comparing answers to questions in linear and diagrammatic form with different figures about the same everyday problem. The answers to the question are discussed in relation to well-known theories about education as well as psychological and neuroscience insight about learning and memory (Cahill et al. 1994; Erk et al. 2003). This literature on neuroscience describing the value of emotions for perception and reasoning process informed the focus of the study on the influence of different representations given with more or less emotions involved (such as image, figure, formula, definitions). The comparison of the influence of different representations is useful to find out which material or picture can evoke misconceptions and which can prevent them.