Children's conceptualization of force: Experimenting and problem solving.

Abstract. The purpose of this research was to examine the effects of constructivist instruction on children's conceptualization of force as compared to instruction based on text and demonstration, and to further identify children's reasoning patterns across levels of conceptualization. The sample consisted of 67 third-graders from four classrooms in two elementary schools in a southeastern state. The experimental group interacted with activities, which are closely bound to the development of the concept of force. The control group learned the same subject matter through lectures and demonstrations designed by the class teacher. Both groups were pre-tested and post-tested on a task instrument. Informal classroom observations were conducted to ensure that the teachers were implementing the treatment as expected. The data were analyzed using descriptive statistics and qualitative research procedures. A chi-square test of independent samples was employed to test the significance of the change. Results showed that constructivist instruction on children's conceptualization of force was more effective than lecture and demonstration method. The chi-square value of change 9.66 (df = 2) was statistically significant (p < .01). Patterns of reasoning related to force were identified in levels of conceptualization.

In this study, the authors examined the effects of constructivist instruction on children's conceptualization of force as compared to instruction based on text and demonstration, and determined children's reasoning patterns across levels of conceptualization. Although children learn about force at a very young age, research shows that conceptual knowledge of physics--especially the concept of force--is not well understood even by most high school students (Clements, 1982; DiSessa, 1982, 1993). Even the few students who take college physics courses find it difficult to understand the principles correctly because of misunderstandings developed at a younger age (Clement, 1982; DiSessa, 1982; McCloskey, 1983; White, 1993). Children of various ages have different ideas than adults do, and they are likely to misinterpret verbal instruction, thus creating misconceptions (Osborne, 1985).

Clement (1982) identified several contributing factors that high school students found difficult about physics, such as abstractness of the material, degree of logical precision required in problem solving, sophistication in the types of reasoning required, and the mathematical skills required. Most students' knowledge is only sufficient to understand the basics of physics, and not the higher-order concepts. Hence, they are able to manipulate formulas and procedures but they do not have the understanding to explain the formulas. According to Clement, this kind of superficial knowledge is evident in students' reasoning about mass, acceleration, and momentum. He suggested that development of innovative instructional techniques that emphasize rigorous understanding of qualitative principles should be encouraged. Clement's findings accord with Piaget's theory (1978), in which he posits that children who have not developed logical mathematical thinking will not be able to solve novel problems and explain them in l ater years.

Constructivist scientists maintain that difficulty in understanding physical knowledge and solving related problems is due to the operation of "intuitive sense mechanisms" (DiSessa, 1993, p. 105), which need to be developed into coordinated schemes so that children can confidently reason about knowledge in the physical realm. Intuitive thought is connected to cognitive schemes, which are partially coordinated and frequently lead to judgments that cannot be empirically demonstrated (Piaget, 1976, 1978). Constructivist theorists (Golub & Kolen, 1976; Inhelder & Piaget, 1958; Kamii & DeVries, 1993; Piaget, 1950, 1970, 1973) have demonstrated that children who have not had opportunities to refine and transform their original concepts will hold on to those understandings, which appear to non-constructivist scientists as misconceptions. Misunderstandings occur not because children do not understand, but rather because the operational structures that lead to higher levels of reasoning are not available for children at certain developmental levels (Inhelder & Piaget, 1958; Piaget, 1973, 1974).

A substantial body of research indicates that children learn and think through interaction with objects, and that an activity approach to instruction is best suited to young children's development of scientific conceptual knowledge (Chaille & Britain, 1991; Duckworth, 1987; Osborne, 1985; Piaget, 1974,1976,1978; Woodard & Davitt, 1987). Physical knowledge activities provide children with opportunities to experiment, observe, and differentiate facts from reality. These activities help children to put into relationships what they already know and to refine their understandings, which leads them to discard intuition-based reasoning and adopt reasoning that is more conceptually true (although perhaps not perfectly true) (Kamii & DeVries, 1993). Operations begin from an autonomous form of knowledge and end up as internal Co-ordinations. They lead to the development of causal explanatory relations, which play a major role in the acquisition of abstract concepts (Piaget, 1976, 1978). Piaget emphasized the role of ac tion and the environment on the development of knowledge and intelligence. Enriched environments may create situations that incite children to invent novel ways of assimilating informational content; thus, they may result in a higher level of competence (Inhelder, Sinclair, & Bovet, 1974). Experience plays an important role in children's cognitive growth, but this role varies according to what is being learned.

Cohen (1983) has proposed an active learning model that comprises three phases: exploration, concept development, and application. In the exploration phase, children are encouraged to interact spontaneously and autonomously with materials, directed by their own interests. In the concept development phase, teachers or parents interact with children to help them develop a concept or principle related to the material used in exploration. In the application phase, children are encouraged to generalize what they learned during the concept development phase. Providing such early opportunities allows children to advance their thoughts so that, later on, they will be able to design and carry out experiments in a purposeful way (Cohen, 1983).

When considering growth of abstract thinking, one also must consider the experiences, concepts, and paradigms peculiar to the content being understood (Selman, Krupa, Stone, & Jaquette, 1982). If the child's underlying capacity for conceptual organization is not considered, the child may accurately assimilate the concepts and information presented.

Research emphasizes that difficulty in understanding physics is due to deficiencies in traditional approaches to teaching, which focus on verbal presentation of information and ignore children's thoughtful actions on materials. Children are able to learn basic physical concepts and models if appropriately designed instruction--specifically. that which includes activities for ex- 

Perimentation--is available (Osborne, 1985; White, 1993). Research supports the theory that active learning is more effective than a verbal instructional approach in helping young children acquire such abstract scientific concepts as gravity, pressure, and flight (Fleege, Gomez, Hall, Ambery, & Crocker, 1995; Gomez, Fleege, Hall, Ambery & Crocker, 1996). Furthermore, early intervention provides opportunities for children to explore concepts such as space, number, substance, quantity, and weight, and it is especially effective for low-SES, high-risk children (Campbell & Ramey, 1990). Increasing opportunities for exploration and experimentation provides a classroom environment that enhances science concepts, and leads to young children's cognitive development. Students with a small number of cognitive structures need to interact with concrete manipulatives in order to construct scientific knowledge (Cohen, 1992). Lawson and Wollman (1976) found that children who were provided with active learning opportunities performed significantly better than children in a control group.

According to DeVries and Kohlberg (1987), Kamii and DeVries (1993), Kamii and Lee-Katz (1982), and Marxen (1995), physical knowledge activities are effective in facilitating the child's construction of knowledge of the physical world. These activities allow children to construct relationships of correspondence between actions and reactions; these relations will gradually evolve, over the course of years, into causal explanatory relations (Piaget, 1976, 1978; Woodard & Davitt, 1987). Teachers should be flexible when planning activities so that they can respond to children's initiatives and intervene in ways that will promote children's efforts to produce and understand particular physical phenomena. The teacher should be a facilitator to the child's construction of knowledge and engage in active intervention (Piaget, 1973) by organizing the environment, providing materials, presenting activities, posing questions and problems, responding to children's ideas, promoting interests, maintaining children's enthusia sm, observing and interacting appropriately, and articulating clearly and consciously what is going on, and why, in the classroom (Chaille & Britain, 1991). Kamii and DeVries (1993) suggest that physical-knowledge activities should be planned and developed with a clear focus.

Much research has focused on the importance of incorporating active learning methods in developing children's understanding about concepts. No research has been conducted, however, to examine 8-year-old's conceptualization of force after having been involved with a constructivist science (physical knowledge) curriculum. The present research tested the hypothesis that participating in a constructivist curriculum, and interacting with physical knowledge activities, may better contribute to children's conceptualization of force than participating in a lecture and demonstrations curriculum. Assessing children on a task-based instrument, which included four variables related to force, may identify patterns of reasoning within levels of children's conceptualizations.

Method

Research Design

A constructivist science curriculum was implemented with an experimental group for a period of six weeks. A control group studied the same subject matter in a manner designed by the classroom teacher, following a lecture and demonstration method. The experimental and control groups were pretested before the treatment and were post tested after the treatment.

Subjects

The subjects selected for this study were 67 third-grade children ranging in age from 7 years, 10 months to 9 years, 11 months, drawn from four classrooms in two elementary schools in a southeastern state. One class in each school was experimental and the other was control. Both groups were made up of intact classes. The mean age of the total sample was 8 years 8 months. The experimental group had 35 children (20 female and 15 male), and the control group had 32 children (17 female and 15 male). The experimental group included 22 Caucasian and 13 African American children, and the control group had 22 Caucasian and 10 African American children.

Instrument

In this study, the pendulum task designed by Kamii and DeVries (1993) for preschool children was used to develop the instrument to assess the 3rd-graders' conceptualization of force. The task was modified by adding four release points marked on curve stands, four adjustable heights, four different weights, three specific distances (which were marked on the board), and a target, designed specifically to identify children's thinking about four variables: 1) release point (i.e., angle of release of the bob), 2) height (i.e., the length of the pendulum string), 3) weight (i.e., mass of the pendulum bob), and 4) distance (i.e., from the center of the bob to the target). A task-related interview was developed to identify children's levels of conceptualization of force. To evaluate the instrument's validity, reliability, and practicability, the modified task was piloted with a group of 22 children, ages 8 to 9, who attended three different schools in the same state over an eight-week period.

The results of the pilot tests indicated that limited variations in the variables and some probes in the interview were not sufficient to reveal the children's exact reasoning patterns. In addition, when the children were absorbed in experimenting and problem solving, they automatically placed the target where they thought suitable, rather than waiting for the experimenter to keep the target, as had been planned in the study. The children needed help in hanging the pendulum after they selected the particular bob and the string, however. Children found it difficult to select the materials when they were not nearby. Based on these findings, the task equipment, the related interview, and the practical aspects of the task were adjusted for their accuracy (Dharmadasa, 1996).

The Task Material

The task instrument--the pendulum stand (see Figure 1)--was constructed on a wooden board 91 cm x 43 cm x 1.3 cm. Two support poles (58 cm high) were fixed to opposite sides of the board, in order to support a crossbar measuring 2.5 cm in diameter and 68.5 cm in length. The distance between these two support poles was 39.4 cm. Holes were made in the two supports to suspend the crossbar at four different levels from the base: 50.8 cm, 43.2 cm, 35.6 cm, and 27.9 cm. A hook for the pendulum fulcrum was fixed to the middle point of the underside of the crossbar. Three points (A, B, and C) were marked on the board lengthwise in line with the center (for the child to place the target to be hit with the pendulum bob): The "A" point lay in the center, where the bob exerted its maximum force; the "B" point was where the bob reached the target with decreasing force; and the "C" point was where the bob reached the target before reaching its maximum force.

A cone-shaped target with a flat top, weighing 340 g, was constructed. Four different bobs, in the form of plastic balls, weighing 113.4 g, 70.9 g, 42.5 g, and 14.2 g, respectively, were made available to the children. The balls were suspended from four strings of different lengths that were made with a ring and a hook attached to the two ends of each string. Four curve stands were constructed with markings of 90 degrees, 75 degrees, 60 degrees, and 45 degrees, indicating four release points, and matching the four different heights of the crossbar.

Interview

The task was introduced to each child by the experimenter, who explained that the child would be given a game to play and that the experimenter expected him or her to teach the experimenter about how children think when they play this particular game. The pendulum stand was placed on a child-sized table, and the child sat on a child-sized chair at the end of the table. The experimenter sat near the child. The materials for the task were laid out on the table in front of the experimenter, in a place where the child could easily reach the materials. The experimenter showed the materials to the child and allowed him or her to examine them before trying out the task.

Before the children started performing the task, they were told that they had to make the target fall by placing it at a certain point on the board and using the pendulum hanging from the bar. The child could select any combination of the 4 heights to place the crossbar, the 4 bob weights, the 4 release points, and the 3 target placement points marked on the board. The experimenter helped the child hang the pendulum onto the bar and adjust the release points. The child was given three tries to perform the task, in the course of which the child had the option to change any of the variables. The correct combination of variables in order to knock over the target was height 51cm., weight of the bob = 113.4 g, release point = 90 degrees, and placement of the target directly beneath the crossbar at point A. The target would not fall using any other combination of variables.

If the child made the target fall on the first try, the experimenter asked the child, "What did you do to make it fall over?" After getting the child's response, the experimenter asked questions for further explanation related to the four variables: release point, weight of the bob, height related to length of the string, and the distance from the bob to the target. For example, the experimenter showed the child the release point that he or she used and asked, "What made you choose this release point?" After the child responded, the experimenter, showing a larger/smaller angle of release point (depending on the child's release point), would ask, "Would the target fall down if you let the bob go from here?" Depending on the child's response, the experimenter prompted, "Explain to me why you think it would/would not make the target fall over."

If the child made the target fall on the second trial, the experimenter followed the same interview procedure as in the first trial. In addition, the experimenter asked the child, "What do you think happened on the first try; why didn't the target fall?" If the child changed the materials for the second trial, depending on the variable, the experimenter asked questions (e.g., "Explain to me why you changed the bob for the second try," "Explain to me why you changed the height for the second try").

If the child made the target fall on the third try, the experimenter followed the same interview procedure as in the second try. If the child did not make the target fall on all three trials, the experimenter asked, "What do you think happened; why didn't the target fall?" If the child changed the materials, depending on the particular trial and the variable, the experimenter asked questions as described above related to changing materials.

Classification of Children's Reasoning

Children's reasoning about the conceptualization of force was categorized into six levels, following the system derived by Piaget (1976, 1978) and Inhelder and Piaget (1958). The categories were as follows:

Level IA. Children who explained exactly what they did emphasizing the object (the bob), but not the action they performed were included in this category. For example, they said, "The ball missed it" and "The ball hit it." Regarding further verification of the four variables, children's explanations indicated only their perception of the qualities of the objects related to the four variables, but not of the relationships of the variables to the action. For example, they said "Because this (the bob) is heavy, this (the target) is not heavy," "Because this string is short, this string is long," "Because it (the target) is far."

Level IB. Children who tried to explain exactly what they did, emphasizing the action of the bob, were included in this category. They made attempts to explain what they did by referring to the action. For example, they said, "The ball did not swing" or "The ball missed it because it went the other way." These children failed to explain the action in relation to what they did. The children's responses showed that they were building nonsystematic correspondences among the four variables. For example, they said, "The target is heavier than the bob" or "The target is too far for the bob to hit." The children's explanations showed contradictory ideas, which were independent of the actions they performed.

Level IIA. Children who explained exactly what they did, emphasizing the action they performed, were included in this category. Their explanation indicated the concept that force is necessary to propel an object. For example, children said, "I pushed the ball and it went through the air and hit the target," "It didn't work," "I missed it," and "I need to aim and push." The children's explanations showed that they attempted to build relationships between the variables and the action, but the explanation among variables showed inverse relationships. Their responses depended largely on the action. For example, they said, "The lighter ball is easy to push" and "The heavy ball is difficult to push."

Level IIB. Children who explained exactly what they did, emphasizing action and speed (momentum), were included in this category. For example, children said, "I pushed the ball from a place closer to the target so that the ball will hit the target with more speed," and "I need to push the ball hard so that it gets more speed." Regarding further verification of the four variables, children's explanations showed that they were attempting to build causal relationships between the action and the variations of the variables. In some cases, though, the word "speed" is included in their explanations. Children's ideas showed inverse relationships among variables. For example, children said, "I pushed the ball closer to the target to get a faster speed." The explanations included words such as "'probably" and "maybe," showing that the children were unsure of themselves. For example, children said, "Maybe the heavier ball may have more speed" and "Could be that the larger height may have more speed." These children fa iled to isolate variables and explain their effects.

Level IIIA. Children who succeeded in performing the task with the correct combination of variables and explained the action, giving simple explanations, were included in this category. For example, children said, "I let the bail go from way up." Regarding further verification of the four variables, children's explanations showed that they were capable of building causal relationships of one or two variables on their action, but could not do so for all of the variables. For example, children said, "I chose the heavier ball so that it will give more speed." The children hesitatingly made efforts to explain the relationship of each individual variable on the action. They made certain inferences, but did not build any systematic relationships among all of the four variables. For example, they said, "Maybe the weight has to do something," "Maybe it's the height," or "Maybe it's the string."

Level IIIB. Children who succeeded in performing the task and explained the action, giving all possible reasons for their action, were included in this category. Regarding further verification of the four variables, the children specifically explained the effect of each individual variable and the effect of their variations on the action. Their explanations showed no hesitation, but rather a clear understanding of the causal relationships of the four variables on the action. Children's responses indicated their correct understanding of the concept of force.

The six levels of reasoning related to conceptualization of force identified by Piaget (1976, 1978) and Inhelder and Piaget (1958) were levels IA and IB--pre-operational, levels IIA and IIB--concrete operational, and levels IIIA and IIIB--formal operational.

Treatment Materials

Constructivist curriculum materials were designed and constructed to focus on activities: push, pull, hit, incline, swing, and balance. The activities were closely bound to the concepts of force that emphasize mass and acceleration. The materials on "pushing" activities included wooden blocks of different weights, sizes, and shapes; 121.9 cm x 61 cm flat hardboards with different surfaces; containers of different sizes; toy trucks and cars; "support blocks"; and "incline stands." The materials on "pulling" activities included hooks fixed to wooden blocks of different weights, sizes and shapes; hooks fixed to containers of different sizes; hooks fixed to toy trucks and cars; double-and single-wheel pulleys; "support blocks"; "incline stands"; yarn; and jumbo binder clips. The materials on "hitting" activities included balls of different weights and sizes; baseball bats of different weights, sizes, and textures; support blocks; 121.9 cm x 61 cm fiat hardboards with different surfaces; and incline stands. The ma terials on "incline" activities included incline stands; wood towers; regular gutters of different sizes, lengths, and surfaces; 121.9 cm x 61 cm flat hardboards with different surfaces; balls of different weights and sizes; wooden support blocks; and small objects such as toothpicks and wooden pieces. The materials on "swinging" activities included hooks fixed to balls of different weights and sizes; hooks fixed to pieces of yarn in different lengths; "swing stands"; targets of different weights and sizes; and hooks fixed to wooden bars. The materials on "balance" activities included "balance stands"; yarn; "S" hooks; handles fixed to clear cups; small wooden blocks of different sizes; plastic washers of different sizes; copper washers of different sizes and weights; jumbo straws; jumbo paper clips; eraser pencil wedges; and dowels. In addition, materials such as spring scales; yard sticks; half-meter sticks; duct tape; clear tape and masking tape; rubber bands; ribbons of different colors; labels; note pads ; and pens and pencils were provided. These materials were aimed at creating possible situations for children's experimentation and problem solving. The children's actions on objects and their observations of how the object allowed the children to structure logical relationships, thus emphasizing the role of reflective abstraction.

The curriculum materials were developed by closely following the state of Alabama's guidelines for 3rd-grade science (Alabama State Department of Education, 1995); classroom science instructional materials suggested by Kamii and DeVries (1993) and Osborne (1985); physics activities for children proposed by Bernstein, Schachter, Winkler, and Wolf (1989), Colton and Richtmyer (1975), Eby and Horton (1988), Epstein (1988), Friedhoffer (1992), Heimler and Price (1989), Jacobson and Bergman (1983), Kutscher (1988), and Webster (1982); and the research findings of Inhelder and Piaget (1958) and Piaget (1974, 1976, 1978). The use of these materials in activities was piloted with a group of children (N = 10) ages 8 to 9, to ensure their practicability and validity. Results showed that all the children were able to use the materials and create various activities in six areas (push, pull, hit, incline, swing, and balance) in their own levels of thinking. The researcher's intervention helped children attempt activities at complex levels, which exhibited higher levels of thinking.

Procedure

The Treatment Condition

The children in the two experimental groups interacted with the treatment materials and were involved in activities related to push, pull, hit, incline, swing, and balance for 45 minutes per day, five days per week, for six weeks in the normal classroom, under the guidance of the teachers.

The Control Condition

The children in the control group attended regularly scheduled class work following a text, teacher demonstrations, and lectures during scheduled times for science in the normal classroom. Each child underwent the learning experiences for the same amount of time on similar subject matter as in the experimental group during the 6week period.

Orientation of the Teachers

The two teachers of the two experimental group classrooms were oriented to the implementation of six areas of physical knowledge activities by the investigator in 4 sessions of one hour each. These teachers were oriented in appropriate ways of arranging materials, introducing them to the children, developing activities with the materials, and asking questions that lead children to higher levels of thinking. The two teachers were given the opportunity to play with the materials and respond to the investigator's questions. The teachers were given time to consider the practicability of these activities and to discuss their ideas and suggestions. Specific instructions given about carrying out the physical knowledge activities, such as promoting the children's reasoning skills, and providing them opportunities to interact with materials and engage in experimentation to test their hypotheses, and were based on the constructivist method of teaching explained by DeVries and Kohlberg (1987).

Teacher Observations

The experimenter conducted weekly informal classroom observations in all four classrooms during the six weeks of the study, to ensure that the teachers were implementing the treatment correctly and keeping up with the scheduled research time plan.

Control Group

To implement the science curriculum, the control group teachers followed the class text and the teacher's guide. When teaching concepts, the teachers first demonstrated the activity and gave a few of the children opportunities with the activity. For example, when explaining to the class how "push" is related to "force," the teacher first demonstrated the activity by pushing a book cart with a heavy load of books and then pushing the same cart without the load of books. Each time, while pushing the cart, she asked the children which cart was most difficult for her to push. The children correctly answered that the cart with the load of books was harder to push. Then, the teacher allowed some of the children to repeat the activity. Teachers repeatedly asked the same two questions of the children, who consistently answered the same way about which cart was easier to push. The teachers explained the content by giving this kind of demonstration. Wholegroup discussions also were held in class. Usually, the teachers directed questions at individual children to assess their understanding. Written assignments were given to the children for further review of the subject matter. Children sat in their places and listened to the teacher.

Experimental Group

In the constructivist curriculum classes, the teachers organized the materials for each day. They discussed with the children what they could do with these materials. Teachers conducted activities by responding to children's initiatives and intervening in ways that promoted children's interests and experimentation. The teachers interacted with children in terms of how they were thinking and asked questions designed to serve the child's construction of knowledge; helped children with practical problems to facilitate their experimentation and observation; offered materials to facilitate comparisons; and modeled new possibilities. Teachers observed children's activities and promoted their thinking and exploration possibilities, asking appropriate questions at appropriate times. For example, if a child was aiming the balls of the same weight at a target on an incline at one level, the teacher (showing a lighter ball) asked such questions such as, "What do you think will happen if you used this ball?" When interac ting with the wood towers and gutters, the teacher (showing a different level of the wood tower where the gutter was kept) asked, "What would happen if you kept the gutter on this level?" If a child was hitting a ball, from top to bottom on a single incline, the teacher asked challenging questions to promote the child to experiment on two incline stands. She attached them lengthwise to make double inclines (to make a V shape) so that the child could see how the ball traveled on both inclines. Also, the teachers encouraged children to share their findings with each other, and fostered children's cooperation.

The physical knowledge activities provided a variety of opportunities for children to experiment with materials in individual situations or in groups. Children were given a choice to exhibit their experiments and make presentations about their findings, such as how mass and weight of the object affect force, the effects of incline on force, and how distance and height affect the force. By allowing the children to ask questions and letting them give suggestions for improvement, the children had the opportunity to reflect on their constructions. Teachers asked probe questions that helped children think about possible ways of connecting variables and make creations that led them to understand the concept of force. Children worked cooperatively, shared information, and remained on-task, which showed that they were physically, as well as mentally, engaged.

The Pretest 

Before introducing the scheduled experiences to the experimental group, all the subjects in both the control and experimental groups were pretested. Each participant was given an identification number before the pretest. The scores on the pretest represented the children's level of conceptualization of force prior to the experimentation.

The Posttest 

After completion of the six-week instructional period, both the control and the experimental group children were posttested, in the same manner as during the pretest. Scores on the posttest were used as measures of the children's conceptualization of force after the six-week period of the treatment.

Collection and Coding of Data

The experimenter collected the data by means of written and audio records, and by conducting task-based interviews with children on an individual basis, devoting about 10 minutes per child. The audio-recorded data were transcribed and matched with the written data for the production of the final response sheets. The data were coded by matching the responses with the patterns identified in the categories of reasoning. To establish the reliability of coded data in observed behavior, randomly selected data sheets were rated by three graduate students who had considerable experience in rating procedures in educational research. Each rater was given the pre- and posttest answer sheets of 10 children to rate. Their ratings for these 30 children were compared to the researcher's ratings. The inter-rater agreement was 90% on these responses.

Analyses of Data

The pretest and posttest data were analyzed using descriptive statistics and qualitative research procedures. A chi-square test of independent samples was employed to test the significance of the change of the proportion of subjects that fell into different categories from the pretest to the posttest. Reasoning patterns of the children associated with the four variables were analyzed in a qualitative manner.

Results

Descriptive statistics and tests of inferences are reported first. The second portion of the results qualitatively describes the patterns of reasoning within the levels of conceptualization of force.

Descriptive and Inferential Data

Table 1 shows children's levels of conceptualization of force in the control and experimental groups both in pretest and posttest. The distribution of cell frequencies of the pretest shows that, in both groups, none of the children had reached levels IIIA or IIIB and that two-thirds of the children in the control group and three-fourths of the children in the experimental group were at the preoperational level. Posttest frequency distributions show that the children of the experimental group moved closer to formal operations than the children in the control group. This finding indicates that the treatment had an effect on the children's conceptualization levels, as related to their understanding of force.

Table 2 shows the distribution of the observed cell frequencies among six operational levels in accordance with the expected cell frequencies in the control group. The comparison of observed cell frequencies with expected cell frequencies shows that, out of the 32 children of the control group, 11 children advanced at least one level, while five children moved backwards at least one level. One-third of the children moved to a higher level in the posttest. Although the children were distributed across level IA to IIIA in the posttest, Table 2 indicates that 81% of the children clustered around levels IB and level IIA.

Table 3 shows the distribution of the observed cell frequencies among six operational levels in accordance with the expected cell frequencies in the experimental group. The comparison of observed cell frequencies with the expected cell frequencies of the experimental group shows that out of 35 children, 24 children advanced at least one level and one child moved backwards. More than half of the children in the experimental group moved to a higher level in the posttest. Table 3 shows that, in the posttest, the children were distributed up to level IIIA, with no children in level IA. Furthermore, 37% of the children were at levels IIB and IIIA, as opposed to 15% for the control group. The frequency distribution indicates that children in the experimental group moved progressively to higher levels than the control group.

Table 4 shows the negative, positive, and nondirectional changes of children's levels of conceptualization of force, and that the chi-square value of change is 9.66 (df = p <.01. It indicates that the constructivist program provided stimuli to construct progressively more mature thinking than did the control group studying the same material using techniques of social transmission.

Patterns of Reasoning

The data analyses of the posttest showed that both the control and experimental group children demonstrated similar patterns in their reasoning processes when they manipulated the four variables related to the problem of force: weight, distance, height, and release point.

Level IA. The data indicated a single pattern in level IA children's operations and reasoning processes. In answering the experimenter's question "What do you think happened?" one child said, "I don't know." This demonstrates that in level 1A, the child manipulates variables but has no understanding of how the variables affect force.

For example, one child who selected the heavy ball "A" responded to the experimenter's question, "What made you choose this ball?" by answering, "Because it is heavy." To the experimenter's counter-suggestion of "Would the target fall down if you chose this ("D") ball?," the child said, "Yes," and explained "Because it was soft." The same child selected height "A" and said that he chose that height because he thought the target would fall down. When the experimenter gave a counter-suggestion, showing height "D," and asked, "Would the target fall down if you chose this height?" the child said, "Yes" and explained, "It will just fall." These responses show that children identify the properties of the objects, but that they cannot coordinate these properties with other variables.

Level IB. The data indicated that children emphasized the action of the object (the ball) when they explained their performance of the task. For example, in response to the experimenter's question, "What do you think happened on the third try?" one child answered, "It (the ball) did not swing hard enough." In level IB, the child understood the properties of the variables and tried to coordinate them with other variables. The child selected ball "A," which was correct, and to the experimenter's counter-suggestion, "Would the target fall if you chose this ("D") ball?" the child said, "No," and explained, "Because it doesn't have weight."

The level IB child attempted to experiment with the concepts of "near" and "far." The child selected the target point "C," which was the closest to the release point "B" that the child selected. To the experimenter's question, "What made you choose this ("C") point to keep the target?" the child answered, "Because if I kept it (the target) on "A" or "B" it (the ball) would not knock it down." In level IB reasoning, some children thought that when they place the target away from the chosen release point, it would be easier to hit. They selected target point "B" and explained "When the target is far away, it is easy to hit."

The data indicated three major patterns in level IB children's operations and reasoning processes, identified here as IB1, IB2, and IB3. Pattern IB1 children built correct correllation with only one of the three variables (weight, height, or the release point) and how it affected force. They attempted to describe properties of one or both of the other variables. Pattern IB2 children's reasoning processes were almost similar to pattern IB1 children's reasoning processes. These children built correct correlations with two of the three aforementioned variables with force. They attempted to describe properties of the third variable. Pattern IB3 children built correlations among three out of the four variables and how they affected "force." Data indicated that some children in this pattern understood distance. They understood that if they placed the target on point "C" it would be too close to hit the target.

Level IIA. Level IIA children attempted the task, but they did not get the correct combination of variables to perform the task successfully. They described force in terms of their actions related to manipulation of variables. For example, in response to the experimenter's question, "What do you think happened?" one child said, "Probably, I did not push it hard enough." It indicated that the child was thinking of force in terms of "push." The word "probably" indicated the hesitant nature of the child's thinking at this level.

The data showed three major patterns in level IIA children's operations and reasoning processes associated with the four variables: IIA1, IIA2, and IIA3. Pattern IIA1 children correctly described one out of four variables and how it affected force. They attempted to describe one or two more variables. These children described force in terms of their actions related to manipulation of variables. Pattern IIA2 children correctly described two out of four variables and how they affected force. They attempted to describe one or two more variables. These children experimented with height and the release point to get more force to their action. Pattern IIA3 children correctly described three out of four variables and how they affected force. They attempted to describe the fourth variable, too. This pattern of reasoning indicated that children built inverse relationships among the variables.

Level IIB. In this level, the children thought of force in terms of speed. The experimenter, showing release point "A," asked the child, "What made you choose this point?" The child answered, "To get speed and weight faster and faster and knock it (the target) down." The experimenter, showing release point "D," asked the child, "Would the target fall down if you chose this point?" The child answered, "No" and explained, "Because it (the release point) is too close to the target. It (the ball) won't get enough speed. It (the ball) is light, it (the ball) won't get speed."

The data indicated two major patterns (IIB1 and IIB2) in level IIB children's operations and reasoning processes. Pattern IIB1 children reasoned correctly how weight, release point, and distance affected force, however. They were unsure about how height affected force. Pattern 11B2 children reasoned correctly how weight, release point, and distance affected force. They attempted to reason how height affected force.

Level IIIA. The data indicated a single pattern in level IIIA children's operations and their reasoning processes. These children reasoned correctly and justified how three of the variables--weight, height, and release point--affected force. They attempted to reason and justify how distance affected force. The experimenter, when showing target point "A," asked the children, "What made you choose this point to place the target?" One child answered, "Because it is in the middle, the ball might fail on." The experimenter, showing target point "C," asked the child, "Would the target fall down if you chose this point?" The child answered, "Kind of no," and explained, "Because it (the ball) would hit on 'A' or 'B' but not on 'C.'"

Discussion

The results were statistically significant, indicated that constructivist instruction had positive effects on children's conceptualization of force. The directional changes of children's levels of conceptualization show that children who followed a constructivist curriculum in the experimental group progressed considerably higher than the children in the control group. This finding supports the idea that constructivist instruction enhances children's reasoning about force.

The changes that occurred in children's operational levels on the posttest, in both the control and the experimental groups (see Tables 2 and 3), show that, overall, children from the experimental group advanced as much as twice the amount of the children in the control group. It indicates that children who interacted with the physical knowledge activities and engaged themselves in experimenting and problem solving were able to reason more logically about the problem of force than the children who followed the regular lectures and demonstrations.

The ratio of positive change in control and experimental groups, 11:24, shows that the number of children in the experimental group who moved to higher levels of reasoning are more than twice the number of children who moved forward in the control group. This shows that constructivist instruction--compared to the lecture and demonstration instruction--better promotes children's development of higher levels of reasoning. Table 2 shows that some children in the control group also progressed to higher levels in their reasoning. It is important to note that in the experimental group, one child from level IA in the pretest progressed to level IIIA in the posttest, and that another child from level IIA in the pretest progressed to level IIIA in the posttest. Inhelder, Sinclair, and Bovet (1974) explain that a positive effect is obtained when an experimenter intervention is used, and that this happens because the intervention itself becomes an assimilatory instrument (i.e., a logical mediator). In a case where a new factor is introduced, it gives rise to a cognitive disturbance and necessitates a compensatory accommodation among conceptual schemes. This regulation is possible only if the subject is competent to effect the new construction. Children in the control group whose schemas are ready and prepared to accept information will function rigorously under the conditions provided in the task. The task-related interview used in this study to measure children's understanding functions as an experiment for them to test their hypotheses about force, and to refine and transform their ideas, thus leading them to higher levels of thinking.

The ratio (5:1) of children who moved backward by levels in control and experimental groups shows that the experimental group children had a minimum tendency of moving one level backward from their present reasoning level, while the tendency in the control group was 5 times larger. It appears that even though the control group children show progress, there is a greater possibility of their moving backward, preventing them from developing their thinking, than there is for the children in the experimental group who followed the constructivist instruction.

Conceptualization of Force

Analysis of the children's responses shows a progressive evolution from a simple idea of "force" to a complex idea of "force." In this task, in order to determine the correct setup for the experiment to work, children have to not only think about the mass of the bob, but also compare it with the mass of the target. They need to think about acceleration, associating it with height, the length of the string, and the angle of release. They have to consider the distance from release point to the target. They also have to think about the different levels of each variable to find the correct combination that would work. The four variables in this task provide the opportunity for children to experiment with different combinations to solve the problem. If children are able to think logically and build relationships among variables, such operations necessitate the formation of experimental schema that help children solve complex problems (Piaget, 1987a, 1987b; Pulaski, 1980).

By studying children's responses to questions about their demonstrations of the task, the authors identified in-depth processes related to children's formation of the concept of force. The reasoning patterns identified show that ideas of force result from simple ideas of action, thus establishing Piaget's (1974, 1976) findings that the idea of force results from differentiation and progressive coordination, starting with the simplest, undifferentiated ideas that originate with the action.

Reasoning patterns associated with the four variables show that first, children separate variables in order to determine their respective effects and build relations among them. Citing Inhelder and Piaget (1958), Sigel and Hooper (1968) explain that the concepts that figure in logical thought result from the coordination of actions in which the children combine, dissociate, order, and set up correspondences. For example, when the experimenter asked a child what made him choose height "B," the child said, "I thought it (the ball) would go. It's (height "B") low enough it would knock. If I stand closer, the ball would knock it (the target) over." Children gradually begin to appreciate the significance of their actions, so that they acquire the form of reversible operations in their minds (Sigel & Hooper, 1968).

Past research (Inhelder & Piaget, 1958; Piaget, 1974) shows reasoning structures of the operational levels, IA, IB, IIA, IIB, IIIA, and IIIB in relation to the conceptualization of force, through generalizing data gathered from various studies. Those research findings do not sharply define distinct categories within levels to show the processes that occur within these levels. The authors discussed here, in-depth, the patterns of children's reasoning processes regarding formation of the concept of force based on children's responses.

Both in experimental and control groups, children's responses reveal similar thought patterns. Although these patterns were similar, more children in the treatment group displayed more advanced patterns than in the control group. This finding supports the thesis that constructivist instruction intensifies children's thinking in the process of conceptualization of force.

Overall, the findings of the present study show three phases in the development of reasoning of the concept of force. The first phase is a Non-Conceptual Phase, whereby children's explanations depend on perceived information. In this phase, children are unable to work with causality problems. This type is centered on children's reasoning structure of levels IA and IB. The second phase is the Transitional Conceptual Phase, in which children attempt to explain information received by perception in their own way and to build connections among variables. In this phase, children attempt to work with some of the causality problems. This type is centered on the children's reasoning structure of levels IIA and IIB. The third phase is the Primary Conceptualization Phase, which is centered on the children's reasoning structure of level IIIA. Such children have not yet fully developed understanding of the concept of force. This phase of reasoning shows that children feel a logical necessity to support their theories by arguments.

Implications

The findings of the present study suggest that it is more effective to implement constructivist curricula in early classrooms in order to enhance children's scientific thinking, especially when teaching complex concepts such as force, than to use a lecture and demonstration approach. Instructional materials should be planned on concrete levels so that they lead to abstract thinking. Such an approach would provide opportunities for children to engage in activities according to their levels of thinking, to test their hypotheses, and to refine and transform their ideas. Intellectual development begins with instrumental activities, which become represented and summarized by individuals in the form of particular mental imagery. Gradually, learners become aware of abstract concepts (Bruner & Kenney, 1970). Bruner and Kenney (1970) further explain that it may be effective and important to design curricula and instructions that will enable students to perform operations at higher levels of thinking with respect to sp ecific concepts.

Children should be given sufficient materials to work with, both individually and in groups. Such materials provide ample opportunities for children to experiment with hypotheses in various ways, compare them, reflect on the findings, and modify and elaborate their knowledge and reasoning. It is also important for teachers to interact with children at the appropriate moment to promote children's thinking. Providing instructional materials that help children engage in physical knowledge activities will enable them to understand the properties of the objects, build relationships among them, and conceptualize correctly the concepts of the physical world.

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[Figure 1 omitted]

Table 1

Distribution of Frequencies of the Pretest and the Posttest

                  Pretest                                    Posttest
Levels     Control   Percentage  Experiment  Percentage   Control

IA            6         18.75         6        17.14          1
IB           15         46.88        21        60.00         17
IIA          11         34.38         6        17.14          9
IIB           0          0.00         2         5.71          2
IIIA          0          0.00         0         0.00          3

Total        32        100.01        35        99.99         32

            Posttest
Levels    Percentage  Experiment  Percentage

IA           3.12          0         0.00
IB          53.13         13        37.14
IIA         28.13          9        25.71
IIB          6.23          5        14.29
IIIA         9.38          8        22.80

Total       99.99         35       100.00
Table 2

Changes of Pretest Frequencies in the Posttest of the Control Group

                      Control Group
        Pretest            Postest Frequency Distribution
Levels      Frequencies    IA      IB         IIA         IIB

IA               6                  3          2
IB              15          1      10          1            2
IIA             11                  4          6
IIB              0
IIIA             0

Total           32          1      17          9          2
Percentage               3.13      53.13      28.13       6.25

             Control
              Group
             Postest
            Frequency
            Distributi
                on
Levels      IIIA

IA          1
IB          1
IIA         1
IIB
IIIA

Total       3
Percentage  9.38
Table 3

Changes of Pretest Frequencies in the Posttest of the Experimental Group

Experimental
    Group
            Pretest            Postest Frequency Distribution
Levels      Frequencies  IA        IB         IIA         IIB

IA               6                  3          3
IB              21                  9          6           3
IIA              6                  1                      1
IIB              2                                         1
IIIA             0

Total           35        0        13          9           5
Percentage                0        37.14      25.71       14.29


             Postest
            Frequency
            Distributi
                on
Levels      IIIA

IA
IB           3
IIA          4
IIB          1
IIIA

Total        8
Percentage  22.86
Table 4

Effect of the Change Due to the Treatment

                  -1    -1%  No change  No change%  +1 or more

Experimental       1   2.85         10       28.57          24
              (3.13)           (13.58)                 (18.28)
Control            5  15.63         16       50.00          11
              (2.87)           (12.42)                 (16.72)

Total              6   8.96         26       38.80          35

              +1 or more%  Total

Experimental        68.57  35

Control             34.36  32


Total               52.24  67

[chi square] (2, N = 67) =9.66, p < .01