BACKGROUND

Jean Piaget (1896-1980), considered to be the most influential theorist on intellectual development in children, emphasizes that children's thought processes are different from those of adults. Children are not merely inexperienced adults, and they are not just less skillfully going through the same thought processes adults use. According to Piaget, the difference between children's thought processes and those of adults is qualitative as well as quantitative. In other words, it is a difference in kind as well as a difference in degree. Piaget supported this conclusion with extensive longitudinal studies of children, including his own.

Based on his research, Piaget contended that children progress through four major stages of intellectual development. Along with the corresponding ages, they are listed as follows:

• The Sensorimotor Stage (from birth to about 1 1/2 years old)
• The Preoperational Stage (from about 1 1/2 to 7 years old)
• The Concrete-Operations Stage (from about 7 to 11 years old)
• The Formal-Operations Stage (from about 11 years old onward)

These ages are approximate and Piaget recognized that some children develop at a faster rate than others, but he insisted that all children go through these four stages in the same order. This is where I question his theory. It is certainly logical that a child would progress through stages of intellectual development from tasks that require lower to higher thinking capacities. However, what if the difference between older children and younger children is not so much a matter of having a particular ability or lacking it? What if the difference is actually one of readily using the ability and using it only in simple tasks of the same nature?

Theory

According to Piaget's Stages of Cognitive Development, there are certain achievements, activities, and limitations that correspond to each stage and approximate age. He concludes that children in the Sensorimotor stage are able to react to sensory stimuli through reflexes and other responses, yet they are limited to little use of language, they do not seem to understand the concept of object permanence, and they cannot distinguish appearance from reality. In the following Preoperational stage, a child develops language, can represent objects mentally by words and other symbols, and can respond to objects that are remembered but not present at the moment. Though they have obtained or learned these abilities, they still lack operations, otherwise called reversible mental processes. This is the mental ability to transform objects and reorganize thoughts. For example, a Preoperational little girl may know that she has a brother because she can understand her relationship to him from her own perspective. However, she cannot reverse her thinking by taking the opposite perspective and understand that her brother has a sister. Preoperational children also lack the concept of conservation. They do not have the ability to understand that quantity stays the same even though it may be presented in a different arrangement, shape, or form. These children focus on one property at a time, thus taking just one aspect of a situation into consideration at a time. In this stage, children still have some trouble distinguishing appearance from reality. The third stage is referred to as the Concrete Operations stage. At this point in development, a child understands conservation of mass, number, and volume. These children can reason logically with regard to concrete objects that can be seen or touched. As far as limitations, children in this stage have trouble reasoning about abstract concepts and hypothetical situations. Last is the stage of Formal Operations in adolescence and adulthood. An individual has reached this level of cognitive development when he/she can reason logically about abstract and hypothetical concepts, develop strategies, and plan actions in advance. There are no limitations beyond this stage other than the occasional irrationalities of all human thought.

Hypothesis

The purpose of this research project is to take one aspect of Piaget's stages of intellectual development and question it. As mentioned above, within the background, Piaget insists that all children go through the four stages in order. Acknowledging one other factor besides age, however, brings me to question this piece. The variable is the difficulty of the task being performed within a stage of development. Piaget theorizes that a child cannot move on to the next stage of cognitive development before they have mastered all of the skills, achievements, and activities in the present stage.

I intend to prove that a child can in fact progress beyond a certain stage of development without accomplishing all of the skills within the prior stage with ease. It is not just a matter of completing a task. The difficulty of the task being performed within a stage of thought is critical. Perhaps a child will fail to perform an extremely difficult task considered to be a Preoperational ability, yet successfully execute a more simplified version of a task in the next stage of concrete operations. If this is true, then it would prove that a child does not necessarily need to progress through the stages in order, or at least not master one stage before moving forward on the scale of cognitive abilities. A child will be capable of performing a simplified conservation task, while still in the Preoperational stage, as opposed to performing Piaget's standard measure of the capability of that particular task

PROCEDURE

In a worthwhile effort to prove my above mentioned hypothesis, narrowing the variables in the study to a practical number will be essential in order to come up with a feasible set of data. An extensive quantity of variables to account for would produce results that may be too broad and generalized to make any clear analysis. For instance, studying children in each of Piaget's four stages of cognitive development at every age level within a particular stage would result in superfluous data for such a controlled study. In order to prevent this potential phenomenon, it is deemed necessary for me to choose two particular stages and work with those as I attempt to prove my hypothesis.

I have chosen to compare the abilities of children in the Preoperational and Concrete Operational stages. Within these stages, the focus will be on the concept of conservation. According to Piaget, children in the Preoperational stage, between the ages of 1 1/2 and 7, lack the concept of conservation. Children between 7 and 11 years of age, who fall within the Concrete Operations stage, however, understand this concept. Piaget specifies that these children understand the conservation of mass, number, and volume.

Therefore, I will be measuring the children's ability to successfully complete tasks in the Preoperational stage. In Piaget's studies, one thing was not accounted for, and that is what I would like to clarify in this study. He failed to make any distinction between more difficult and more simplified tasks within an area of cognition development. As children progress within a stage, it is likely that they will be able to apply their knowledge in order to accomplish more difficult tasks of the same nature. If this is true, then it is also possible that a child assumed to be in the Preoperational stage, and thus lack any concept of conservation, might actually be capable of performing a concrete operational task. That is, if the task is simplified.

In order to consistently measure these abilities, it is essential to have operational definitions for difficult tasks and simplified tasks. If the level of difficulty were not precisely defined, there would be a confounding variable of what people consider being simple or difficult. A problem may be measured as difficult to one person, yet quite simple to another individual. So, in measuring these cognitive abilities, I will begin with the standard conservation tasks as a baseline. Then, for the children in the Preoperational stage, I will simplify the task. To do this, I must convey precisely what the standard task consists of and define what will be used a simplified task of the same cognitive ability.

There are three typical tasks used to measure conservation. Using the results of Piaget's study, these tasks will be used as a point of reference throughout the study.

Conservation of Number

Method: Make a row of seven identical objects spaced fairly close together. Then make another row of the seven identical objects directly underneath and lined up with the first row.

Preoperational children say that the two rows have the same number of objects

Method: Make a row of seven identical objects spaced fairly close together. Then make another row of the seven identical objects underneath the first row, but space them further apart so that the row extends beyond the first row.

Preoperational children say that the second row has more objects

Conservation of Volume

Method: Fill two identical containers with the same amount of water

Preoperational children say that the two same-size containers have the same amount of water

Method: Pour one of the containers of water into a taller, more slender container

Preoperational children say that the taller, thinner container has more water

Conservation of Mass

Method: Present the child with two identical balls of clay with the same size and same shape.

Preoperational children say that the two same-size balls of clay have the same amount of clay

Method: Leave one of the balls of clay the same size and shape, but squish the other one into a pancake.

Preoperational children say that the squashed ball of clay contains a different amount of clay that the same-size round ball of clay

There are two components of each measurement of conservation. They are both essential in determining whether or not a child has learned these concepts. Now the procedures for proving my hypothesis must be executed. My method is to simplify these same tasks and analyze the responses of the children in the Preoperational stage.

Conservation of Number

Method: Instead of using seven objects, I will use just three and arrange them in the same manner as above.

Conservation of Volume

Method: I will use different containers that are more obviously identified as similar. The difference between the shape and size of the two containers will not be so drastic.

Conservation of Mass

Method: Again, I will use smaller balls of clay and not squish the second one into such a completely different shape the second time around.

More specifically, there are concise questions I will ask the children participating in the study. In order to collect consistent and reliable data, the questions will be phrased in exactly the same way for each child. The data would not be accurate if one child was given help with the problem at hand, having an unfair advantage over the others. This is not a study of what children can do with help. It is a study of what tasks a child can perform on his/her own.

PROCEED NEXT

Unfortunately, out of the nine pieces of data I collected, only three supported my hypothesis. The results were probably skewed by a few details in regard to how I carried out the experiment. I did not expect these little ones to be so analytical! This showed particularly in the conservation of volume part of the study. In the simplified task, I had two identical glass containers and poured sixteen ounces of water into each one. When I asked "Which container has more water, or do they both have the same amount?" the participants lowered down to eye level and examined them so carefully and intently. In my mind, this was supposed to be the obvious, baseline part of the experiment. I expected them to answer that both containers had the same amount of water, without putting much thought into it. I was proven wrong in this instance. As each child studied the two containers, they usually guessed that one container had more water in it than the other; and these were measured out amounts! Even what may have appeared as a centimeter of difference was enough for these kids to say that the water levels were different.

In order to prevent these things from distorting the results next time, I have thought of two strategies. First of all, I need to put a line on the containers. Marking a certain measurement with a piece of tape, numbering it like a measuring cup, and pouring the water exactly up to that line would make it much more clear for the participants and thus probably help to solve this inconsistency. Secondly, I have considered rephrasing the question. I asked each child, "Which container has more water in it, or do they both have the same amount?" Since the first thing they hear is, "which container has more water, the children may have blocked out the possibility that they might actually be the same. In that way, it was more like a trick question. If I phrase the question, "Do both containers have the same amount of water, or do they contain different amounts?" the question of whether they are the same may stand out in their minds. They may not automatically assume that one container does in fact have more water in it, no matter how microscopic of a difference there may be!

This close analysis on the part of the children also presented a challenge in the conservation of mass part of the study. When I asked, "Which ball of play-dough has more, or do they both have the same amount?" the children immediately inspected the two balls for the most minuscule difference. Two things can be done to prevent this in the future. First of all, instead of rolling the balls of clay myself, I should put the play-dough in some sort of a mold. This way, it will be more obvious that the two are the same. I could also rephrase this question as well. Instead of starting with "which ball of clay has more . . ." I could ask, "Are both balls of clay the same size, or are they different?" Or perhaps just leave it short and simple: "Are both balls of clay the same?" and have it be a clear yes or no response.

Since only three out of nine responses support my hypothesis, I have drawn quite a few conclusions. First of all, as I mentioned above, I need to refine my method of asking the questions. Secondly, based on some observations of the children while participating in the study, I might benefit from changing my approach with each child. One thing that I did not take into account beforehand is the short attention span of four, five, and six year olds. One child in particular brought this to my attention very bluntly. As I was asking him questions, he piped in and asked me, "When are we going to be done?" This is a boy who was even really excited to be chosen to participate in the study! That question certainly caught my attention. It has caused me to contemplate how many questions I should realistically ask each child. This time, I had each participant do both the standard and simplified task for all three types of conservation. Now I am considering having each child just do the standard and simplified task for either the conservation of volume, conservation of number, or conservation of mass. In this way, they will not get bored so easily, which probably caused them to not give their best response or full effort by the end of their session before.

The oldest of the children seemed to perform the best when evaluating the conservation of number. It is the most black and white out of the three conservation studies. It deals with numbers which they are familiar with. With the standard measure of cognitive ability, the children did guess that the more spread out row had more Starburst candies in it because the row was longer. However, they performed well when the task was simplified. This is what I was trying to get at the whole time! When presented with two rows of three Starburst candies, whether spread out evenly or not, the kids were able to apply their addition skills. Therefore, they were able to correctly answer my questions and support my hypothesis.

In response to the majority of my data not supporting my original hypothesis, I am considering changing my study in two significant ways. First of all, I am tempted to just focus on one conservation experiment and perform that single one with every child. Not only would I be able to collect more data with extra time, I have a particular interest in the conservation of number study based on my observations. I found it exemplary that the children used their addition skills in this simplified experiment to approach the question with logic. It caused me to wonder whether the children realized their change in method from the standard to simplified task, going from appearance to logical analysis. If a child was presented with the standard test for a second time, after using their addition skills in the simplified test, would they think to apply that method in the standard test if given a second opportunity? Maybe so. Surely, kindergarten level children would know how to count up to seven. It would just be a matter of applying their knowledge. This would be a very interesting experiment.

The second way in which I have considered altering my study is by beginning with a completely different hypothesis. Thus, the experiments would be approached in a different way as well. The idea concerns implications for education. In the process of researching the cognitive development of children, I came across some interesting material on the Russian psychologist Lev Vygotsky (1978). He disagreed with some aspects of Piaget's Stages of Cognitive Development. One implication of Piaget's findings is that children have to discover certain concepts, such as the concept of conservation, mainly on their own. Teaching such concepts is mostly a matter of directing children's attention to the key aspects and then letting them discover the concepts for themselves. Another implication frequently drawn from Piaget's work is that teachers should determine a child's level of functioning and then teach material that is appropriate to that level. In contrast to this view, Vygotsky argued that education cannot simply wait for children to reach the next stage of development on their own. Rather, children have to learn in order to develop. According to Vygotsky, children have a zone of proximal development, which he defined as the distance between what a child can do on his or her own and what the child can do with the help of adults (or other children). For example, children improve their recall of a story if adults provide appropriate hints and reminders; children can solve more complicated math problems with an adult's help than they can alone; and some children can solve Piaget's conservation tasks with just a bit of adult help and encouragement.

It is thought that children may provide cues as to how much further an educator can successfully push a child's development. For example, several preoperational children who are asked which beaker has more water may all point to the tall, thin one; however, the children who could most easily learn conservation of volume describe the various beakers while using hand gestures that indicate both height and width (Goldin-Meadow, Alibali, & Church, 1993). I am excited to come across this material after having done some of the conservation tests with a few children because it proved to be true of my experience. Two out of the three children I worked with did indeed use hand gestures in order to describe the height and width of the containers. It is not even something that I was looking for, but my observations relate perfectly. I find this astounding!

With this experience and new information, I am considering changing the hypothesis of my study to "Education within the zone of proximal development can advance a child's reasoning abilities." In order to execute the study, I will focus on the conservation of number. Since this experiment is less time-consuming than the others, I will be able to collect more data within the time they give me at the school. My procedure would be in line with what I asked in the conservation of number study this time around, but after going through the standard and simplified measure, I will go back to the standard measure. I will encourage the students to use their addition skills for the more difficult problem, just as they did with the simplified one. This would then be the operational definition for "giving them guidance." The children with which I carry out this exercise will be the experimental group. Then, I will also have a control group. With this group, I will ask the questions just as I did before. They will answer the questions regarding the conservation of number for the standard and simplified versions, but I will not give them any guidance. When I bring the control group back to the initial, standard problem, I expect that their answer will remain the same. However, in terms of the expected outcome, it seems that the experimental group will succeed with some help and guidance in applying logic.

QUESTIONS

Based on the amount of time it took to get through all of the conservation tests with just three children, would it be better to focus on just one conservation task; and thus be able to collect more data with one particular experiment?

Would performing just this one conservation test with each child also prevent them from losing interest when their attention span time has elapsed?

Just focusing on one conservation task, is it likely that I would collect enough data to adequately support my hypothesis (or not support it, for that matter)?

Based on my observation of the children using their addition skills to perform the simplified conservation of number task successfully, would it be wise to take this information and respond by changing my hypothesis?

I find the implications of education in guiding children through an experiment, so that they are inclined to use their skills and solve the problem logically, very interesting. Do you think that this would prove to be an interesting study?

If I decide to use Lev Vygotsky's zone of proximal development as the focal point of my study, how will I determine the operational definition for the variable of "help/guidance"?

How much help should I offer/provide the children when we return to the standard measure of conservation of number.

Would the following be a good question: "You see how you counted to see that the two rows have the same number of Starburst candies? Can you use the same addition skills to count the longer rows? Let's try it."

After posing this question, I could then proceed to determine whether the child applies their knowledge, given a second opportunity to complete the standard task. If they do, it would prove my hypothesis that education within the zone of proximal development can advance a child's reasoning abilities.

One observation I made is that some of the participants were distracted by what else was going on in the classroom. Should I perform the study in an individual room, so that it eliminates the potential of this confounding variable?

Do you have any suggestions for me?

10. Am I on the right track?

Is there anything that I have not accounted for in my study thus far?

This is my primary question because I am having difficulty deciding what to do:

In your opinion, should I keep my original hypothesis and just focus on the conservation of number (and probably come up with more conclusive data than I did with all three experiments combined), OR should I go with the implications of education study, having a control and experimental group (given no help, and given guidance, respectively)? They are both interesting to me, but what would be best for this particular research project?!