Psychology of Thinking and Reasoning - Term Paper Example

The Psychology of Reasoning Thinking and reasoning happen in the brain at the same time during the same situations, but there is a fine distinction between thinking processes and reasoning processes. Thinking is more objective: the processing and storage of memories; sorting out sensory inputs; commanding physical reactions, whether they are deliberate or automatic; and contributing power to the subjective processes of reasoning. Reasoning can be variously described as figuring things out, working things through, and forming conclusions or arguments. There are five different types of reasoning which are important for children to develop (and for teachers to teach whenever possible). Hypothesis testing is important in all reasoning processes; children must formulate a best guess solution and test it by thought experiment or physical experiment. Deductive reasoning allows the child to look at a problem at hand and come up with a solution based on those facts. Inductive reasoning, by contrast, calls upon the child to make reasonable assumptions or to apply previous knowledge to situations. Statistical reasoning skill is the ability to manipulate data in various ways to find solutions; interpreting statistics requires a different kind of “language” ability to make sense of abstracts. Finally, problem solving combines these other reasoning skills and calls upon the strengths of each one to arrive at answers, conclusions, or solutions. Reasoning skills are “soft” skills that can be practiced, but not in the same straightforward way one practices arithmetic or spelling or a musical instrument. While it may seem difficult to teach children each of these reasoning skills separately, certain types of lessons do exercise each area even as they teach more concrete knowledge. Using the example of a Frog Unit for Grade 2 (Turturice, 1996) throughout the next sections demonstrates a practical application for each type of reasoning. Simply following the steps in the unit gives children the opportunity to sharpen their reasoning skills and engages them in learning. Children use good reasoning skills under certain circumstances, but more often their skills are rough and lead them to incorrect conclusions. As a type of intelligence, the ability to reason is inborn but poorly manifested; it can be further developed through exercise and experience (Mayer 144). Reaching proficiency takes time and practice, and as children reach into their memories and past experiences to solve problems they will apply what they know whether it works or not (Garnham and Oakhill 224). In addition, they bring their own limited perspectives into interpretations, calling upon their own schemas to find the meaning of what they read, for instance (Mayer 254). Giving children problems to solve (such as a series of similar math problems) only goes so far to teach them the rules of problem solving; the practice is helpful once they have internalized the rules, but they need to know both the rules and how to apply them (Nisbett 170). So, not only is the teacher teaching the material, he or she is teaching the rules, a complex task to say the least. Hypothesis Testing: Determining the Best Guess Hypothesis formation and testing is the most straightforward reasoning skill to teach. The instructor could simply ask leading questions, ask the children for their best guesses, and directly lead them through the reasoning process to test their guesses. This is possible when the teacher already knows the “correct” answer—but many problems do not have a single answer, or more than one alternative solution could bring about the best results. In these cases, the teacher is hypothesizing as much as the students. Garnham and Oakhill (146-149) use the example of the 2-4-6 problem to illustrate hypothesis testing. Subjects are given a set of numbers (2, 4, and 6) in sequence and asked to guess the rule the experimenter has applied to the numbers. The experimenter simply answers “yes” or “no” to questions posed by the subject, and the subject must eventually elicit enough information to properly guess the rule. What is interesting about this experiment is that subjects will often stick to a hypothesis which has been proven wrong through questioning—in other words, they fail to eliminate wrong guesses because they get stuck in their own thinking processes. In the 2-4-6 experiment, the rule in mind is more general than those which subjects eventually announce when they think they’ve got it, showing that people are looking for more specific answers than the experimenter. This is important because hypotheses can certainly be specifically tested, but generalizing either the process or the conclusion is a skill which can be transferred from the individual experience into other situations. Because of their limited experiences and internalized rule systems, children will often apply incorrect reasoning to test hypotheses. For instance, if the class is reading a story together and the children are asked, “What do you think will happen next?” the teacher could get a dozen different answers depending on how the children view the characters and the plot—in other words, how the characters and plot fit into their personal schemas. Teachers can create situations in which children must apply hypothesis testing. Practicing the skill sets the child up for mastery of it; in other words, by applying thought experiments or physical experiments, a child can make a guess and test it. With young children, opportunities to sharpen this skill come along very frequently, and the teacher can encourage students to think their questions through (“What do you think?”) rather than simply answering for them. The Turturice frog lesson plan (1996) uses hypothesis testing extensively. Under the “Procedure” section, the teacher prepares the students to study tadpoles and how they change into frogs—both through supporting materials and first-hand experience. To begin, the teacher asks the children leading questions about tadpoles and what they already know (para. 3), and explores various concepts before showing them a film on frog development (para. 7). The teacher is leading the children in forming hypotheses about frog development, then confirming or correcting their knowledge through the learning materials. As the class moves along in the lesson, the teacher asks for more best-guesses and shows the children how to test those guesses. Deductive Reasoning: Using Facts to Reach Conclusions Deductive reasoning is the skill most frequently used by both children and adults, and is fairly easy to practice. Deduction simply states that if a set of inferences is true, they cannot lead to a false conclusion (Garnham and Oakhill 81). Testing the truth of assumptions can be straightforward and based upon observation and sensory inputs. Teachers can set up experiments of any size which allow children the opportunity to test their deductive reasoning skills. Reasoning errors can easily arise from faulty deductive reasoning (Mayer 140). For instance, if the class is reading a mystery story, all the clues might be contained in the story but the children may not be able to connect the dots to discover who committed the crime. Humans tend to over-generalize their internalized rules and ignore negative facts. Children bring a set of rules and methods of deductive reasoning into the classroom with them, based on past experiences and memories. They tend to use their deductive reasoning skills better when they are familiar with the parameters of a problem—when they enter the situation with enough information (or the skill to find needed information). Unfortunately, if there is a lack of information, the children will sometimes find it, even if it is not there to be found. A specific example of deductive reasoning processes can be found in learning vocabulary words. Many words in the English language can be subject to logical rules, such as quantifiers or qualifiers (Garnham and Oakhill 71). Exact numbers such as first or fifth, or some, few, and any are quantifiers. Beyond that, many words are subsets of categories: a desk is furniture; a carrot is a vegetable. When children encounter unfamiliar words in the context of a sentence, they can often figure out the meaning through deduction. Taking this skill one step further, when a child reads a passage from a book, he or she can deduce the meaning of unfamiliar words, certainly, but also the theme behind the passage through deduction. Since this is one of the skills children are frequently tested for, strong deductive reasoning is vital to academic and life success. Turning again to the Turturice frog development lesson plan, deductive reasoning is applied at various points in the unit. The children draw pictures of the tadpoles several times, requiring them to observe what they are actually seeing and translate that to another medium. In addition, the tadpoles are moving, requiring the children to make small cognitive leaps to produce an accurate representation. Straightforward conclusions can be drawn at various points in the unit using data sets or obtained knowledge. Developing if-then scenarios (“If the tadpoles don’t have enough to eat, then they will die”) helps the children connect different parts of the unit together into a larger whole. Finally and on the broadest level, the unit helps children understand the place of frogs in the environment, and hopefully the place of different kinds of animals (including humans) in the greater whole. Inductive Reasoning: Another Layer of Good Guessing Inductive reasoning asks the observer to produce hypotheses from limited information. Nisbett’s oft-cited example of the tropical island which has three blue shreebles is an example of induction (Nisbett 56). You encounter an unfamiliar creature which you deduce is a bird, and since the three you see are all blue, you could use induction to assume that all shreebles are blue. Experimenters then ask the important question: How probable is your assumption? Children work with extremely limited information because they lack experience, so they are constantly inducing conclusions about everything they encounter. In fact, adults encourage children to spend time in fantasy worlds (through books, television, and stories) and are somewhat disappointed when children realize there is no such thing as the Easter Bunny. Strong inductive reasoning skills ask children to think through their conclusions and uncover probabilities; probabilities can be formed through comparison with past experience or through the facts at hand. Induction can lead to stereotyping, which is faulty reasoning. Stereotyping of people is a separate issue; stereotyping of objects or ideas also affects how children use inductive reasoning to draw conclusions. Another word for stereotyping in this instance is categorizing, which all people do with new information. Since children have a limited number of categories to work with and they tend to be broad, new information is lumped together with old information. As they gain experience, children are more able to sort experiences into more logical categories (such as adults might use) and they re-categorize learned information. This is a process that develops over time, but stereotyping and assumptions are automatic. A person who is familiar with the sport of football is less willing to make assumptions based on viewing one try-out performance, for instance (Nisbett 57). By the same token, a child who observes a process such as the teacher helping another child solve a problem may assume the teacher supplied the answer and not probe further into the interaction to see the child’s input. Thus, the observer makes an incomplete assumption, and when the teacher helps the observer solve a problem, may not understand his or her place in the interaction. Rules can be determined from inductive reasoning. Overall, it is easier to induce rules from positive hypotheses than from negative instances (Mayer 92). In other words, when an observation supports the assumption, the test supports the rule; when observations negate assumptions, the rules must be adjusted to fit. Negative instances require holding more information in immediate memory, and calling on more past experience to prove or disprove the rule. Grammar rules can be especially tricky for children, because the rules seem to arbitrarily change for unclear reasons. Thus, a child who memorizes the “I before E” spelling rule will succeed in correct spelling a majority of the time but not always, because there are exceptions. Inductive reasoning is used in the Turturice frog development unit. The children are shown a film and asked to use other supporting learning materials to find out general information about tadpoles and frogs. The teacher guides the children in applying this outside knowledge to the creatures living in their classroom. Under the “Science” section of the procedures, children listen to/watch a CD about frogs; later they are asked to connect various frog calls with the types of frogs which might have made them (para. 23). Through inductive reasoning, the children can figure out highly probable answers to questions, formulating hypotheses and accepting or rejecting them based on the sensory inputs from the CD. Statistical Reasoning: A New Set of Rules A discussion of statistical reasoning throws out everything researchers know about other types of cognitive processes. Statistics has its own type of logic and grammar, in some ways completely unrelated to reasoning based on language or intuition (Garnham and Oakhill 153). Thus, it must be learned and practiced deliberately and not as an element of other kinds of learning. Since statistics is far more abstract than most other types of learning, tapping into this skill requires experience with statistical problems and schemas (Nisbett 91). By presenting children with math problems which can be readily solved and reinforcing learning immediately, the rules become internalized. Garnham and Oakhill describe an experiment in which balls of various colors were put inside an urn and drawn out randomly (157). Test subjects were asked to predict the color of the next ball after observing for a short time. It is possible, in an experiment such as this, to know the absolute numbers of balls of different colors; one would simply dump out the urn and count. Predicting probabilities uses statistical reasoning to determine the chance that a certain color will be next; there is no definite right answer, only a good guess. However, a good guess can be right most of the time if the subject has used observation combined with knowledge of statistics and probabilities. In this way, statistical reasoning can be leveraged to discover a “good” answer, even if it is not the “right” answer. Statistical hypothesis testing often involves chance (Garnham and Oakhill 157; Nisbett 138). Chance, of course, introduces the possibility of error into the reasoning, a sign of faulty reasoning. When a child has little experience with integrating chance into statistics, it can seem like a frustrating block to finding the right answer. Most math involves straightforward application of numbers and operators (2+2=4) with limited application of reasoning. Math skills can be learned to mastery with enough practice (or at least teachers can dream of such an ideal world). Chance, unfortunately, never finds a comfortable place in the child’s statistical reasoning processes, because they are taught (by adults and by experience) that everything has an explanation, and everything has a purpose of some kind. Helping children explain chance—and not dismiss it—is important to sharpen their statistical reasoning skills. Game playing is a good way to teach the role of chance in statistics. Statistical reasoning is used at several points during the Turturice frog development unit. As a science experiment, it is quite easy to include various data-gathering activities and teach the children how to manipulate the data into visual representations or math problem solutions. For instance, under the “Mathematics” section, the plan instructs the children to guess how many frogs will survive into adults (hypothesis formation) and to show how many of them have reached various stages throughout the unit (paras. 17-18). The statistics are presented visually and combine raw numbers with the passage of time, showing how statistics can be graphed in multiple dimensions. Under the “Social Studies” section, the children learn about overpopulation; the teacher could ask them to reason out how big an environment must be to sustain the population which is present in the classroom (paras. 25-26). Problem Solving: Combined Reasoning Processes Bringing different types of reasoning skills together and applying them to situations or experiments is problem solving. As an example, statistical reasoning dovetails with linguistic skills in the mathematical word problem. This type of problem solving requires multiple skills and cognitive abilities. Analyzing a word problem requires five types of knowledge: linguistic, semantic, schematic, strategic, and procedural (Mayer 458). During the problem solving process, the words and numbers are converted into mental images (translated, so to speak). By the end of the problem solving process, the child converts these mental images back into the mathematical solution. This complex process happens inside the brain at a fast rate, but certain parts of it can be focused upon so that we understand how it is working. Returning once more to the Turturice frog development lesson, we can see how problem solving enters into learning in many ways. Since problem solving is a synthesis of hypothesis formation, inductive and deductive reasoning, and statistical analysis, the Turturice lesson plan asks the children to solve problems on multiple levels throughout the time of the unit. They begin with very little information and end with an understanding of the processes of frog development, certainly, but they also have the opportunity to apply their learning in numerous ways and transform their problem solving abilities into other learning areas. Since the lesson is sustained and actively involves the children, they will remember it—perhaps until the end of the school year, but perhaps for their lifetimes. The problems which they solved during the unit will come up for them again in different situations and they will need to apply the reasoning skills which they learned in this isolated instance. Problem solving is about much more than finding the straightforward answer to a question (2+2=?). The child who is using problem solving is figuring things out from the facts at hand (deduction), supplying missing information (induction), measuring or calculating probabilities (statistics), and formulating a best guess answer (hypothesis testing). The process may be obvious (the child talks to herself) or may be entirely internal (she stares off into space). Each person approaches problems differently, and identifying and focusing upon strengths helps children to sharpen their problem solving skills. Concluding Remarks The three types of reasoning (deductive, inductive, and statistical) tend to overlap one another during hypothesis testing and problem solving. While each of these skills can be studied in a simplified manner through experimentation, taking reasoning out of context leads to mixed conclusions. However, understanding the basis of reasoning gives the teacher a look into what might be going on inside a child’s brain. While historically reasoning has been seen as a set of rules or schemas, there is something to be said for the instances based theory of reasoning (Nisbett 361). Anyone who has observed young children can see that they do tend to recall past actions or ideas and apply those to current situations, rightly or wrongly. A combined approach to understanding children’s learning is most in order, in which exposing children to multiple experiences is combined with teaching them the rules of reasoning. Watching for reasoning errors, pointing those errors out in positive ways, and guiding children into better reasoning methods will help them sharpen each type of reasoning skill. However, teachers must keep in mind that each child has strong and weak reasoning skills as part of their mental makeup, so asking a child strong in visual reasoning to use words to describe a problem may not be helpful; showing children a variety of reasoning methods (visual, statistical, logical, verbal, etc.) and allowing them to practice each type helps them integrate the learned skills with their innate strengths. Instances of practical application for reasoning can be found in both lesson plans and spontaneous teaching moments. If a teacher keeps types of reasoning in mind while formulating lesson plans, those opportunities can be maximized, and paying attention to spontaneous situations can introduce further opportunities to explore reasoning. Practicing these “soft” skills leads a child down a clearer path to understanding. Works Cited Garnham, Alan, and Oakhill, Jane. Thinking and Reasoning. Cambridge, MA: Blackwell Publishers, 1994. Mayer, Richard E. Thinking, Problem Solving and Reasoning. 2nd edition. New York: W.H. Freeman and Company, 1992. Nisbett, Richard E. Rules for Reasoning. Hillsdale, NJ: LEA, 1993. Turturice, Lisa. “Frogs: A thematic unit plan.” SUNY/College at Old Westbury, 1996. Accessed 19 October 2009 from http://www.eduref.org/Virtual/Lessons/Interdisciplinary/INT0025.html. Read More