Raths, Wasserman, Jonas, and Rothstein (1986) define thinking as a way of learning. Thinking is different from memorizing in that it requires decision making by the learner. Thinking causes one to not simply memorize “facts” but to understand and “acquire facts” through the process of making judgments based on available information.
Making a cause-and-effect relationship is a basic thinking operation. When children discover that they can cause a change, they model that process at every opportunity. When they find that pushing a button on the television causes the television to light up and make noise, this is what they choose to do. Children test an idea based on observing other people doing similar activities, and thus continue to test the idea until they learn that this is not a good idea, usually from a parent or caregiver.
Using thinking skills such as examining cause-and-effect relationships also promotes the development of questioning. Words that children use, such as how, why, and where, indicate they are examining cause-and-effect relationships. These words are critical in development, because they allow children to wonder, probe, explore, and ask questions as well as request tools, information, and knowledge. As language skills develop, children quickly become virtual questioning machines asking hundreds of questions each day: “Can I paint?” “Why do I have to do this?” “Will you help me?” “How can I do that?”
How we respond to these questions is critical to the formation and development of a child’s attitude toward their active thinking and inquiring. If they are met with criticism and admonishment, they will infer that adults do not want them to think and ask questions. If they are met with answers, they will infer that questioning is a good way of learning what they want to know. If they are met with conversation, discussion, and available resources and materials, they will infer that questioning is a good way to promote and examine ideas. These opportunities are critical for their development of inquiry skills and confidence in analyzing ideas on their own. For every question that children verbalize, they internalize several more questions. Opportunities for children to play on their own terms give them the freedom to explore their own ideas at their own pace. Nondirected play is critical to the early development of questioning skills. Through play, children do not have to develop a formalized verbal question. They can formulate a concept and test it without trying to verbally share their ideas with others. They can repeat and revise the process at their own will. Individual nondirected play has no time constraints.
It is difficult to comprehend what is going on in the mind of a child. Consider the following example. Grandma and Grandpa had that great opportunity to take their grandson, Brandon, for an afternoon drive. Not wanting to waste the opportunity, they bombarded the child with questions for discussion. “What did you and Daddy do this morning? What would you like for dinner? What’s your favorite toy?” But each question was met with silence. Brandon just looked outside the car, apparently oblivious to all discussion. Exasperated, Grandpa asked, “Brandon, what are you thinking?” Again he was met with total silence for an extended period. Finally, Brandon said, “I am thinking... I am thinking about the birds.” Again, a pause. “I am thinking about how the birds fly.”
We as parents, teachers, and caregivers become so determined to communicate with and help children grow that we sometimes forget that we need to, at times, get out of the way and let children internalize, explore, and think through their ideas.
If Grandpa had not asked Brandon what he was thinking and had not given Brandon the time to respond, one could have interpreted that, being a 2-year-old child, Brandon had not readily developed the ability to understand and communicate at a basic conversational level. In reality, at this time, the basic conversation was getting in the way of Brandon’s framing and developing a complex concept. It was important to Brandon to think about this idea, and it was not an easy inquiry for Brandon to verbalize into a clear question. He needed to exclude external forces and the time to think and phrase his question.
Questions involving “when” tend to be verbalized a little later in the development of a child, because “when” incorporates the concept of time, which requires more abstract development. For example, child wakes up at sunrise and says, “It’s morning.” Later in the day after a nap, he wakes up and says, “It’s morning!”
Raths et al. (1986) identify specific thinking and reasoning operations that are basic to the development of young children. These include observing, imagining, problem solving, and collecting and organizing data.
By identifying, understanding, and appreciating these specific operations, we can monitor each child’s development in thinking and reasoning. We can also monitor our skills as teachers in supplying classroom activities that promote the development of the child’s skills in thinking.
Observing
Observing is the skill of using the five senses to take in information, organize it, and respond to it. We take in thousands of observations each second. Our mind records these observations and makes decisions based on what we observe; for example, we observe that it is snowing and we put on a coat to stay warm. To become efficient, we develop skills in selective observation, and thus ignore much of what we see. Indeed, this becomes a matter of survival. We learn to filter out disruptive noise when reading. When we look at a photograph, we focus on details of the photograph and ignore the hand holding the photo.
Developing skills in observation involves deciding and recording what observations are important. With children, when we promote being good observers, we usually are referring to the amount of detail that the children observe. “What do you see when you look at the tree? What type of bird do you think built this nest in the tree? What do you think the bird is doing on the branch above the nest? Do you hear the baby robins?” Good observations identify detail that gives us information and contributes to our learning.
We can conclude that observing real things in our world is quite important in the development of logical thinking and reasoning in the mathematical and scientific minds of young children. It is also important for children to use their thinking processes within their own imaginations and thinking.
Imagining
Imagining is forming ideas about something that does not exist, dreaming in the mind ideas that have not occurred. Imagining tends to be a pleasant exploration of the mind. While imagining, we are not prohibited from ideas because of practicality or reality. We can design an intricate machine without worrying about how the gears will mesh. We can be an astronaut, hit home runs, and build cities. Imagining is personal. The ideas remain private in each person’s own little world.
As teachers we sometimes have concerns about our children daydreaming. We desire for them to be involved in the classroom tasks at hand and paying attention. Their daydreaming is prohibiting them from learning whatever we want them to learn. Obviously we have little idea what they are daydreaming about. The ideas that they may be formulating could be far more complex than those we are trying to get them to learn. Perhaps, at times, our classroom is getting in the way of children using their highest levels of thinking.
Creativity is a form of imagining. When we use the term creativity, we are inferring that the creative thoughts go beyond the internal ideas to an expression of those thoughts. Creativity infers that the ideas are communicated to others through symbols, written words, story problems, drawings and diagrams, graphs, models, or illustrations.
Our greater goal as teachers is to help students learn to expand their daydreams beyond the mental images to hard-copy ideas that they share with their classmates, teachers, and families. Our classroom activities need to be created to encourage new and different ideas. We need to design our children’s projects so that each child can express individuality. Can our classroom displays express different ideas rather than 25 similar drawings of a sunrise?
Observing and imagining are rich ways of being present in the world. Young children should be nurtured and encouraged to use these wonderful skills to solve problems.
Problem Solving
Problem solving has been defined as “what you do when you don’t know what to do.” If you know what to do, it is not a problem, it is an exercise (Keller, 1993). We often give to our students tasks that we present as problems; however, we often explain to them how they should complete the task. When we outline the process for students, we take away the opportunity for them to use their actual skills in problem solving.
Problem solving is a hallmark of mathematical activity and a major means of developing mathematical knowledge. It is finding a way to reach a goal that is not immediately attainable. Problem solving is natural to young children because the world is new to them, and they exhibit curiosity, intelligence, and flexibility as they face new situations. (NCTM, 2000, p. 116)
Kolb (1984) and Polya (1971) both identify four stages of problem solving as follows:
The four stages of problem solving.
- Define the problem.
- Develop a procedure for solving the problem.
- Conduct the procedure.
- Draw conclusions.
One can enter and exit this cycle at any area depending on the task at hand. Problem solving is a necessary part of life. We are constantly put into predicaments in which we need to develop a solution. Why won’t my car start? How can I find enough money to buy a new car? Why won’t the rolls that I am baking rise like mother’s rolls? In each of these situations, the answer is not obvious. We have to make decisions about how we will solve the problem.
Traditional classrooms tend to approach student learning through predesigned procedures. Teachers explain to the students how they should answer each problem. In mathematics we explain the “correct” process for adding two numbers together. In science, we give students a step-by-step procedure that they need to follow if they are to develop the correct results. These practices cause children to feel uncomfortable when they are put in actual problem-solving situations. Having been taught specific processes that they are required to follow in classroom situations, students become unsure when they have to make decisions about how to go about solving this new problem. An example of this is the insecurity that many children feel when asked to do a science fair project. They are concerned that regardless of how they do their project, it will not be done in a way that the judge or teacher would consider correct. They have been “taught” that there is only one correct way to do it.
During early development, children are highly responsive to direction by any authority figure. If they are constantly directed on how they should do things, they will look for additional direction from an authority figure rather than try to go it on their own. If they are encouraged to explore and try doing things their own way, they will feel comfortable experimenting. This attitude is critical for their developing confidence in handling daily responsibilities. Even in adulthood, we see people who have little confidence. They feel uncomfortable being put in decision-making situations because they might not do it the “accepted” way.
Children look at problems differently when they are able to self-define them. The difference is ownership. The question that they are examining is their question. They thought of the question and they want to answer it. Questions raised by other people such as teachers tend to not be as interesting or as important. An important skill for teachers to develop is to encourage students to ask questions and to use students’ questions in leading classroom activities and projects. The Concept Explorations presented in this book give examples of activities in which children are encouraged to explore questions that they design and want to study.
Collecting and Organizing Data
Collecting and organizing data are basic thinking skills that relate directly to problem solving. In basic problem solving, the procedures that are developed often require the collection of information or data: “How high can the water rocket go?” “How many of the seeds germinate?” “How long does it take to run around the track?” These types of activities are important to the development of children because they require the students to collect and organize data.
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