Psychologist Jerome Bruner views is very similar to Piaget’s but there are some essential differences. Bruner, like Piaget is concerned with the process by which knowledge is acquired. They both believe in the discovery method which claims that the child must learn for himself if the learning is to be meaningful. Since knowledge is not transmitted at the verbal level at this stage, learning must begin with concrete manipulative materials. Bruner believes a person categorizes new objects and events that occur in his environment according to the properties they are seen to have in common with each other objects and events previously categorized. Bruner disagrees with Piaget concerning the acceleration of learning. This is due to Piaget’s belief that the child’s stage of development determines his reasoning ability and these stages can be accelerated very little, if at all. Bruner believes that “any subject can be taught effectively in some intellectually honest form to any child at any stage of development” (Copeland, 1972).
Behaviourism
B. F. Skinner (1904-1990)
Behaviorist theory of learning focuses only on the objectively observable aspects of learning. Some of the most important researchers include Ivan Pavlov, Edward Thorndike and B.F.Skinner. They believe learning is evident by a change in behavior, the environment shapes behavior and the principles of relationship with time and reinforcement are central to explaining the learning process. Skinner’s work focused on the relation between behaviour and its consequences. For example, if a student’s behaviour is immediately followed by pleasurable consequences, the child will engage in that particular behaviour more frequently. This is referred to as operant conditioning.
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For behaviorism, learning is the acquisition of new behavior through conditioning (Slavin, 2006). Teachers are a primary source of reinforcement which is any means of increasing the likelihood that an event will be repeated. They can also guide students towards goals by reinforcing the many steps that lead to success, which is a technique called shaping. Some of the principles of behavioural learning include the role of consequences, reinforcers, punishers, immediacy of consequences, shaping, extinction, schedules of reinforcement, maintenance, and the role of antecedents (Slavin, 2006). Behaviourism emphasizes the learning of facts and skills that authorities, such as teachers or school boards, have decided are important. Behavioural teaching and learning tends to focus on skills that will be used later. The theories support a number of different approaches to teaching. Almost all of them fall under the category of “direct”, or “teacher-centered” instruction. The approaches taken in the classroom include, drills, games, tutorials, programmed instruction, simulations, graphic organizer/semantic web, and integrated learning systems.
Constructivism
It is believed that students need to construct their own understanding of each scientific concept, so that the primary role of teaching is not to lecture, explain, or attempt to ‘transfer’ scientific knowledge. It is to create situations for students that will foster their making the necessary mental constructions. They do not absorb ideas as teachers present them rather they create their own knowledge through play and interaction with their environment. Constructivism focuses on how people learn. It suggests that knowledge in mathematics and science results from people forming models in response to the questions and challenges that come from actively engaging mathematics problems and environments. The teacher is required to “create experiences that engage the student and support his own explanation, evaluation, and application of the mathematical models needed to make sense of the experiences” The teacher can also improve teaching by discovering for various ways to engage individual students, develop rich environments for exploration and eliciting and communicating student perceptions and interpretations.
According to Paul Ernest (1996) the forms of constructivism such as weak, radical and social lead to pedagogical implications. Some of the implications are sensitivity toward and attentiveness to the learner’s previous constructions such as informal knowledge, previous conceptions and previous knowledge to build on; use of multiple representations which provide more avenues for students to connect previous conceptions; using cognitive conflict techniques to remedy misconceptions which allows students to think on their own and develop their own meanings or rectify the conflict; awareness of the importance of goals and social contexts (Ishii, 2003).
Some constructivists believe that people are born with an innate ability to deal with small integers (such as 1, 2, 3, 4) and to compare estimates of large numbers. The human brain has components that can adapt to learning and using mathematics and vary significantly in their instinctive mathematical abilities or intelligence. The also believe students from the time of kindergarten have varying levels of mathematical knowledge, skills and interests because the mathematical environments they grew up in varied (Moursund, 2006).
A constructivist teacher uses raw data and primary sources, along with manipulative, interactive, and physical materials. They allow student responses to drive lessons, shift instructional strategies, and alter content. The teacher inquires about students’ understandings of concepts before sharing their own understanding of those concepts. They also allow significant wait time after asking questions and engage students in dialogue, encouraging discussion (Ishii, 2003).
Cognitivism
Cognitive
Jean Piaget (1896-1980)
Jean Piaget is an influential psychologist that has contributed greatly to the understanding of cognitive psychology. Jean Piaget’s work on children’s cognitive development has acquired much attention within the field of education. One contribution of Piagetian theory concerns the developmental stages of children’s cognition. His work has afforded mathematics educators with critical insights into how children learn mathematics concepts and ideas. In general, the knowledge of Piaget’s stages aids teaches with understanding the cognitive development of the child as the teacher plans stag-appropriate activities to keep students active. Piaget believed that a child developed through a continuous transformation of thought processes. He believed that children develop steadily and gradually throughout varying and that the experiences in one stage form the foundation for the movement to the next (Berk, 1997 cited in Ojose, 2008).
Piaget has identified four primary stages of development: sensorimotor, preoperational, concrete operational and formal operational. In the sensorimotor stage (birth to age 2), an infant develops his mental and cognitive attribute from birth until the appearance of language. At this stage babies and young children explore their world by using their senses and their motor skills. A particular characteristic of children at this stage is their ability to link numbers to objects, for example, one dog, two cats, three pigs an so on (Piaget, 1977 cited in Ojose, 2008). In order to develop the mathematical capability of a child in this stage, he should be allowed sufficient opportunities to explore his environment in unrestricted but safe ways. As a result, the child’s ability might be enhanced thus enabling him to start building concepts (Matin, 2000 cited in Ojose, 2008). “Evidence suggests that children at the sensorimotor stage have some understanding of the concepts of numbers and counting” (Fuson, 1988 cited in Ojose, 2008).
Ojose (2008) recommends that educators of children during this stage should lay a solid foundation of mathematics by providing activities that incorporate and thus enhance children’s notion of the development of number. Teachers and parents can do so by helping the children to count their fingers, toys, and candies. They can also ask children as young as two or three questions such as “Who has more?” or “Are there enough?” making this part of their daily lives. Providing children with books that contain pictorial illustrations can be beneficial as they can link numbers to objects from seeing pictures of objects and their respective numbers simultaneously.
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Following this stage is the preoperational stage which begins at age two to seven years old. While infants learn about and understand the world through manipulating objects psychically, children at this stage have greater ability to think about things and can use symbols to mentally represent objects (Slavin, 2006). In this stage children should engage with problem-solving tasks that incorporate available materials such as blocks, sand, and water. The teacher should encourage conversation from the child while he is working with a problem. His actions on the materials as well as his verbalization, provides a basis that allows the teacher to deduce the method of the child’s thought processes (Ojose, 2008). There is also a lack of logic and rational thought at this stage as the child is unable to link together unrelated events, reverse operations, understand point-of-view and sees objects as possessing life. For example, a child at this stage who understands that adding three and five equals eight cannot yet perform the reverse operation of taking three from eight. Ojose (2008) also states that children’s perceptions at this stage are generally restricted to one aspect or dimension of an object at the expense of the other aspects.
In his research, Piaget tested the concept of conservation by pouring a liquid into similar containers of equal amount. He then poured the liquid from one container into a third, wider container. The level is lower and the child thinks there is less liquid in the third container. In this instance, the child is using one dimension, height, as the basis for his judgment of another dimension, volume. The teacher should utilize effective question about characterizing objects. For example, when students investigate geometric shape, the teacher could ask the students to group the shapes according to similar characteristics. Following the investigation, the teacher can ask questions such as, “How did you decide where each object belonged? Are there other ways to group these together?” Such discussion or interactions the students engage in can with stimulate the children’s discovery of the variety of ways to group objects and at the same time, help them think about the quantities in novel ways (Thompson, 1990 cited in Ojose, 2008).
The third stage is called the concrete operational stage which is characterized by remarkable cognitive growth. Children at this stage utilize their senses in order to know and are now able to consider two or three dimensions simultaneously instead of successively. The child also develops seriation and classification which are both essential for number concepts. Hands-on activities are an important factor at this stage since they provide students with an avenue to make abstract ideas concrete. It also allows students to get their hands on mathematical ideas and concepts as useful tools for problem solving (Ojose, 2008). It is suggested that teachers use manipulatives with their students in order to explore concepts such as place value and arithmetical operations. Some materials include algebra tiles, algebra cubes, pattern blocks, Cuisenaire rods, geo-boards, tangrams, counters, dice, and spinners. Teacher can also use non-commercial materials such as paper folding and cutting.
It was stated that one of the important challenges in teaching is to help students make connections between the mathematics concepts and the activity because children may not make connections manipulative materials and the corresponding abstract mathematics that they worked with automatically. “Children tend to think that the manipulations they do with models are one method for finding a solution and pencil-and-paper math is entirely separate” (Burns & Silbey, 2000, p.60 cited in Ojose, 2008). For example, it may be difficult for a child to understand how a three by seven inch rectangle built with wooden tiles relates to three multiplied by seven, or three groups of seven. The teacher can assist the students in making the connections by showing how the rectangles can be separated into three rows of seven tiles each by demonstrating how the rectangle is another representation of three groups of seven. By representing the mathematics in multiple ways acknowledges the uniqueness of students and provides various paths for making ideas meaningful. It also creates opportunities for students to present mathematical solutions in various ways, for example, graphs, symbols, tables and words (Ojose, 2008). The final stage is called the formal operational. The main characteristic of this stage is where the child can reason and consider at the abstract level without having to resort to the physical world. This is from age eleven and onwards.
Constructivism
Constructivism
It is believed that students need to construct their own understanding of each mathematical concept, so that the primary role of teaching is not to lecture, explain, or attempt to ‘transfer’ mathematical knowledge. It is to create situations for students that will foster their making the necessary mental constructions. They do not absorb ideas as teachers present them rather they create their own knowledge through play and interaction with their environment. Constructivism focuses on how people learn. It suggests that knowledge in mathematics results from people forming models in response to the questions and challenges that come from actively engaging mathematics problems and environments. The teacher is required to “create experiences that engage the student and support his own explanation, evaluation, and application of the mathematical models needed to make sense of the experiences” The teacher can also improve teaching by discovering for various ways to engage individual students, develop rich environments for exploration and eliciting and communicating student perceptions and interpretations.
According to Paul Ernest (1996) the forms of constructivism such as weak, radical and social lead to pedagogical implications. Some of the implications are sensitivity toward and attentiveness to the learner’s previous constructions such as informal knowledge, previous conceptions and previous knowledge to build on; use of multiple representations which provide more avenues for students to connect previous conceptions; using cognitive conflict techniques to remedy misconceptions which allows students to think on their own and develop their own meanings or rectify the conflict; awareness of the importance of goals and social contexts (Ishii, 2003).
Some constructivists believe that people are born with an innate ability to deal with small integers (such as 1, 2, 3, 4) and to compare estimates of large numbers. The human brain has components that can adapt to learning and using mathematics and vary significantly in their instinctive mathematical abilities or intelligence. The also believe students from the time of kindergarten have varying levels of mathematical knowledge, skills and interests because the mathematical environments they grew up in varied (Moursund, 2006).
A constructivist teacher uses raw data and primary sources, along with manipulative, interactive, and physical materials. They allow student responses to drive lessons, shift instructional strategies, and alter content. The teacher inquires about students’ understandings of concepts before sharing their own understanding of those concepts. They also allow significant wait time after asking questions and engage students in dialogue, encouraging discussion (Ishii, 2003).
Humanism
Multiple Intelligences
Brain Based Approaches to learning/ Neuroscience
My Personal Instructional Theory
Conclusion
Conclusion
All of the theories examined are important contributors to the teaching and learning of Science. ****Piaget’s stages of cognitive development have shown the reasons why some topics in Science are done at a higher level than in the lower ones. Constructivists believe that children learn from their interaction with the world and from their experiences. Behaviourists also believe the rewards from teachers are important to the conditioning of the child to want to achieve in Science, since more praise a child receives for doing well the more he will want to do well.
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