The different models and manipulatives to help elementary students in understand the concept and backbone of mathematics has been in place for some quite time. The most recent pioneers in this field are Jean Paiget (1896-1980) and Zoltan Dienes (1916-). In 1952 Piaget suggested that children begin to understand symbols and abstract concepts only after experiencing the ideas on a concrete level. Piaget emphasized that children learn best when they are active and seek solutions for themselves by making discoveries reflecting on them, and discussing them, rather than by blindly imitating the teacher (Santrock, Page 386). This also applied to Vygotsky’s theory which states that the teacher should encourage the student to focus on real life experience …show more content…
Models and Manipulatives not only allow students to construct their own cognitive models for abstract mathematical, they also provide a common language with which to communicate these models to the teacher and other students. In addition manipulatives have the advantage of engaging students and increasing both interest in and enjoyment of mathematics. Students who are presented with the opportunity to use manipulatives report that they are more interested in mathematics. Long-term interest in mathematics translates to increased mathematical ability (Sutton & Krueger, 2002). In fact one teacher that worked hand in hand with Constance Kamii another theorist commented that after introducing the nontraditional way, her class displayed a love for math. During her experiment Constance Kamii results where astonishing. When two classes undertook the same exam, there was not that much difference between the class that was thought math in the constructivist way than the class that was though the conventional way. Another group of researcher from Purdue University presented problems to student to …show more content…
It uses Dienes ten block system, so that the student can visualize the multiplication. Billstein, gives us a perfect example on how to find the product 4 x 12. (Page 152). This can be computed by using block models. The student will prepare 4 rows under each other of twelve blocks. The student will group ten blocks to create a 10 and two individual units of one. By regrouping each individual line, the student can count the blocks easier and faster. Another alternative multiplication algorithm is the Lattice Multiplication. This low-stress algorithm has the advantage of delaying all additions until the single-digit multiplication are complete. (Billstein Page
Jean Piaget and Lev Vygotsky spent their lives constructing theories to explain human growth and development. Both theorists are, today, considered leading contributors to the field of developmental psychology. The purpose of this paper is to explain how a better understanding of Piaget’s and Vygotsky’s theories will provide you with a better understanding of how we ourselves learn and grow as students in today. This will be accomplished by summarizing, comparing,
Another major difference seen in Lourenco’s (2012) article is that Piaget felt that instruction lead to memorization and not a functional understanding. Piaget felt that we keep children from understanding something completely when we teach them something they could have discovered on their own. Concepts are formed naturally and scientific concepts are not gained by a teacher. Vygotsky on the other hand found that children did better with guidance form an adult. He felt that scientific concepts are gained from teachers and that the child-adult relationship promoted development. In his theory the adult or higher-functioning peer plays an important role in the child’s development and knowledge. Whereas Piaget’s theory looks at social relationships as two equal peers, Vygotsky’s theory looks at an authority based
...ts work on the lessons independently or with a preservice teacher by using manipulatives or other mathematical tools it will allow them to fully grasp the concept that is being taught so they can do well in the long run of learning more complex mathematics.
Piaget’s theory is developed from the idea that the child constructs their knowledge individually whereas Vygotsky argued that children develop tools of learning by communicating with more knowledgeable others (O. Lourenco 2012). Piaget suggested that children develop through a series of four stages in their thinking – the sensorimotor, preoperational, concrete operational and formal operational stages each of which causes broad changes in the child’s intelligence structure and their logic (reference). These four structures are mental operations which are applied to anything in the child’s world these mental operations are referred to as schemas which grow and change from one stage to the next (book). Vygotsky had very different idea on this subject although they both agreed that the child is the active constructor of their own knowledge
All children learn differently and teachers, especially those who teach mathematics, have to accommodate all children’s different capacities for learning information. When teaching mathematics, a teacher has to be able to use various methods of presenting the information in order to help the students understand the concepts they are being taught. Most teachers in the past have taught mathematics through procedural lessons. Procedural lessons consist of having the students work with a concept over and over again until it is memorized. For example, children could be given homework assignments with the equation three times five over and over again until that equation is memorized.
There are five ways in which Piaget’s theory of cognitive development and Vygotsky’s theory of the Zone of Proximal Development. The very first way that teachers can use these theories to teach constructively is by providing scaffolded instruction within the ZPD for their students (292). In other words, a teacher must be able to assist children in achieving a goal that may be slightly too difficult for them to reach alone. An example of this would be if a teacher had decided that her class should do an experiment on how well plants grow based on the amount of water they receive, she could challenge her students to make a hypothesis about what they think will happen. This teacher could allow her students to individually plant their seeds and then guiding her students to predict or hypothesize what they believe will happen if one plant gets more water than another. This example directly correlates with Vygotsky’s idea of ZPD because
Lev Vygotsky developed his theory of learning in the 1920’s but it was not until the late 1960’s that his ideas about learning became popular and were used to contribute to “Constructivism” as a method of teaching. (Krause [et al.] 2010 p. p81).
Wu, Y. (2008). Experimental Study on Effect of Different Mathematical Teaching Methodologies on Students’ Performance. Journal of Mathematics Studies. Vol 1(1) 164-171.
I believe children should be encouraged to learn, that as a teacher it is my job to help them find the way of learning that works best for them. I feel that students should be able to explore the world around them and learn from hands on activities. This type of learning style goes along with both Piaget and Vygotsky’s theories on learning. My theory leans more closely to Vygotsky’s theory due to the fact that I believe that the “play and exploration” should be structured and directed so that as a teacher I can help to guide the information that the students are learning. Such as in the case of the students exploring the playground outside, I feel that I should tell them what we are focusing on the insects that we can find in the playground. This directing helps to keep the students on topic and task while
Piaget’s theory was guided by assumptions about how a learner interacts with their own environment and how they integrate new knowledge and information into existing knowledge. Briefly, he proposed that children are active learners who construct knowledge from their own environment. They learn through assimilation and accommodation in complex cognitive development. Furthermore, interaction with physical and social environments is the key and development occurs in stages. An example of Jean Piaget theory carried out in the classroom is that it gives children a great deal of hands-on practice, by using concrete props and visual aids.
Vygotsky theory has provided educators with the ability to better understand the importance of scaffolding, which allows educators to be able to diagnose children’s learning needs and develop teaching techniques to meet them. To conclude, although Vygotsky’s theory isn’t as complete as other theories, his theory is one that is important for educators to adopt. . Reference List: Berk, L. (2013). Child development.
Piaget and Vygotsky’s biggest differences is their assessments of a child’s progression of development. Piaget believes that development is individual; Vygotsky believes development heavily relies on social aspects. Piaget insisted that learning happens after development, while Vygotsky believed that learning takes place before development can occur. Piaget’s theory has four phases; Vygotsky assumed there were no set stages, only three components. Piaget and Vygotsky both believe that development can be a result of a cognitive conflict. They agree that children are active learners; children learn quickly and development declines with age. In both theories, teachers serve as facilitors and guides.
One hundred years ago, Jean Piaget (1896-1980) was a young man developing new insights about learning. He was one of a handful of constructivist-minded writers and educational theorists of the time. Learning theories open educators up to new ideas. They are necessary to expand our knowledge of how learning works. Piaget’s work is a well-tested and educators around the world should be aware of Piaget’s Theory of Cognitive development in particular because it will improve the quality of their teaching. Once a teacher knows this theory, they can plan lessons appropriate to their students’ cognitive ability and build upon students’ earlier knowledge in a constructivist way.
Research has shown that ‘structured’ math lessons in early childhood are premature and can be detrimental to proper brain development for the young child, actually interfering with concept development (Gromicko, 2011). Children’s experiences in mathematics should reflect learning in a fun and natural way. The main focus of this essay is to show the effectiveness of applying learning theories by Piaget, Vygotsky and Bruner and their relation to the active learning of basic concepts in maths. The theories represent Piaget’s Cognitivism, Vygotsky’s Social Cognitive and Bruner’s Constructivism. Based on my research and analysis, comparisons will be made to the theories presented and their overall impact on promoting mathematical capabilities in children. (ECFS 2009: Unit 5)
Towers, J., Martin, L., & Pirie, S. (2000). Growing mathematical understanding: Layered observations. In M.L. Fernandez (Ed.), Proceedings of the Annual Meetings of North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ, 225-230.