Critical Issues in Mathematics Education: Constructivism - Literature review Example

Running Head: CRITICAL ISSUES IN MATHEMATICAL EDUCATION \ Critical issues in Mathematic Education: Constructivism Student’s Name Course Number: Course Title Instructor’s Name Date Abstract There are four basic learning theories: Cognitivism, humanism, behaviorism and constructivism. The four have been in use by many schools but constructivism is taking center stage in the recent times. Researchers and scholars across the globe have investigated the scope of the issue and have come up with many arguments concerning it. They have arrived at a general consensus that indeed constructivism has transformed education in many aspects. The paper is aimed at examining some of the issues underlying constructivism as a new approach to education. It will take an overview approach of issues of constructivism that have been detailed in literature and further present some arguments for and against the concept. Finally, it will reflectively discuss use of constructivism in a real class in order to demonstrate its effectiveness. Literature Survey Critical judgments on education, especially in mathematics is nothing new. Despite the fact that maturation in the field of mathematic education has been observed, concerned issues have been raised about the nature of teaching. Different theories and strategies have been evaluated in the teaching of mathematics in all levels of teachings (Smith & Armstrong, 2002). Constructivism is one of the argued strategies of teaching especially in elementary schools. Constructivism is understood as a theory of learning whereby students are able to construct knowledge through the learning process as they interact with phenomenon; this is continuous with the development of a shared –meaning of phenomenon through interactions within a culture. Other authors have observed it as a specific philosophical position that holds a specific reality, in the most concrete and immediate sense, the mental construction of them that believe that they have already discovered and investigated it well. Going along with this perspective, learning can therefore, be understood as a process that is self-regulated of resolving internal conflicts that may become apparent through experience, concrete discussion and reflection (Sriraman, 2007). The ideas on constructivism are not very new. The knowledge was developed as far as 470 B.C, where famous critics such as Vico and Kant are said to develop the aspects of constructivism. However, the development of constructivism is mostly credited to Jean Piaget, who worked in the twentieth century (Sriraman, 2007).Piaget argues that the students are expected or should first learn by constructing own understanding as they are doing hand-on tasks that are appropriate in development and creating more abstract ideas. In education in recent times, constructivism has gained profound implications. It has been widely applied in the United States, Unite Kingdom, Taiwan and Germany. In 1989, in the United States, the National Council of Teachers of Mathematics did issue its Curriculum and Evaluation Standards for School Mathematics which endorsed constructivism as the basic standard in the country. This was a result of many educators believing that constructivism is a basic in learning (Gellert & Jablonka, 2007). Constructivism does differ from traditional teaching. Traditional teaching is seen to be mostly defined as being content-based, objectivist, and scheme-lend the tutor-as- information-giver. For example, in a mathematical class, this pattern was mainly followed; reviews were done by the teacher correcting the home work, introduction of new concepts of the blackboard as the students took notes, the tutor directed the student through some practices and eventually the students did the problems individually (Gutstein, 2006). However, in constructivism, the students identify the topic or issues and apply the needed concepts. In other words, the students take active role in the learning in the class. In constructivism, the role of teachers in the classroom is to develop a thorough and deeper understanding of the mathematic curriculum which helps them to be able to direct the students in the coverage of the curriculum. The teacher is expected to be more flexible and risk taker as they have the understanding that the students have different understanding capacity. Basically, the teacher should be a valuable resource to the student. Arguments for and against constructivism Many academicians and philosophers have detailed many advantages of constructivism. In his research Boaler (1998) found out that use of constructivism in the classroom played a major part in motivating students, they became more interested and excited about math, applied the concepts of math in real life issues and it enhanced accommodation of all genders. Indeed, students in the traditional class are more conversant with mathematical problems and they know more mathematics as compared to those in a constructivism class. However, it is quite clear that students in a constructivism class are in a better position to interpret and perceive the problems hence they can use them in real life situations unlike the traditional approach which focuses more on rules, computations and procedures. Constructivism builds confidence in the student in the use of math and it actually enables them to be flexible in terms of changing procedures whenever there is need to do so (Gregory, 2004). Another advantage of constructivism that has been observed is the aspect of alternative assessment style that is one of the key features of constructivism. Under this kind of assessment, students are able to evaluate themselves and gage performance for themselves unlike in the traditional approach where students were labeled based on their academic performance. Through self-assessment, students are able to understand themselves in terms of learning and career directions thus take responsibility of their lives. Students as well as their parents can make sound decisions on suitability of tutors based on evaluation of concepts and skills. It is also quite clear that constructivism prepares students for the real world of employment and business. Constructivism encourages teamwork and communication during problem solving and decision making which is quite vital in any given organization. In addition to this, teaching has moved from the more the traditional approach to a more computer intensive approach where repetitive tasks can now be performed using machines. Constructivism therefore, equips students to be adequate and useful community resources (Pon, 2001). Besides these concrete advantages, there are many arguments against constructivism. Firstly, constructivism has ultimately transformed mathematics from an objective, static and respectable discipline of knowledge to a socially subjective wasteland. According to Gregory (2004), mathematics under constructivism becomes subjective by the fact that it is made by a single individual and only becomes objective once it is published, formulated, reviewed and discussed. However, the issue of subjectivity recurs when the objective knowledge is reconstructed and internalized by other individuals. Mathematics, according to rules and conventions is regarded as a linguistic knowledge that which though made in a subjective manner should be able to be made into objective knowledge when published. Another shortcoming of constructivism is that it allows students to construct and believe their own concepts. According to Pon (2001), it is inappropriate for students to develop personal truths and concepts concerning math but instead they should construct a true math understanding that is in line with the real world. The issue of private truths therefore, brings about identifiable misunderstandings among students in class and ultimately in the society. Thirdly, many scholars have argued that constructivism actually increases the load of the curriculum instead of reducing it to manager size for students. However is under controversy as survey indicates that big curriculums enhance performance. Fourthly, the process of re-educating parents and students on a new way of approach of teaching is proving difficult for the education sector. Additionally, the new concept requires that teachers receive adequate training and some have to undergo retraining to fit into the new approach which is sometimes expensive for schools. Students who graduate out of schools that use constructivism also find it hard to find jobs since the large society has not yet embraced the concept (Boaler, 1998). Real Experience To get a real sense of constructivism in a mathematical class, I spent a day in one of the public schools. The 10 class was undertaking statistics. The teacher was not in a position to explain whether the students would lead the class. Therefore, it was interesting to watch the teacher react to the class ideas and questions. The teacher commenced by having the students go through a few newspapers in small groups and identified the articles that did contain statistics. Students were passionately enjoying the task and of course genuine questions did rise up (Gutstein, 2006). They were very eager to come up with statistical articles with their own design. The teacher gave handouts that posed questions that were to be solved in the processing of designing the article. As much as the students were not familiar with problems in the handouts, they were very much motivated to try the task at hand. In their groups, their started applying their interest and individual strength in creating a newspaper. They planned to use different resources which included individual member of the group, their teacher, computer resources and books. The motivating factor was that they were eager to show the fellow student and their family the final products. This discovery made the students view statistics in a meaningful way and become more memorable. From this experience, one may be view constructivism as one of the tool o be used in teaching. Conclusion In the past, traditional approach of teaching has been embraced whereby educators simply put knowledge into students. However, this is gradually being replaced by constructivism which is making education easier to understand. It is for this reason that more and more people are considering teaching and learning using constructivism. Many scholars and academicians have demonstrated many significant and positive implications of constructivism education more so in mathematics. However, some have argued against the concept insisting that the traditional method is more appropriate. Before constructivism is fully integrated into the society, it is important that public awareness is intensified, more teachers trained and more resources directed towards the new venture. This accomplishment will enhance better grades in schools and ultimately make better working population. I am extremely excited and optimistic with the new concept as it will make math a joyful and powerful tool for students. REFERENCES Smith, J. & Armstrong, S. (2002), If the world was a village. Tonawanda, New York: Kids Can Press. Sriraman, B. (2007), International perspectives on social justice in mathematics education. The Montana Mathematics Enthusiast Monograph 1, Missoula, Montana: University of Montana Press Gellert, U, & Jablonka, E. (2007), Mathematisation and demathematisation: Social, philosophical and educational ramifications. Rotterdam: Sense Publishers. Gutstein, E, (2006), Reading and writing the world with mathematics: pedagogy for social Justice. New York: Routledge. Pon, N. (2001), Constructivism in the secondary mathematics classroom. Nancy Pon and EGallery journal, volume 3, issue 2. Boaler, J, (1998), Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29(1), 41-62. Gregory, R, (2004), The oxford companion to the mind. Oxford: Oxford University Press. Read More