Research Essay: Theoretical Stance for the Teaching of Mathematics –
As a pre-service teacher, my philosophy of teaching Mathematics is based on a constructivist, student-centred approach. I have learned, through my practicum experiences, as well as Mathematics Education courses, which advocate this approach, that it is the most effective way to teach Mathematics. This essay will explicitly describe my philosophy, as well as explain and justify the specific teaching and learning strategies related to this philosophy, supported by the research and literature.
Philosophy of Mathematics Education: Constructivist, Student-Centred Approach –
When learning Mathematics through a constructivist approach, the students are able to build their own understandings of concepts and problems, actively constructing knowledge in relevant contexts, while the teacher supports this construction of knowledge. The focus is on the personal ways of understanding and the actual process, rather than the answers. Constructivist Mathematics instruction encourages “reflective thinking, higher-order learning skills, testing viability of ideas and seeking alternative views”. The learner also understands how this knowledge of particular mathematical concepts and rules are applicable to real life problems and situations. (ict site)
Student-centred learning is vital for students to construct their understandings and commit them to memory in ways most appropriate for them. Activities that include engaging, participatory experiences, discussion, multiple tools and modes of representations and interactive demonstrations are successful in fostering learning and enthusiasm. Learning in an interactive way, with the teacher, a partner or small group makes t...
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...ent of students” in small group work and can be used to enhance investigations and learning of concepts. Technology is an integral part of students’ everyday lives so incorporating computers will allow for students to be thoroughly engaged in activities. Technology also allows students to explore and express their understandings on a world wide platform via the internet, through information gathering, networking and publishing programs. (computer supported collaborative learning)
Conclusion –
Effective maths teachers use a variety of teaching approaches, strategies and tools. Through personal experiences, applications and research I have found that these various constructivist, student-centred strategies and tools are very effective in developing not only mathematical knowledge and understanding, but also supporting apprehensive or struggling students.
John Dewey once said, “Education is not preparation for life; education is life itself.” You may ask why John Dewey should be given merit for anything he says. In truth, John Dewey was one of the biggest supporters of constructivism in classroom. On a basic level, constructivism is described as learning by doing. This concept, while not necessarily new, is considered progressive. Today, we will explore the history and details of this concept, analyze how constructivism effects the modern classroom, and wrap it up with some concluding remarks.
If you are a parent or plan to be a parent, Do you want your child to sit in a desk all day while the teacher lectures them on information that they need to know for life or would you rather have your child learn constructively? Constructivism has been labeled as the philosophy of learning that proposes learners need to build their own understanding of new ideas (Constructivism and the Five E?s,2001). Learning something new, or attempting to understand something familiar in greater depth, is not a linear process. The purpose of this research paper is to explain the theoretical foundations of the constructivist approach to teaching and learning, and to provide concrete examples to show the effectiveness of the constructivist approach with respect to student learning.
While children can remember, for short periods of time, information taught through books and lectures, deep understanding and the ability to apply learning to new situations requires conceptual understanding that is grounded in direct experience with concrete objects. The teacher has a critical role in helping students connect their manipulative experiences, through a selection of representations, to essential abstract mathematics. Together, outstanding teachers and regular experiences with hands-on learning can bestow students with powerful learning in
Problem solving approach in mathematics has impacts on behavioural changes, students ' self-concept, self-esteem and social interactions in the learning environment (Shen ,Leon, Callaghan & Shen ,2007:274). Problem-solving approach (PSA) is only one type of a larger category of thinking skills that lecturers use to teach students how to think. Other means of developing thinking skills are problem-based learning, critical thinking skills, creative thinking skills, decision making, conceptualizing, and information processing (Ellis,
This practise of effective teaching and learning has relatively new in classrooms but has already made a great difference in the students’ abilities and interests both in and out of their studies. Constructivist teaching recognises and validates the student’s point of view rather then the necessity of a correct answer. The child is then able to reassess their knowledge and understandings, which in turn boosts self-esteem and confidence. It also encourages children to be involved in classroom activities by self-questioning, seeking answers, comparing situations and establishing links between different ideas. This is possible as constructive learning is transferable between different ideas. (Tutorial Notes, 28th July, 2004)
Brooks, J. G., Brooks, M. G. (1999). In Search of Understanding: The Case of Constructivist Classrooms, with a new introduction by the authors. Retrieved from http://site.ebrary.com/lib/ashford/Doc?id=10078162&ppg=28
The term constructivism has been used to explain everything from school reform to teaching styles, and most importantly related to a learning theory. As you can imagine the term Constructivism has the potential to develop many misconceptions since it lacks a universal definition. “Constructivism is an important theory of learning that is used to guide the development of new teaching methods”(Baviskar, Hartle & Whitney, 2009, p.541). The framework of constructivism is built upon the understanding that “learning is an active process that is student centered in the sense that, with the teachers help, learners select and transform information, construct hypothesis’, and make decisions”(Chrenka, 2001, p.694). It is important to understand that when speaking about constructivism we are referring to a learning theory not teach...
We must first look at the need for a constructivist approach in a classroom, to do this we think back to our days in primary school and indeed secondary school where textbooks we like bibles. We were told to take out our books, look at the board, and now complete the exercise on page z. This approach in a class is repetitive, the teacher holds authoritarian power and learning is by no means interactive. “In a traditional classroom, an invisible and imposing, at times, impenetrable, barrier between student and teacher exists through power and practice. In a constructivist classroom, by contrast, the teacher and the student share responsibility and decision making and demonstrate mutual respect.” (Wineburg, 2001) This approach focuses on basic skills and strict adherence to the curriculum. Children are being forced to learn through repetit...
Naylor, S., & Keogh, B. (1999). Constructivism in Classroom: Theory into Practice. Journal of Science Teacher Education, 10(2), 93-106. Retrieved from http://link.springer.com.ezproxy.liberty.edu:2048/article/10.1023%2FA%3A1009419914289#
Mathematics teachers teach their students a wide range of content strands – geometry, algebra, statistics, and trigonometry – while also teaching their students mathematical skills – logical thinking, formal process, numerical reasoning, and problem solving. In teaching my students, I need to aspire to Skemp’s (1976) description of a “relational understanding” of mathematics (p. 4). Skemp describes two types of understanding: relational understanding and instrumental understanding. In an instrumental understanding, students know how to follow steps and sequential procedures without a true understanding of the mathematical reasons for the processe...
A somewhat underused strategy for teaching mathematics is that of guided discovery. With this strategy, the student arrives at an understanding of a new mathematical concept on his or her own. An activity is given in which "students sequentially uncover layers of mathematical information one step at a time and learn new mathematics" (Gerver & Sgroi, 2003). This way, instead of simply being told the procedure for solving a problem, the student can develop the steps mainly on his own with only a little guidance from the teacher.
Considering student achievement based upon the classroom environment, research shows that teachers who use constructivism in their classrooms have students whose achievement is more significant than those who learn by using traditional methods. (Singh, Yager, Yutakom, Yager, & Ali, 2012) It has become vitally important in this age for students to construct knowledge and apply it to both social and scientific situations in the real world. Additionally, the job market has changed, and employers are looking for more in potential employees. There are numerous skills being sought after that center around independent problem solving, a skill that can be taught using a constructivist approach. (Lew, 2010)
One very important factor in every life is the education received as we mature. Education in all subjects is necessary to become a well-rounded individual. Even so, I feel that my subject area has more significance in one’s future because every person uses mathematics every day. Students need to understand why mathematics is important and why they will need it in the future. The way to do that is integrated into the views of the role of the teacher. Teachers need to be encouraging role models that provide students with safety, nurturing, and support in the classroom, along with providing excellent instruction by allowing students to explore and expand their minds in the content of mathematics. Teachers should set high expectations for all students and persuade the students to live up to those expectations. Along the same lines, teaching and learning are complementary concepts. Students need for the teacher to provide them with the knowledge that will be used not only in that class but also in their future endeavors. ...
Devlin believes that mathematics has four faces 1) Mathematics is a way to improve thinking as problem solving. 2) Mathematics is a way of knowing. 3) Mathematics is a way to improve creative medium. 4) Mathematics is applications. (Mann, 2005). Because mathematics has very important role in our life, teaching math in basic education is as important as any other subjects. Students should study math to help them how to solve problems and meet the practical needs such as collect, count, and process the data. Mathematics, moreover, is required students to be capable of following and understanding the future. It also helps students to be able to think creativity, logically, and critically (Happy & Listyani, 2011,
Technology has many different effects on education, one of them being enhancing the students learning. Technology may enhance the students learning and may assist most students in achieving their academic standards. When technology and appropriate teaching methods are combined, technology may increase the academic achievement. Positive effects have been found in all major subject areas, from preschool to higher education, both regular and special needs students. Educational technology has been found to have a positive effect on a student’s attitude toward learning and on self-concepts. The introduction of technology into the learning environment has allowed the learning to be more student-centered, to encourage group learning, and helps to stimulate an increase in the student-teacher interaction. Technology has shown a shift from a focus on a student’s memorization to their problem solving. Through technology’s use, learning opportunities have become unrestricted by time or place, allowing lifelong learning. Student use of technology through communications can also help to enhance access to a career and continued education. Students are more likely to use a computer to get help because they can to it themselves. Technology is helping students to become independent.