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.
As a middle school math teacher in Chippewa Falls, WI, Steven Reinhart often found that even his extensive planning and detailed lessons yielded less than high achievements from his students. He wanted to know why, that no matter how perfect his lessons were, his students’ level of achievement was so low. It even caused him to question his own methods of teaching. So Reinhart developed an idea to commit to gradually changing his ways of teaching by 10% each year. With the goal of simply teaching a single topic in a better way than the previous year, he “collected and used materials and ideas gathered from supplements, workshops, professional journals, and university classes” to achieve this goal (Reinhart, 2000).
This essay is the first of three short reflexive papers intended to identify the issues and implications that result from viewing mathematics education through a semiotic lens. By mathematics education I mean to include consideration of mathematics itself as a discipline of on-going human activity, the teaching and learning of mathematics, and any research that contributes to our understanding of these preceding enterprises. More specifically my current interests are in disentangling the confusion among the mathematics education community regarding the epistemological foundations of mathematics, the meaning and usefulness of constructivism as a theory of learning, and how these two issues are related to the learning and teaching of formal mathematical proof. Because I have found interdisciplinary approaches to the study of most anything both more fruitful and more enjoyable, I will employ such strategies in these papers. As a result, it may not always be clear that mathematics education is my main concern--please rest assured that it is and that if I gain insight of value in that domain I will do my best to render to Caesar what is his.
In the article “Never Say Anything a Kid Can Say!” Steven C. Reinhart shares his struggle of finding the fundamental flaw that existed in his teaching methods. He is a great teacher, explained mathematics well, he was dedicated and caring, but his students were not learning and with low achievement results, Reinhart had to question his teaching methods. He began to challenge himself. He committed to change 10% of teaching each year and over many years he was able to change his traditional methods of instruction to more of a student-centered problem-based approach. This article promotes students to engage through the use of questioning.
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.
Learning, “as an interpretive, recursive, building process by active learners”, interrelates with the physical and social world (Fosnot, 1996). “Assuming the role as ‘guide on the side’ requires teachers to step off the stage, relinquish some of their power, and release the textbooks to allow their students to be actively engaged and take some responsibility of their own learning” (WhiteClark, DiCarlo, & Gilchriest, 2008, p. 44). Furthermore, constructivism involves developing the student as a learner through cooperative learning, experimentation, and open-ended problems in which students learn on their own through active participation with concepts and principles (Kearsley,
The article “Tying It All Together” by Jennifer M. Suh examines several practices that help students to develop mathematical proficiency. It began with a mathematics teacher explaining that her students began the year struggling to understand basic mathematics concepts, but after implementing the following practices into the classroom throughout the year, the students began to enjoy mathematics and have a better understanding of math concepts.
This approach emphasizes the student's prior knowledge. The strategy demonstrates the theory of constructivism, because the constructivist pedagogy proposes that new knowledge is constructed from old. It holds the educational belief that as teachers, it's essential that we make connections between what new is being presented with students' prior experiences.
The curriculum implies that teachers will teach students the skills they need for the future. Valley View’s High School math department announces, “Students will learn how to use mathematics to analyze and respond to real-world issues and challenges, as they will be expected to do college and the workplace.” Also, the new integrates math class allows students to distinguish the relationship between algebra and geometry. Although students are not being instructed a mathematical issue in depth, they are rapidly going through all the different topics in an integrated math class. Nowadays, students are too worried to pass the course to acquire a problem-solving mind. Paul Lockhart proclaims the entire problem of high school students saying, “I do not see how it's doing society any good to have its members walking around with vague memories of algebraic formulas and geometric diagrams and dear memories of hating them.” A mathematics class should not be intended to make a student weep from complicated equations, but it should encourage them to seek the numbers surrounding
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
In this essay it will discuss Angileri’s, 2006 quote, by going into depth about how constructivism is the best approach to teaching and learning mathematics to children, comparing constructivism to behaviourism and how maths has changed over time from rehearsal to playfulness, fun and creativity. The chosen theory of constructivism was selected as the best approach to teaching and learning mathematics to children as this theory is built on two main theorists working Vygotsky’s and Bruner’s that are both supportive, that learning is an active process that participation is critical and providing support to children with strengthening and support prior knowledge as well as new insights being taught. Comparing constructivism to behaviourism is
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...
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,
When I graduated from high school, forty years ago, I had no idea that mathematics would play such a large role in my future. Like most people learning mathematics, I continue to learn until it became too hard, which made me lose interest. Failure or near failure is one way to put a stop to learning a subject, and leave a lasting impression not worth repeating. Mathematics courses, being compulsory, are designed to cover topics. One by one, the topics need not be important or of immediate use, but altogether or cumulatively, the topics provide or point to a skill, a mastery of mathematics.
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.