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.
My role in this environment is that of a guide, presenting tools and strategies for the class to discover and reason through mathematics. The more students see that there are different ways of thinking about the same situation, the more they will be able to access resources when they encounter a problem on their own. For instance, in a 7th grade classroom, we used two color counters to introduce integer operations. For the exit exercises, some students still needed the idea of chips while others had established generalizations. Through guided discovery, they took away a level of understanding that best suited them.
We have worked in groups and collaborated on the big ideas of each unit. On our own we have presented to the class both answered problems and productive failures. We have enjoyed reading books and articles related to math, teaching, and this course. We have learned through inquiry based learning and were able to use other materials such as manipulatives, videos, and our peers. As individuals and a class we were able to reflect on what is working, why its working, and how to be best prepared to be math teachers.
This paper provides a brief overview of my pedagogical content knowledge of math, describes my motivation to be a better instructor and ideas for whole school improvement. The basis of my paper are reflections on my practice. I understand that teaching is a highly complex activity that draws on many kinds of knowledge. Teaching is a complex cognitive skill occurring in an
This allows the student to scaffold their learning through cognitive processes that are facilitated by teaching in a resource rich and collaborative environment (Thompson, 1994, p.69). Constructivist learning Constructivist learning in mathematics should endeavour to encourage students to “construct their own mathematical knowledge through social interaction and meaningful activities (Andrew, 2007, p.157).” I want students to develop their own conceptual frameworks, experiences, surroundings and prior knowledge. With learning being a social process, students can discuss in small groups their solution strategies rather than silently working at their desks (Clements et al., 1990, p.2). Constructivist teaching I consider the role of the constructivist teacher to enable to guide and facilitate a student’s thought processes and support the invention of viable mathematical ideas. A skilled teacher will also construct an appropriate classroom environment where students openly discuss, reflect on and make sense of tasks set before them (Clements et al, 1990).
Ask almost any student what they think of math class and their answer will be quite similar, “I do not like it because it is too hard.” Mathematics has a negative image by people of all different ages because many people think of it as making a simple thing complicated, but the reality of the situation is mathematics makes life much easier. Negative thoughts about math can also come from poor math teachers, weak curriculum, or one bad experience ruining the fun of mathematics for many individuals. Being that the subject of mathematics is so complicated it takes an efficient teacher to be able to successfully teach students the correct steps in solving mathematical equations. Teaching math cannot be done successfully by reading some vocabulary words, filling in the blanks on a worksheet, and then taking a quiz, mathematics needs to be taught in ways were students get to explore problems and follow the necessary steps to solve the problem. Most importantly students need practice in math and that can be done in many different ways.
The focus and largest use of philosophy in my classroom will be essentialism. Essentialists believe in training the mind. Students must first understand basic subjects before expanding their ideas and thinking abstractly. This concept is very important in mathematics. It is impossible to understand trigonometry without the basic knowledge of geometry.
In other words, student‟s disposition to study Mathematics depends a lot on how students understand the content and find the subject within his/her reaches. This study specifically explores students‟ disposition towards Mathematics. It is understood that both cognitive and affective factors are important in the learning of
Importance of “Write to Learn” The use of the “write to learn” strategy is very important in content subjects, specifically mathematics. First, this strategy allows teachers to comprehend students’ thought process, their understanding of the material and what areas might need re-explaining (Vacca et al., 2011). These activities give teachers a look at their students’ understanding and it allows them to prepare lessons accordingly in order to address problems students may have or even reward students for their understanding. Second, these activities allow students to clarify their learning and they engage students in the lessons (Vacca et al., 2011). Through these... ... middle of paper ... ...rite to learn” method is very influential and useful in content classrooms, specifically in mathematics.
I want to learn how to use manipulative during math lessons to get my students engaged. I want to learn instructional strategies and techniques to help my students understand. Some of the strategies may include using appropriate materials to teach all children with different learning styles. I look forward to learning the critical mathematics concepts relevant to the early childhood mathematics Common Core Standards for Mathematics. The Common Cores Standards are very important because it provides teachers, parents, and students with a set of clear expectations.