“Understanding is a measure of the quality and quantity of connections that a new idea has with existing ideas. The greater the number of connections to a network of ideas, the better the understanding (Van de Walle, 2007, p.27).”
My philosophy of a constructivist mathematics education
At what point does a student, in all intents and purposes, experience something mathematical? Does it symbolise a student that can remember a formula, write down symbols, see a pattern or solve a problem? I believe in enriching and empowering a student’s mathematical experience that fundamentally stems from a Piagetian genetic epistemological constructivist model. 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). Through peda...
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...trategies discussed provide opportunities for students to actively create and invent their own mathematical knowledge through a meaningful and contextualised environment. Lastly, with learning being a social process, students are encouraged to co-operatively work together in groups where they learn to value their peers opinions and observations. I finish on a quote that symbolises the ideas at the crux of my philosophy,
“In constructivist classrooms, teachers (a) create environments where students are allowed to engage in actions and activity; (b) foster student-co-student interaction in and out of the classroom; (c) design activities that will agitate weak mathematical constructs students possess; (d) structure learning tasks within relevant, realistic environments; and (e) bring out several solutions and representations of the same problem (Driscoll, 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.
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,
Using a constructivist approach, teachers facilitate learning by encouraging active inquiry, guiding learners to question their tacit assumptions, and coaching them in the construction process. This contrasts with the behavioralist approach that has dominated education, in which the teacher dissemina...
Restivo, Sal, Jean Paul Van Bendegen, and Roland Fischer. Math Works: Philosophical and Social Studies of Mathematics and Mathematics Education. Albany, New York: State University of New York Press, 1993.
Pateman, Neil A., Ed, et al. Proceedings Of The 27Th International Group For The Psychology Of Mathematics Education Conference Held Jointly With The 25Th PME-NA Conference (Honolulu, Hawaii, July 13-18, 2003). Volume 3. n.p.: International Group for the Psychology of Mathematics Education, 2003. ERIC. Web. 23 Apr.
Constructivism theorists believe that learning is an ongoing collective application of knowledge where past knowledge and hands on experience meet. This theory also believes that students are naturally curious. If students are naturally curious, their curio...
Powell, Katherine C, Kalina, Cody J “Cognitive and social constructivism: Developing tools for an effective classroom” Education, Winter2009, Vol. 130 Issue 2, p241-250, 10p
Using literacy strategies in the mathematics classroom leads to successful students. “The National Council of Teachers of Mathematics (NCTM, 1989) define mathematical literacy as an “individual's ability to explore, to conjecture, and to reason logically, as well as to use a variety of mathematical methods effectively to solve problems." Exploring, making conjectures, and being able to reason logically, all stem from the early roots of literacy. Authors Matthews and Rainer (2001) discusses how teachers have questioned the system of incorporating literacy with mathematics in the last couple of years. It started from the need to develop a specific framework, which combines both literacy and mathematics together. Research was conducted through
Constructivism is a method that says students learn by building their schema by adding to their prior knowledge by the use of scaffolding (Rhinehart Neas). Because the students are basically teaching themselves new information, the teacher is there mainly for support and guidance for the students.
Among many teaching styles and learning theories, there is one that is becoming more popular, the constructivist theory. The constructivist theory focuses on the way a person learns, a constructivist believes that the person will learn better when he/she is actively engaged. The person acts or views objects and events in their environment, in the process, this person then understands and learns from the object or events(P. Johnson, 2004). When we encounter a certain experience in our life, we think back to other things that have occurred in our life and use that to tackle this experience. In a lot of cases, we are creators of our own knowledge. In a classroom, the constructivist theory encourages more hands-on assignments or real-world situations, such as, experiments in science and math real-world problem solving. A constructivist teacher constantly checks up on the student, asking them to reflect what they are learning from this activity. The teacher should be keeping track on how they approached similar situations and help them build on that. The students can actually learning how to learn in a well-planned classroom. Many people look at this learning style as a spiral, the student is constantly learning from each new experience and their ideas become more complex and develop stronger abilities to integrate this information(P. Johnson, 2004). An example of a constructivist classroom would be, the student is in science class and everyone is asking questions, although the teacher knows the answer, instead of just giving it to them, she attempts to get the students to think through their knowledge and try to come up with a logical answer. A problem with this method of learning is that people believe that it is excusing the role of...
As a secondary subject, society often views mathematics a critical subject for students to learn in order to be successful. Often times, mathematics serves as a gatekeeper for higher learning and certain specific careers. Since the times of Plato, “mathematics was virtually the first thing everyone has to learn…common to all arts, science, and forms of thought” (Stinson, 2004). Plato argued that all students should learn arithmetic; the advanced mathematics was reserved for those that would serve as the “philosopher guardians” of the city (Stinson, 2004). By the 1900s in the United States, mathematics found itself as a cornerstone of curriculum for students. National reports throughout the 20th Century solidified the importance of mathematics in the success of our nation and its students (Stinson, 2004). As a mathematics teacher, my role to educate all students in mathematics is an important one. My personal philosophy of mathematics education – including the optimal learning environment and best practices teaching strategies – motivates my teaching strategies in my personal classroom.
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...
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)
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.