Philosophy of Education

Socio-cultural Philosophy of Education

By

Merck Smith

Introduction

Mathematics is a language. And, like any other language, mathematics is based upon vocabulary, rules, syntax, and construction. In order to fully learn mathematics, one must be to able master all areas of this language. When learning a foreign language, one often equips oneself with a dictionary that translates words from English into the new language and vise versa. However, to master this new language one must also learn sentence structure, syntax, tenses, and a variety of other rules and particulars. And each task learned is used to build on additional tasks to master the new language. Mathematics is no different. The use of a calculator is like that of a dictionary and is only an aid in applying knowledge to gain a solution. In order to learn mathematics you must also master concepts, properties, rules, and foundations that make up this language. From the earliest years of school, students are not given the proper foundation of the principles but only the aid of the calculator. It is this gap in knowledge coupled with the principles of learning a new language that form my socio-cultural philosophy of education as it relates to mathematics education.

Epistemology

Epistemology is the study of how people learn and what people learn. It is often referred to as the “theory of knowledge.” One principle of epistemology is that of constructivism. “Constructivism emphasizes the importance of the knowledge, beliefs and skills that an individual brings to the experience of learning” (Garbett, 2011, p.37). This principle therefore takes a person’s previous knowledge and uses this knowledge to construct new knowledge. In mathematics, a critical component of learning new skills is to build upon previously acquired skills and knowledge. It is therefore my belief that a constructivist approach is the proper principle on which to base my socio-cultural philosophy of education. The student is an active participant in the process of learning. The student is able to use what he/she knows and apply this knowledge to new information in order to broaden his/her knowledge base of mathematics. The main flaw in this approached addressed by Hennessey, Higley, and Chesnut (2012) in Persuasive Pedagogy: A Paradigm in Mathematics Educations is that students often retrieve misinformation when learning new skills because they have gaps in their knowledge. These factors cause the student either to learn the new information incorrectly, or to lack the ability to build upon prior knowledge in order to process the new information.

The adoption of constructivism as the theoretical underpinning for learning and pedagogy in mathematics classes provides no mechanism for teachers to explicitly acknowledge and correct the implicit beliefs held by individuals about the knowledge they have gained and that they are trying to learn. (Hennessey, 2012, p. 188)

These above cited authors therefore advance a theory of constructivism with persuasive pedagogy. In this approach, the teacher practices the traditional procedures of allowing the students to learn based on prior knowledge, but also persuades the student that this knowledge might be flawed and that the students must rethink and examine the foundations upon which they build their new knowledge. “One reason persuasive pedagogy has value in the mathematics classroom is that the practices of justification, argumentation, and discussion are fundamental aspects of this teaching pedagogy that not only confront student misconceptions, but also student beliefs about knowledge” (Hennessey, 2012, p. 189). It is for this reason that I have adopted this epistemology of constructivism with persuasive pedagogy in order to correct gaps in and misconceptions of prior knowledge to correctly understand and gain new knowledge in mathematics.

The Optimal Learning Environment for Students

The environment within which a student learns is one of the key elements as to how much and how well that student is able to process and retain new information. “In pedagogic models based on constructivist theory, the student constructs his own knowledge instead of passively absorbing it in a classroom or by consulting textbooks” (Garcia, 2013, p. 28). It is therefore important to create an environment where the student feels comfortable in the process of discovery through trial and error while still receiving the required support and information to succeed in learning new information. The classroom should therefore afford the student the opportunity to receive instruction, participate in collaborative sessions, and further explore concepts on his own. This optimal learning environment is best provided through segmented learning sessions that promote self-reflection and group participation, as well as the process of learning from the failed attempts and mistakes. The student is then able to practice and reflect upon the subject matter during homework assignments.

Teaching Strategies

“Students learn in different ways such as by seeing and hearing; reflecting and acting; reasoning logically and intuitively; memorizing and visualizing. Consequently, teaching methods also have to vary” (Akib, 2013, p. 4). In order to effectively educate all of the students in a class, the teacher must therefore not only address the different learning styles, but must also address the different ways that students process information. To address the second concern, I always try to incorporate auditory, visual, and tactile methods of presenting information to the students in each lesson. In order to address the different learning styles, the material is also presented in a variety of ways, and students are given the freedom to explore each new topic in a way that fits their preferred learning style. Because it is impossible to infuse all of these variations and techniques into every lesson, students that struggle with a concept are always provided additional methods and resources to aid in their particular learning process.

My lessons are routinely broken down into segments that include a warm up, mini lesson, main body, closing, and some sort of exit assessment. Within these segments different strategies are used to accommodate different types of learners. Some days may be targeted more heavily toward one type of learner. On these days particular attention is given during group sessions to other types of learners that might be struggling. Technology is used whenever possible; however, the basic tools of a ruler, compass, and protractor are routinely used to accommodate all types of learners. This method also provides a basic understanding of how and why things work. Scheduled tutoring sessions are provided twice a week after school and I am also available before and after school on other days. The goal is to accommodate all levels and styles of learners in order to gain a fundamental understanding of the concepts of mathematics.

Theory of Learning

My theory of learning is fundamentally rooted in the theory of collaborative and dialogic learning techniques. During lecture, I like to use a dialogic format for addressing questions. Through this strategy, I avoid assuming the role of a dictator, and instead take the role of a participant in a democratic process of education. In an article by Kasi Allen (2011), entitled Mathematics as Thinking, A response to ‘Democracy and School Math’,” the author stresses that learning mathematics should be a democratic process. “They [scholars] recognize that democratic mathematics education occurs when students do math, rather than have math done to them” (Allen, 2011, p.3). Therefore, by utilizing strategies of collaborative learning and dialogic learning, the students are active participants in the learning process and able to learn through this democratic process.

Conclusion

Our system of mathematics education is flawed starting with its roots in elementary education. The initial lack of understanding sets our students on a downward spiral that is patched with band-aids and supplemented with shortcuts to get them to high school. In order to put our students back on track, a constructivist approach must be used with persuasive pedagogy. The best way to implement this strategy is to provide our students with a learning environment that is culturally sensitive and designed to meet the needs of all types of learners. We must then employ strategies of collaborative and dialogic learning in order for the students to correct inaccurate information and fill gaps in their knowledge. This process will allow them to engage in discovering the principles and foundations of mathematics.

References

Akib, I. (2013). Student Learning Style on Mathematics Through Bugismakassar

Culture. Indian Streams Research Journal, 3(5), 1-5.

Allen, K. C. (2011). Mathematics as Thinking. A Response to "Democracy and School

Math". Democracy & Education, 19(2).

Garbett, D. (2011). Constructivism Deconstructed in Science Teacher Education.

Australian Journal Of Teacher Education, 36(6), 26-49.

Garcia, I. I., & Pacheco, C. C. (2013). A Constructivist Computational Platform to

Support Mathematics Education in Elementary School. Computers & Education, 6625-39.

Hennessey, M., Higley, K., & Chesnut, S. (2012). Persuasive Pedagogy: A New

Paradigm for Mathematics Education. Educational Psychology Review, 24(2),

187-204. doi:10.1007/s10648-011-9190-7