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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. 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... ... middle of paper ... ...S. and Stepelman, J. (2010). Teaching Secondary Mathematics: Techniques and Enrichment Units. 8th Ed. Merrill Prentice Hall. Upper Saddle River, NJ. Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26. Retreived from: http://math.coe.uga.edu/olive/EMAT3500f08/instrumental-relational.pdf Stinson, D. W. (2004). Mathematics as “gate-keeper” (?): Three theoretical perspectives that aim toward empowering all children with a key to the gate. The Mathematics Educator, 14(1), 8-18. Retrieved from http://files.eric.ed.gov/fulltext/EJ848490.pdf Towers, J., Martin, L., & Pirie, S. (2000). Growing mathematical understanding: Layered observations. In M.L. Fernandez (Ed.), Proceedings of the Annual Meetings of North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ, 225-230.
Kieren, T., Gordon-Calvert, L., Reid, D. & Simmt, E. (1995). An enactivist research approach to mathematical activity: Understanding, reasoning, and beliefs. Paper presented at the meeting of the Ame rican Educational Research Association, San Francisco.
Reys, R., Lindquist, M. Lambdin, D., Smith, N., and Suydam, M. (2001). Helping Children Learn Mathematics. New York: John Wiley & Sons, Inc.
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.
Reys, R., Lindquist, M., Lambdin, D., Smith, N., & Suydam, M. (2001). Helping children learn mathematics. New York, NY: John Wiley & Sons, Inc.
Trujillo, K. M., Tracing the Roots of Mathematics Anxiety through In-Depth Interviews with Preservice Elementary Teachers http://findarticles.com/p/articles/mi_m0FCR/is_2_33/ai_62839422 [accessed July 2007]
Wu, Y. (2008). Experimental Study on Effect of Different Mathematical Teaching Methodologies on Students’ Performance. Journal of Mathematics Studies. Vol 1(1) 164-171.
...ett, S. (2008) . Young children’s access to powerful mathematical ideas, in English, Lyn D (ed), Handbook of international research in mathematics education, 2nd edn, New York, NY: Routledge, pp. 75-108.
Silver, E. A. (1998). Improving Mathematics in Middle School: Lessons from TIMSS and Related Research, US Government Printing Office, Superintendent of Documents, Mail Stop: SSOP, Washington, DC 20402-9328.
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
Kirova, A., & Bhargava, A. (2002). Learning to guide preschool children's mathematical understanding: A teacher's professional growth. 4 (1), Retrieved from http://ecrp.uiuc.edu/v4n1/kirova.html
Many seem to think of mathematics as being nothing more than a series of numbers and formulas that they must learn, in order to pass a particular requirement for their college degree. They rarely, if ever, stop to think about the importance of mathematics and how it actually affects them and the people around them. It is ...
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.
When thinking of a philosophy of teaching, four major issues need to be considered. Those issues are one’s views on education, the role of the teacher, teaching and learning, and on the children. This is something that someone entering the teaching profession needs to give serious thought to and realize the importance that this will hold in the future. The following essay will express my philosophy of teaching.
Teaching is a daunting task that I do not intend to take lightly. Becoming a teacher has been a dream of mine for several years. I always knew that teaching would be the career for me, especially when I began working in the school system as a substitute secretary. I loved working in the school environment; coming in contact with children everyday made me realize how much I would enjoy teaching a classroom full of students.
Allowing children to learn mathematics through all facets of development – physical, intellectual, emotional and social - will maximize their exposure to mathematical concepts and problem solving. Additionally, mathematics needs to be integrated into the entire curriculum in a coherent manner that takes into account the relationships and sequences of major mathematical ideas. The curriculum should be developmentally appropriate to the