“The only way to learn mathematics is to do mathematics.” –Paul Halmos
Mathematics teaching is the pursuit of providing students with the skills necessary to be critical thinkers and problem solvers in real-life situations. Mathematics is not simply about getting an answer it is more about the discovery and learning that takes place along the way to that answer. A teacher of mathematics must convey that mathematics is beautiful, useful, and necessary in order to be a productive member of society. Mathematics is arguably the most important subject in the modern day curriculum. I believe that mathematics is a language that occurs naturally around us, there for us to discover and learn. I also believe that the language of mathematics is accessible to those who immerse themselves deep enough into it. Mathematics is all around us, “Dig deep enough into something and you’re bound to find mathematics at its core.” It’s almost impossible to think of something that’s made without the help of mathematics. Mathematics is everywhere. Construction, technology, medicine, transport… all aspects of life rely on numbers, measures, calculations and models. This series of insightful animated shorts illustrates how mathematics, though one big abstraction, makes things possible and real (DaVinci Learning). Those students who truly believe that mathematics is involved in everything are the ones who understand that mathematics is the basis of life. Furthermore, mathematics is about acquiring the tools necessary to solve problems. The study of mathematics should be focused on applications and real world problems. The student who simply memorizes formulas, rules, and math tricks but does not understand when to employ those formulas, rules, and math tricks it devoid of truly understanding the purpose of mathematics. This fundamental truth about mathematics is even more salient in every changing time of computer science, app development, medicine, and technology. Many students can and will take different approaches to get to the same result and it is important to foster the multitude of problem solving strategies and attempts that students take. Creating an environment that is student-centered and focused on the problem-solving aspect of mathematics leads to the most meaningful learning of mathematics. To reach all modalities of learners’ students will be encouraged to use and explain their own logical approach. To achieve this environment and foster students’ uniqueness the teacher needs to provide authentic opportunities to collaborate and differentiate instruction when appropriate to reach all students. In addition, accommodations and modifications in the forms of manipulatives and other concrete learning resources must be present to meet those students who have not reached the abstraction phase of their understanding of mathematics. Mathematics is challenging and students should be challenged while they engage in the learning of mathematics.. In my classroom students will be expected to go beyond rote memorization and use the mathematics to construct the understanding to real world applications. The theory of how people learn, constructivism, will guide my mathematics instruction. "Students need to construct their own understanding of each mathematical concept, so that the primary role of teaching is not to lecture, explain, or otherwise attempt to 'transfer' mathematical knowledge, but to create situations for students that will foster their making the necessary mental constructions. A critical aspect of the approach is a decomposition of each mathematical concept into developmental steps following a Piagetian theory of knowledge based on observation of, and interviews with, students as they attempt to learn a concept." (Calculus, Concepts, Computers, and Cooperative Learning). Only when students are challenged and given the opportunity to struggle with the material to construct their own understanding, can they realize their full potential and understanding in mathematics. To support students in realizing their full potential, the teacher must provide opportunities for students to construct their own knowledge, to use technology, and to collaborate with peers.