Reflective Paper – Math 213 Math 213 is a class packed full of information valuable to the development of a professional math teacher. There were several major mathematical concepts addressed in the class ranging from problem solving, numeration systems and sets, whole numbers and their operations, to algebraic thinking, integers and number theory, rational numbers as fractions, decimals and real numbers, and proportional reasoning, percents, and applications. This class enhanced my understanding of math in general, as well as enabled me to explore strategies on how to best present mathematical concepts in an elementary classroom setting.
Since children learn differently than adults do, and do not have prior knowledge to draw meaning from, an important characteristic of a professional math teacher is to have the ability to create a classroom environment where students are encouraged to take risks and explore problems while learning problem solving strategies. According to the class textbook, A Problem Solving Approach to Mathematics for Elementary School Teachers, “If problems are approached in only one way, a mind-set may be formed. ” (Billstein, R. , Libeskind, S. , & Lott, J. 2010) Teachers need to give students a tool box of strategies, such as, look for a pattern, examine a related problem, identify a subgoal, make a diagram, or work backwards. While developing student’s problem solving skills, professional math teachers must begin to teach students to understand the meanings of whole numbers. This step will serve as scaffolding for students as they encounter more advanced concepts. Teachers should encourage the use of manipulatives, such as base-ten blocks, as they will help students relate whole numbers to something real.
Teachers can also use Venn diagrams as they allow students to graphically organize material, which aids in the development of their analytical skills and teaches them to draw conclusions based on specific criteria. Once mathematics teachers are able to create a solid base of knowledge, they can encourage their students to explore algebraic thinking, and expand their ability to think critically by the use of estimation and mental math. It is up to teachers to give students the skills to set up and solve algorithms that will help to build their math confidence and motivate them to expand on what they have learned.
Teaching the concept of integers and number theory is a fundamental part of math curriculum. The ability of a professional mathematics teacher to tie in real world experiences, using hand on activities and manipulatives is essential in enabling students to build on mathematic ideas and understand how they interconnect. Also important is the concept of rational numbers as fractions, decimals, and real numbers. Teachers need to help ease the transition from whole numbers by clearly explaining the new rules and definitions students are unfamiliar with.
By teaching the importance of ratios, proportions, proportional reasoning, percents, and their real life applications, teachers are giving students the skills they need to become productive members of society. Proportional reasoning is one of the big ideas in math and if students are able to grasp this concept, they will be able to apply it in many instances in their lives. Teachers can assist students with this by providing interesting, well thought out problems that represent situations students will encounter in the future.
This course influenced my philosophy on teaching math by helping me realize how important it is to facilitate mathematical learning through a variety of different learning experiences. I realized that there are often many ways to come up with the same answer, therefore problems should be presented in many in different contexts, as a means of seeing the same thing in a different light. This class also influenced my realization of the important role a math teacher plays not only in presenting information, but in determining where a student went wrong when they do not grasp that information.
I realized that for a teacher to be able to do this they must acquire a deep amount of pedagogical content knowledge and need to promote more than just procedural understanding when teaching math to their students. They need to present the “why”, and they need to be able to teach their students to make sense of mathematics by using reasoning and proof. This conceptual understanding comes from time and practice in a variety of contexts. Providing students with a multitude of mathematical experiences will help them understand math both inside and outside of the classroom.
Most importantly, I realized that professional math teachers need to be good motivators. There were times in this class that I felt confused and wanted to give up. It was as if I were walking in my student’s shoes. This experience taught me that I will need to give my students positive encouragement and plenty of feedback along the way. I will aim to challenge them mentally while providing the support they need to become successful learners. References Billstein, R. , Lineskind, S. and Lott, J. (2010). A Problem Solving Approach to Mathematics for Elementary School Teachers (10th ed. ). Boston: Pearson Education, Inc.