## Math 214 Final Reflective Paper

Math 213 gives new teachers the tools needed to further understand what they will be facing when entering the classroom. There is a wide range of mathematic concepts covered throughout this course. Among them the major topics included: the principals and process standards for elementary school mathematics defined by the National Council of Teachers of Mathematics and the application of problem-solving strategies using numerical patterns.
Additional major concepts covered were the relations and functions to solve problems, base value, language sets, the value of the Venn diagrams, how to make reasonable estimates, and how to apply number theory to applications. Week one was the exploration of the six principles of elementary school mathematics: equity, curriculum, teaching, learning, assessment, and connection. These standards outline the understanding, knowledge, and skills student should acquire in each grade level. NCTM’s establishes focus and coherence into teacher’s efforts in improving mathematics.
NCTM offers teachers examples and recommendations of a wide variety of educational circumstances that serve in the best interest of the student. They serve as a support group in guiding every educator in their efforts to improving how math will be presented in the classroom. Week one was also dedicated to showing the differences in how adults and children learn while investigating problem-solving strategies. The action of students with no prior knowledge of mathematics was quite overwhelming. When time is not an essence and logic does not exist students are surprisingly able to grasp concepts of mathematics.

Revealing this process illustrates the importance of encouraging students to take risks while exploring problem solving. With the right tools put into place students can excel and possibly lead the way into higher mathematics. Week two covered several number systems, functions, patterns, and problem solving strategies. We thoroughly examined the Hindu-Arabic, Tally, Egyptian, Mayan, Roman, and Babylonian number systems. With the introduction of language sets the Venn diagram proved to be a valuable tool. The use of visual aids and hands on tools for establishing base values are a necessity when introducing the fundamentals.
Manipulation techniques and visual aids give students the opportunity to explore math beyond the numbers and presents ides that students can relate to. After grasping knowledge of the fundamentals students can use them to connect with higher levels of mathematics. Week three was the analysis of algorithms and the discovery of the importance in giving students the freedom to contemplate their own. Many studies have shown students who create their own algorithms have a stronger mathematic grasp on the skills needed to work out problems on their own. Also introduced in week three was the importance of mastering addition prior to multiplication.
Students who master addition realize that multiplication is repeating addition and can use it as a tool when checking their multiplication answers. The number line and group activities used during this week incorporated concepts of estimation and rounding and demonstrated how students can judge the accuracy of their answers. Carrying forward was the introduction of multiplication properties. They include: Commutative Property, changing the order, Associative Property, changing the grouping factors, and the Identity Property were one is the same as the other.
The knowledge of these operations makes it easier for students to understand multiplication. The concepts in week three set a foundation needed to expand on. Students must have an understanding of numbers and the different ways they are represented. These concepts are useful application to present and future math challenges. Week four covered the difficulties that students have with fractions. Visual aids, manipulation, and using realistic relationships prove to be useful as teacher interpret fractions, decimals, percents, and problems solving techniques to students.
Circular shape objects create a superior surface in showing a whole numbers and are a good starting point when explaining the meaning of the numerator and the denominator. Manipulation of objects and relating math concepts to everyday life may help students with other styles of learning. Beans and blocks are just some objects teachers can use in manipulation and the score to last nights football game might be something students can relate to. There is great deal of sources available to teachers that illustrate and explain different approaches that can help students grasp mathematic concepts like fraction, decimal, percent, nd problem solving. Teachers have formed support groups online, around the nation, that are dedicated to helping students connect to math. Finally, my reflection after week five proves to be filled with valuable information needed for the development of a professional math instructor. This course has improved my understanding of math in general and has given me the tools to explore a student’s mind. Through thorough investigations I have found different approaches that may best suited in presenting mathematic concepts into a classroom.

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