Identifying research topics and academic focus areas

¶ … relearn several mathematical concepts and learn how to instruct other about them. It also became necessary to learn the different components of educating students on math based upon their current knowledge and abilities and how the teacher will evaluate the students to make that determination. Not only did I learn how to teach the subject, but I was also instructed on how to submit and fulfill standards. In short, this class taught me how to be an effective and efficient math teacher for students from kindergarten up to the eighth grade. This class had good moments, difficult moments, and has influenced both what concepts I will teach my students and how I will teach them when the time comes.

It is hard determining which of the components learned in this class were the most important. Each mathematical concept will be necessary when entering the teaching profession. Certainly it was useful relearning certain math concepts with the eyes of an adult after leaving them behind for a period of time. However, more than the actual math was the knowledge I gained about how to adequately instruct my present and future students in all the various mathematics. A math teacher has to know how to teach for all potential audiences in elementary and middle school. It is also important to know that although components may be similar, for example teaching geometry, but that the audience you are teaching will have a direct effect on how the subject is taught. With younger students, it is more important to teach the basic concepts, such as the number of sides and angles a given geometric figure will have. With older students, the teacher can take the subject to a higher level of complexity, such as understanding angle measures and how lines, points, and planes all relate to one another. This may be the most important lesson I learned in this class: how to formulate curriculum to the correct audience that is being taught.

In the process of learning, some components will always be more difficult to master than others. In teaching math to students, I have found that usually one of the most challenging concepts to master is the understanding of fractions, percentages, and decimals. I remember being a child and having personal difficulty understanding fractions and how the decimals related to parts of a whole unit. Even as an adult remembering the rules for multiplication and division of fractions can be challenging. When dealing with a student who is struggling with math, whether it be the concepts here described or others, the most important thing is to remember to be patient. What comes naturally to some students will not be as easy for others to master. The first thing is to make sure you introduce a new concept with detail, not so much that the lesson becomes tedious, but detailed enough that the students should be able to understand the concept and how one solves a problem. Then, the teacher should practice the new concept with some problems with the class as a whole. This allows students who do not quite understand based on instruction to have some first-hand experience in the problem solving. After this, the teacher should ask the class if the concept and the instructions are clear enough. Some students will not admit to misunderstanding. Part of this is because they do not wish to be singled out or made to feel stupid in front of their peers. The teacher should also state that should a student need additional help or support, they can discuss it with the teacher during recess or before or after school.

The National Council of Teachers of Mathematics has six principles and five process standards for the teaching of math to students. The principles are: equity, curriculum, teaching, learning, assessment, and technology. Equity ensures that all students are able to have the same access to mathematics education as anyone else, no matter the gender, ethnicity, or religion. The other principles ensure that educators have distinct definitions for each topic, such as learning which the NCTM defines as a combination of "factual knowledge, procedural facility, and conceptual understanding" (Billstein 2010). The process standards are: problem solving, reasoning and proof, communication, connections, and representation. This means that no matter what specific component of the curriculum the students are working on, whether it be addition or subtraction or the more complex geometry or algebra, students need to not only be able to find the answers to problems, but to understand the various steps required to formulate the necessary answers.