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Math Reflective Paper

Summary of major mathematical concepts Data analysis is a fundamental concept that we covered in the first week through the course. This involves processes used to inspect, clean and model data to derive useful information. In this context, data refers to raw information obtained from the field or a real experiment. Real data is more complex than data used for class practice. Complexities of real data required us to apply data analysis software such as SPSS and Stata. Moreover, data collection is a costly procedure and, therefore, statisticians require the knowledge of probability. The concept of probability explains the outcomes of random events and likelihood of certain occurrences. These concepts are useful in determining samples in a field study or a survey. The concepts of probability are established on the existence of a sample space consisting of possible outcomes and ratios that represent each possibility. For example a coin tossing experiment has two outcomes and a sample space sample S = {H, T}, with P (H) =P (T) = ?. In the third, fourth and fifth week we covered the concepts of geometry. Geometry provides essential mathematical concepts that are used to describe the size, shape and relative position of an object. Basic concepts of geometry covers the Euclidian geometry which assumes that all the aspects used to describe an object can be expressed in a three dimensional space. Different theories relating to the three-dimensional space can be used to predict useful physical phenomenon such as speed, velocity distance acceleration and angular velocity. This extension falls under applications of geometry, which we covered in fifth and sixth weeks. Application of geometry is based on fundamental elements of geometry, which include length, curvature, angles, gradient (rate of change) and mass. This concept provides the basics for measurements. Measurement involves quantifying of an object or a phenomenon through direct measurements or/and estimation. Determination of errors is a fundamental aspect of measurement. Theories of estimation are critical to the concept of measurement and, hence the need for the notion of error (Selinger, 2009). Course concepts The courses capture the three most fundamental elements of mathematics that are critical to mathematics teachers. Firstly, mathematics involves figures and numbers. This indicates that a sufficient mathematic teacher should have concrete information on statistical data analysis. The course on data analysis has also enabled me to gain an essential skill that can also be utilized in an alternative field. . Secondly, a professional mathematical teacher should have the ability to explain certain occurrences in nature. In addition, the beauty of teaching mathematics lies in ability to manipulate figures and equations to realize an analytical solution to a problem. Analytical solutions are the foundations of mathematics and they make mathematics a reliable language for explaining physical concepts. Geometry concepts covered in the course enabled me to acquire useful an analytical skills, which will be essential in my future career. Mathematical ideas and philosophy Initially I considered a teacher as a primary source of information. I considered this concept as the basic philosophy of teaching. However, concepts from the course have enabled me to realize that a teacher is expected to provide guidance and access to information for the students. Thus, teachers should equip
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