Mathematical Concepts - Essay Example

This paper seeks to discuss mathematical concepts of a course. The paper will offer a summary of the concepts learnt in the course, relevance of the concepts to the characteristics of a mathematics teacher as well as analysis of the influence of the learnt concepts on my personal ideas and philosophy of teaching. Summary of the major mathematical concepts One of the mathematical concepts discussed in the course is problem solving. This concept is described as an approach towards finding a solution to a problem.

The concept of problem solving involves a number of steps that starts from understanding the problem at hand, developing a strategy, exploring any applicable pattern and finally using logic to ascertain the nature of the solution. Strategy to problem solving, according to Billstein, Libeskind and Lott, involves a series of steps that include “understanding the problem, devising a plan, carrying out the plan, and looking back” over the solution (Billstein, Libeskind and Lott, 2010, p. 4). In order to understand a problem, it is necessary to be able to acculturate and paraphrase the problem before identifying the next course of action.

The necessary information in the problem that can be used in its solution is then extracted and the unknown that is to be solved identified (Billstein, Libeskind and Lott, 2010) . As an approach to describing numbers through notations, numeration systems include Hindu Arabic system and Tally system among others. The concept of sets on the other hand involves definition of sets and set operations such as unions and intersections. The course also covers concepts of operation of whole numbers that includes addition, subtraction, multiplication, and division with stepwise procedures for carrying out the operations.

The course also described the concept of algebra that covers variables, equations, and functions. Variables refer symbols that can take more than one values. In numerical concepts, a variable can represent more that one number or quantities and is represented using a letter. Algebraic equations are on the other hand used to represent values, either algebraic or a combination of both algebraic and numerical, which are assumed to have similar magnitudes. Equations can then be used to solve for exact values of unknowns in given problems.

Relationship between variables is further explored through functions (Billstein, Libeskind and Lott, 2010). Like operations of whole numbers, the course covers basic rules in operation of decimal numbers and fractions. It explores algorithms of basic operations, addition, subtraction, multiplication and division, with respect to decimals and fractions. The final set of mathematical concepts, as covered by the course includes proportions, ratios, and percentages. The basis of ratios, percentages, and proportions as expression of relationship between variables, and understanding of their concepts is important in solving real life problems such as interest and interest rates among other practical relationships (Billstein, Libeskind and Lott, 2010) Relevance of the learnt