Problem-Solving Reflection and Analysis
Problem-solving is a skill that traverses all aspects of life, from mathematical exercises in a classroom to social and career issues. In order to succeed in life, individuals need to posses the skills necessary to engage in effective problem-solving. Specifically, problem-solving in mathematics begins at an early age, where elementary school students need to figure out how to solve for a single variable using addition and subtraction. At the high school level students need to learn how to solve for multi-variable equations using a system of equations. The problem-solving skills developed throughout one's educational journey will help them to become successful individuals in the work force.
As a future mathematics educator, I use a hierarchy of problem-solving skills in order to find the solution to any mathematical problem. For example, given a word problem, I first underline and highlight the information that will contribute to the development of the solution. Using this information, I isolate the formulas and strategies necessary to solve the problem and input the given values to find the solution. Every situation, whether a problem on a mathematics exam or a financial issue your boss asks you to ameliorate, requires preparation and planning. Without these skills success may be stifled. As a future educator, therefore, my job is to provide students with the problem-solving skills necessary to help them reach their highest potential.
My favorite math problem discussed below requires students to use prior knowledge from a variety of mathematical concepts in order to arrive at the correct solution. First, they must recall the angles and sides of special right triangles and the properties of different geometric figures. From there, they remember that equivalent values can be substituted into equations in order to find the length of FC, the missing side. This is one of my favorite math problems because it is multi-dimensional and requires students to following the problem-solving process discussed above.
Problem-solving is a skill that traverses all aspects of life, from mathematical exercises in a classroom to social and career issues. In order to succeed in life, individuals need to posses the skills necessary to engage in effective problem-solving. Specifically, problem-solving in mathematics begins at an early age, where elementary school students need to figure out how to solve for a single variable using addition and subtraction. At the high school level students need to learn how to solve for multi-variable equations using a system of equations. The problem-solving skills developed throughout one's educational journey will help them to become successful individuals in the work force.
As a future mathematics educator, I use a hierarchy of problem-solving skills in order to find the solution to any mathematical problem. For example, given a word problem, I first underline and highlight the information that will contribute to the development of the solution. Using this information, I isolate the formulas and strategies necessary to solve the problem and input the given values to find the solution. Every situation, whether a problem on a mathematics exam or a financial issue your boss asks you to ameliorate, requires preparation and planning. Without these skills success may be stifled. As a future educator, therefore, my job is to provide students with the problem-solving skills necessary to help them reach their highest potential.
My favorite math problem discussed below requires students to use prior knowledge from a variety of mathematical concepts in order to arrive at the correct solution. First, they must recall the angles and sides of special right triangles and the properties of different geometric figures. From there, they remember that equivalent values can be substituted into equations in order to find the length of FC, the missing side. This is one of my favorite math problems because it is multi-dimensional and requires students to following the problem-solving process discussed above.
ABCD is a unit square, ABE is an equilateral triangle, and F is the point of intersection of AC and BE. Find the measure of FC.