The student will arrive at the correct solution by employing a couple of other ideas instead of just using mathematical calculations. Reasoning and proof

Thinking on their feet students will learn how to be analytical of every situation they are encountered with. They will not only apply this analytical thinking in mathematics but will also apply it to other situations that they encounter. For the problem given in the, the first thing a student will need to analyses is how many legs chickens have and how many legs pigs have. Once they have this they can be able to determine how many pigs there are since the number of chickens has already been stated.

Communication

Holding discussions and communicating how they arrive at their solutions allows student to aqcuire problem solving skills instead of just arriving at the correct answer. The discussions challenge a student to defend how they got the solution and the methods they used. This encourages a student to be geared towards problem solving rather than merely getting the correct answer.

Connections

Having practical examples instills deeper knowledge in the students. Performing mathematical calculations while incorporating other subjects and ideas apart from mathematical ideas, will teach the students how to better understand how to solve problems. Working on real life situations and using mathematics allows students to use their knowledge and get a solution to the problem.

Representation

Using symbols allows students to understand better how they can solve a problem. Representation of the actual idea using symbols allows the student to understand easily and are able to solve problems. Graphical representations...

Examples are given to illustrate how mathematical problems can be solved using the different processes, and how to motivate students and encourage them. The process standards show how different teaching methods are used to teach students mathematics. The standards also indicate the need for using real-life scenarios and graphical representations. Encouraging students to participate in challenging discussions will also benefit them as they learn how to justify their answers and methods used to reach the answer.
Learning how mathematics can be applied in real-life situations would benefit the mathematics teacher greatly. Learning how to connect the mathematics taught in different grades to ensure connections are maintained when the students move between the different grades. The readings will allow a teacher to understand better the different needs of students in the different grades. Mathematic teachers can use the reading to increase their mathematics teaching skills, and encourage their students.

Teachers can use the information to prepare their students for the interesting world of mathematics. Showing students how interesting mathematics can be would encourage them to use mathematics in their everyday life, for analyzing situations, making connections, and improving their communication skills.

References

Mathematics, N.C. o. T. o. (2000). Principles and standards for school mathematics. 1906 Association Drive, Reston, VA 20191-1502: National Council of Teachers of Mathematics.