Mathematical process standards: problem solving, reasoning, communication, and connections

¶ … Standards

Five process standards

Describe the mathematical process standards

Problem solving

Engaging in a task without knowing the solution method in advance is what is referred to as problem solving. Drawing from their knowledge, the students are better equipped to find a solution for the problem, and while doing this the students will develop a new understanding of mathematics. The students are also able to solve any other problems they encounter both in mathematics and other life situations using their problem solving skills for example, "I have pennies, dimes, and nickels in my pocket. If I take three coins out of my pocket, how much money could I have taken?" Mathematics, 2000()

Problem solving involves the application and adaptation of various strategies to assist the student in solving problems.

Reasoning and proof

To gain better understanding on a wide range of phenomena, a student will need to have a strong mathematical reasoning and proof. Thinking and reasoning analytically allows a person to identify structures, patterns, and regularities in symbolic objects and real world situations. To better understand mathematics, a student needs to be able to reason. A good example is "Write down your age. Add 5. Multiply the number you just got by 2. Add 10 to this number. Multiply this number by 5. Tell me the result. I can tell you your age." Mathematics, 2000()

Students are able to better evaluate and develop their own mathematical arguments by employing reasoning and proof.

Communication

For the teaching of mathematics, communication is an integral part. It provides an avenue for the students and lecturers to share ideas, and make clarification where necessary. Challenging students to communicate their mathematical results and reasoning will help them learn to justify themselves in front of others, which leads to better mathematical understanding. Working on mathematical problems with others and having discussions will allow students to gain more perspectives when solving mathematical problems e.g. "There are some rabbits and some hutches. If one rabbit is put in each hutch, one rabbit will be left without a place. If two rabbits are put in each hutch, one hutch will remain empty. How many rabbits and how many hutches are there?" Mathematics, 2000()

Connections

A students understanding is deepened when they are able to connect mathematical ideas. By continuously developing and teaching students' new mathematics that are connected to what the students had learnt previously, the students are able to make connections. Learning mathematics by working on problems that arise from outside mathematics should be incorporated into the curriculum. These connections will give the students an opportunity to connect what they learn in relation to other subjects or disciplines. Mathematics is connected to many other subjects, and it is very important that students get to experience mathematics in context.

Problem solving

Using problem solving to solve a mathematical problem, the student does not know which method they will use when they start tackling the problem to reach the solution. 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 are easier to remember, and one can use them when they need to and in any situation.

Plan

The reading has provided vital information regarding how mathematics can be taught in the different grades. 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.