Teaching Values Through A Problem Solving Approach to Mathematics | Math Goodies

 

problem solving approach to mathematics

Jul 15,  · There are many paths to strong problem-solving skills. Mathematics is the shortest. Problem solving is crucial in mathematics education because it transcends mathematics. By developing problem-solving skills, we learn not only how to tackle math problems, but also how to logically work our way through any problems we may face. The purpose of this article is to suggest one of the many ways in which values education can be incorporated into existing mathematics curricula and approaches to teaching mathematics. In particular, it will focus on ways in which values education can be enhanced by utilising a problem-solving approach to teaching mathematics. The 5 Steps of Problem SolvingStep #1: Stop and Think Before Doing kaapstadvsa.cf #2: English-to-Equation Translation. The second step in solving word problems is turning Step #3: Solve for Whatever You’re Interested kaapstadvsa.cf #4: Make Sure You Understand the kaapstadvsa.cf #5: Use Your Result to Solve Other Problems.


Mathematics Through Problem Solving | Math Goodies


For many reasons, the state of society has reached a stage where it is more critical than ever to educate people in the traditional values of their culture. In recent years there has been considerable discussion about whether it is the responsibility of schools to impart values education. There is growing pressure for all teachers to become teachers of values, through modelling, discussing and critiquing values-related issues. There are many opportunities to teach the principles of values education through existing subjects and topics.

The purpose of this article is to suggest one of the many ways in which values education can be incorporated into existing mathematics curricula and approaches to teaching mathematics.

In particular, it will focus on ways in which values education can be enhanced by utilising a problem-solving approach to teaching mathematics. The articles include quotations, printed in italics, from the Sathya Sai Education in Human Values program, which originated in India and is now active in more than 40 problem solving approach to mathematics around the world. Teaching mathematics encompasses skills and functions which are a part of everyday life.

Presenting a problem and developing the skills needed to solve that problem is more motivational than teaching the skills without a context. It allows the students to see a reason for learning the mathematics, and hence to become more deeply involved in learning it. Experience with problem solving can develop curiosity, confidence and open-mindedness. This section will describe the types of problem solving which can be used to enhance the values described above, and will give some suggestions of how it can be used in the mathematics program.

Problems which require the direct use of a mathematics rule or concept. They increase in difficulty as they require more steps:. Sometimes it is important to give problems which contain too much information, problem solving approach to mathematics the pupils need to select what is appropriate and relevant:.

Last week I travelled on a train for a distance of kilometres. How far had I travelled? These problems are often called Fermi problems, named after the mathematician who made them popular. When people first see a Fermi problem they immediately think they need more information to solve it.

The solution of these problems relies totally on knowledge and experience which the students already have. Lam wanted to teach her class of ten-year-olds about problem solving approach to mathematics value of money, and to appreciate what their parents were doing for them:.

In solving the problems, I think that students can have a better understanding of the concept of money, not simply as a tool of buying and selling things. Peter failed to persuade his parents to buy expensive sportshoes as his problem solving approach to mathematics present and thought that his parents did not treat him well. The parents also felt upset as they regarded this son as an inconsiderate child.

They thought that he should understand that the economy is not so good. They asked Peter if he knew about how much money was being spent on him throughout the whole year. Unfortunately, Peter could not produce the answer immediately. So I asked the class if they could help Peter. I asked them to find answers to the following problems:. Later, the groups were asked to present their data and the way of finding out the answer.

Finally, I concluded that this is an open question as each person may have different expenditure along with some common human basic needs such as food, clothes and travelling fares, problem solving approach to mathematics. Anyway, the answer should be regarded as a large sum of money and thus give them a better understanding of their parents' burden.

Sometimes pupils can be asked to make up their own problems, which can help to enhance their understanding. Non-routine problems can be used to encourage logical thinking, reinforce or extend pupils' understanding of concepts, and to develop problem-solving strategies which can be applied to other situations.

The following is an example of a non-routine problem:. Bohan, Irby and Vogel suggest a seven-step model for doing research in the classroom, problem solving approach to mathematics, to enable students to become "producers of knowledge rather than merely consumers" p.

Step 1: What are some questions you would like answered, problem solving approach to mathematics. The students brainstorm to think of things they would like to know, questions they would like to answer, or problems that they have observed in the school or community.

Establish a rule that no one is to judge the thoughts of another. If someone repeats an idea already on the chalkboard, write it up again, problem solving approach to mathematics.

Never say, "We already said that," as this type of response stifles creative thinking. Step 2: Choose a problem or a research question. The problem solving approach to mathematics were concerned with the amount of garbage produced in the school cafeteria and its impact on the environment. The research question was, "What part of the garbage in our school cafeteria is recyclable?

Step 3: Predict what the outcome will be, problem solving approach to mathematics. Step 4: Develop a plan to test your hypothesis. Step 6: Analyse the data: did the test support our hypothesis? What mathematical tools will be needed to analyse the data: recognising the most suitable type of graph; mean; mode; median? What did we learn? Will our findings contribute to our school, our community, or our world? How can we share our findings with others? If we repeated this experiment at another time, or in another school, could we expect the same results?

Why or why not? Who might be interested in our results? Their findings may contribute to the knowledge base of the class, the school, the community, or society as a whole. Their findings may affect their school or their world in a very positive way " Bohan et al.

Mathematical investigations can fit into any of the above three categories. These are problems, or questions, which often start in response to the pupils' questions, or questions posed by the teacher such as, "Could we have done the same thing with 3 other numbers?

At the beginning of an problem solving approach to mathematics, the pupils do not know if there will be a suitable answer, or more than one answer. Furthermore, the teacher either does not know the outcome, or pretends not to know. The use of this approach makes it difficult for pupils to just carry out routine tasks without thinking about what they are doing. Bird believes that investigational problem solving can be enhanced if students are encouraged to ask their own questions.

She suggested that the teacher can introduce a "starter" problem solving approach to mathematics the whole class, ask the students to work at it for a short time, ask them to jot down any questions which occurred to them while doing it, and pool ideas. Initially it will be necessary for the teacher to provide some examples of "pooled" questions, for example:. The pupils can be invited to look at each other's work and, especially if they have different answers, to discuss "who is right".

While these are all important mathematics skills, they are also important life skills and help to expose pupils to a values education that is essential to their holistic development. References and Useful Reading. Bird, M. Generating Mathematical Activity in the Classroom. West Sussex, U.

ISBN 0 0 6. Bohan, H. The ideas presented in this article suggest some ways in which teachers can explore the integration of values education into the existing mathematics program without needing to add anything extra. Further ideas have been presented in a book written by the author Taplin, As well as giving teaching ideas, problem solving approach to mathematics, the book summarises recent research and suggests some questions for action research or discussion that teachers can use in their own classrooms.

By signing up, you agree to receive useful information and to our privacy policy. Shop Math Games. Skip to main content. Search form Search. These quotations are concerned with the following values: equipping students to meet the challenges of life developing general knowledge and common sense learning how to be discriminating in use of knowledge, that is to know what knowledge is appropriate to use for what purposes integrating what is learned with the whole being arousing attention and interest in the field of knowledge so it will be mastered in a worthy way Why Can Values be Enhanced by Teaching Mathematics via Problem Solving?

Examples: reading a map to find directions understanding weather reports understanding economic indicators understanding loan repayments calculating whether the cheapest item is the best buy Presenting a problem and developing the skills needed to solve that problem is more motivational than teaching the skills without a context.

Examples: The problem that we worked on today had us make a hypothesis. Through testing, our hypothesis was proven incorrect.

The problem solving approach allowed our group to find this out for ourselves, which made the "bitter pill" of our mistake easier to follow. I found this activity to be quite a challenge. I felt intimidated because I could not see an immediate solution,and wanted to give up. I was gripped by a feeling of panic. I had to read the question many times before I understood what I had to find. I really had to "dig down" into the depths of my memory to recall the knowledge I needed to solve the problem.

Seeing patterns evelop before my own eyes was a powerful experience: it had a stimulating effect. I felt that I had to explore further in a quest for an answer, problem solving approach to mathematics, and for more knowledge.

Each of these problem types will be described in more detail below. They increase in difficulty as they require more steps: Examples: 7 children went mushrooming and agreed to share. They picked mushrooms.

How will they find out how problem solving approach to mathematics they will get each? How much time does he spend helping her in 1 week?

Recently it was discovered that a clean engine uses less fuel. An aeroplane used litres of fuel, problem solving approach to mathematics. After it was cleaned it was found to use litres for the same trip.

 

Problem-Solving - TeacherVision

 

problem solving approach to mathematics

 

COUPON: Rent A Problem Solving Approach to Mathematics for Elementary School Teachers 12th edition () and save up to 80% on textbook rentals and 90% on used textbooks. Get FREE 7-day instant eTextbook access! The Role of Problem Solving in Teaching Mathematics as a Process. Problem solving is an important component of mathematics education because it is the single vehicle which seems to be able to achieve at school level all three of the values of mathematics listed at . Texts: A Problem Solving Approach to Mathematics for Elementary School Teachers, 10th Edition, by Billstein, Libeskind, and Lott Supplies: calculator, several paper folders, 3-ring binder with 8 dividers/tabs, several plastic sleeves/pockets for a binder, graph paper, a GOOD compass, protractor, ruler.