# Mathematics Problem Solving

Views:

Category: Education

Mathematics

## Presentation Transcript

### Mathematical Problem Solving:

Mathematical Problem Solving Namita S. Sahare

### The ultimate goal of any problem-solving program is to improve students' performance at solving problems correctly. The specific goals of problem-solving in Mathematics are to: :

The ultimate goal of any problem-solving program is to improve students' performance at solving problems correctly. The specific goals of problem-solving in Mathematics are to: 1 . Improve pupils' willingness to try problems and improve their perseverance when solving problems. 2. Improve pupils' self-concepts with respect to the abilities to solve problems. 3. Make pupils aware of the problem-solving strategies. 4. Make pupils aware of the value of approaching problems in a systematic manner. 5. Make pupils aware that many problems can be solved in more than one way. 6. Improve pupils' abilities to select appropriate solution strategies. 7. Improve pupils' abilities to implement solution strategies accurately. 8. Improve pupils' abilities to get more correct answers to problems.

### Mathematical Problem Solving:

Mathematical Problem Solving

### Mathematical Problem Solving:

Mathematical Problem Solving In Mathematics, Problem Solving is central to the curriculum at all levels . It involves both the understanding and application of Mathematical concepts, procedures and processes to a range of situations that include non-routine, open-ended and real-world problems. The curriculum also emphasizes the affective aspects of Mathematics learning, that is, the attitude towards learning Mathematics which includes appreciation, interest, confidence and perseverance as well as the Meta-cognitive dimension of being aware of and the ability to control one’s own thinking and learning in the problem solving process

### Learning Mathematics:

L earning Mathematics The curriculum also emphasizes the affective aspects of Mathematics learning, that is, the attitude towards learning Mathematics which includes : Appreciation, interest, confidence and perseverance Meta-cognitive dimension of being aware of and the ability to control one’s own thinking Learning in the problem solving process

### Learning in the problem solving process:

Learning in the problem solving process

### Learning in the problem solving process:

Learning in the problem solving process

### Self improvement. :

Self improvement. If one wishes to enhance their creatively and problem solving skills than exercising the brain is a must . One can choose to look at situation from another side of the coin but in the process, continue to develop problem solving skills through the many trainings (available in the internet. ) Look within us because change starts from us and it is inevitable.

### If we take time and think a little deeper, the problem really can be solved in a more peaceful and effective manner.:

If we take time and think a little deeper, the problem really can be solved in a more peaceful and effective manner. 1. Do not panic or react / over react emotionally 2. Do not make a rash decision 3. Step back and view the subject objectively 4. Identify the problem 5. Decide if this is your problem, or is it someone else’s 6. Think about what you can do about the problem 7.Re-frame the situation in a positive light 8. Try to find a positive emotion in the situation 9.Do not do anything to make the problem worse 10. Do not think in terms of right or wrong, rather, in terms of effective and ineffective 11. Make sure that whatever you decide to do is the most effective thing for you to do in the situation 12. Do what you can do to improve the situation to solve the problem. Do not make rash decision. In the book, “Blink” by Malcolm Glad well it states that we should trust our instinct especially on topics that we are expert in. An example, a tennis coach will be able to tell how the ball will travel and how much to hit the ball back. I tend to dis-regard the expert part.

### Identify the problem:

Identify the problem

### Word Problems:

Word Problems Word problems allow students the opportunity to apply their math skills in authentic situations. All too often, children are able to do numeric problems but when given the word problem, they often aren't sure what to do. Some of the best problems to do are those where the unknown in either at the beginning or at the middle of the problem. Try changing the position of the unknown to create critical thinkers with our math students/children. 1. Each case of oranges has 12 rows of 12 oranges. The school principal wants to buy enough oranges to make sure that every student gets an orange. There are 524 students in the school. How many cases does the principal have to buy? 2. The 421 students at NMV School are going on a trip to the zoo. There are two types of buses, one bus holds 72 students and the other bus hold 58 students. There are also 20 teachers going on the bus to supervise the students. What type of bus and how many buses are needed to make sure that all 421 students are able to go swimming?

### 'Pieces of the Puzzle Approach':

'Pieces of the Puzzle Approach' The 'Pieces of the Puzzle Approach' is a deductive reasoning activity in which each group member is given a piece of information to share with the rest of the group. The mathematical solution cannot be found without everyone's contribution. Thus, an important aspect of the approach is that the group assumes 'ownership' of the task yet individuals retain personal responsibility within the group. This style of activity was developed and used effectively by the EQUALS group in the U.S.A (1989).  Rules   You are responsible for your own work and behavior. You must be willing to help any group member who asks. You may only ask the teacher for help if everyone in the group has the same question These rules assist in avoiding some of the pitfalls of co-operative group work. Once the children have had experience with these rules, the situation of one person dominating by collecting all the pieces of information and taking control should not occur. Similarly, a group member should not opt out of the activity and sit back and let the rest of the group solve the problem. The ability of the children to successfully follow the rules will improve with each session, and will be influenced by teacher led discussions about the purpose of each rule.

### The structure of this approach is intended to provide positive opportunities for: :

The structure of this approach is intended to provide positive opportunities for:  Risk taking   - pupils are more likely ask questions of each other and put forward ideas in a small group situation, particularly with Rule 2 in place. Mathematical language development   - usually the clues for the tasks are communicated with words. The group needs to negotiate their interpretation of the mathematical vocabulary. They also must talk to each other, listen to others and explain their ideas clearly. Peer coaching  - pupils are able to clarify their understanding of mathematical concepts, correct misconceptions and test out ideas during the process of finding a collective solution to the problem. Teacher's role as a facilitator and observer   - the independence of the groups gives the teacher freedom to move around the class, observe language and strategies, interact with groups as required and assess their progress. Effective learning   - the tasks generally incorporate the manipulation of physical objects to produce a final product, which promotes the linking of verbal knowledge with visual imagery. Mixed ability class teaching  - the features listed above combine to make this approach particularly suited to use with mixed ability classes. Every child should be able to make a contribution to the problem solving process, learn from the activity and have received attention from the teacher when needed.

### References:

References http://www.bipolarcentral.com/articles http://www.mindtools.com/pages/main http://www.skillsyouneed.com