FYI: Math problem solving tips for parents

[Arcadia]

Found this on a Singapore elementary school webpage and thought people here might be interested. The first section is for the students. Scroll down for the section on Parents helping children with math homework. Sorry it is a long post.

 

"Problem-Solving

Mathematical problem solving is central to mathematics learning. It involves the acquisition and application of mathematics concepts and skills in a wide range of situations, including non-routine, open-ended and real-world problems.

 

One of the aims of mathematics education is to develop the mathematical thinking and problem solving skills and apply these skills to formulate and solve problems.

 

Steps for problem-solving

George Polya, a mathematician, devised a general approach that one can take to solve a problem.

 

4 Steps for Problem-Solving

 

Step 1: UNDERSTAND the problem

Read the problem carefully to understand what is required in the problem.

Break up the problem into smaller sections and understand each section thoroughly before moving on to understand the next section.

Draw or write down the information given in the problem in a simpler form to help you understand better.

 

Step 2: PLAN what to do/Devise a plan

Choose a heuristic to use to solve the problem

 

Step 3: DO it/Carry out the plan

Use computational skills, geometrical skills and logical reasoning to carry out your plan to solve the problem.

 

Step 4: CHECK the solution/Review

Check the reasonableness of your solution

Improve on the method used

Seek alternative solutions

Extend the method to other problems

 

In short, the 4-steps for problem-solving is

Understand

Plan

Do

Check

 

For Parents: Helping your child with homework

 

Solving word problems

Go through the steps for problem solving together.

 

Step 1: UNDERSTAND the problem

Help your child understand the problem by getting him to read aloud one sentence at a time. Ask your child to explain his understanding of the sentence read in his own words. Once your child understands the sentence, move on to the next sentence.

 

Step 2: PLAN what to do

After understanding the problem, prompt your child to think of how to solve the problem. Give your child time to explore different methods to solving the problem. Encourage him to talk about what he is thinking. Challenge your child to find alternative ways to solving the problem.

 

Ask leading questions such as...

"What should you do next?"

"Will your method work?"

 

Step 3: DO it

Advise your child to write proper mathematical sentences to show the process of solving the problem. Develop the habit of showing all working clearly as method marks will be awarded in the examinations.

 

Your child should read the question again and answer according to what is asked for. Reading the question and writing the final answer statement is a checking mechanism to ensure the correct answer is given. (e.g. Giving the answer in the unit required)

 

Step 4: CHECK the solution

Ask your child to check his answer. Ask leading questions such as...

"How did you get this answer?"

"Is your answer reasonable?"

"How do you know that your answer is correct?"

"Did you use another method to check if your answer is correct?"

 

Going through the steps for problem solving, will help your child to become an independent thinker and problem solver.

 

Helping your child when his answer is wrong

If your child gets a wrong answer, ask your child to explain how he solved the problem. His explanation may help you discover if he needs help with computational skills such as addition, subtraction, multiplication and division or with the concepts involved in solving the problem.

 

Remember:

Don't provide the answers immediately. Giving the answers will not help your child. Learning mathematics is more than finding the correct answer. It is a process of solving problems and applying mathematical knowledge to new problems.

 

Common reasons why some children do not do well for long structured questions

 

Using a tedious method

The key to doing well in Mathematics is learning when to apply the methods learnt. There is a basic set of methods which children have learnt that can be used for all questions e.g. unitary method, listing, working backwards.

 

Although children know how to use various different problem-solving methods, they have difficulty knowing when to apply them effectively. Many children often choose the wrong (and often more difficult) methods instead of the ones mentioned above. If children choose the wrong or more time-consuming methods (e.g. Guess and Check), they may not have enough time to sufficiently complete and check their solutions during an examination.

 

Poor time management

Sometimes children spend too much time on questions that they cannot solve easily. If they encounter difficulty solving a question, they should skip that question and continue to solve the remaining questions. They can come back to attempt the question again when all the other questions have been completed.

 

Spending too much time on a question may result in less time or insufficient time for other questions that could be solved easily."