December Edition—The World Needs Good Problem Solvers!
There are three parts to learning mathematics: skills, concepts, and problem solving. It is fairly easy to understand why we teach the first two. Skills are essentially the tools of mathematics, such as learning how to add two numbers together to get a correct answer. Concepts are the ideas in mathematics (such as the concept of a triangle) which we need to understand before we can do mathematics. But problem solving is harder to explain. If you think of skills and concepts as what we need to know in mathematics, then problem-solving is the ability to apply mathematics we know in different situations. Problem solving is important because it requires us to combine skills and concepts in order to deal with specific mathematical situations — we call these problems. If you know your mathematics skills and concepts well, but cannot put them together in a particular situation, then you cannot do mathematics well. Skills, concepts, and problem solving used together in real situations lead to mathematical literacy.
January Edition—Helping Your Child Solve Problems
One painless way to provide help to a child solving a problem is to ask simple questions. Below is a list of questions that you can ask, one-by-one, to help your children gradually make sense of a new problem, especially ones they don’t immediately know how to solve. A well-timed question can open up your child’s thinking about the problem at hand and often help a student remember what he/she learned in class.
1. Help your child understand the problem before he/she begins to solve it. Ask:
✔ Can you state the problem in your own words?
✔ What are you trying to find or do?
✔ What are the unknowns?
✔ What information can you obtain from the problem?
✔ What information, if any, is missing or not needed?
2. Help your child devise a plan or strategy for solving a problem by choosing a problem solving strategy.
✔ Guess and test
✔ Look for a pattern
✔ Make a drawing or model
✔ Act it out
✔ Work backwards
✔ Simplify the problem
✔ Eliminate possibilities
✔ Make a systematic list
✔ Write an equation
3. Once your student has chosen, help your child carry out his/her strategy ask:
✔ Why did you pick (that) problem-solving strategy?
✔ Is there another related problem like this one that you have solved before? What strategy did you use for that problem?
✔ How will you use this strategy? What will you do first? Next?
✔ Did you check each step as you worked? Don’t forget why you are doing each step!
✔ Is there another strategy for finding the solution to the problem? Do you think it is better?
✔ Can you explain to me how you are sure this strategy worked?
4. Help your child reflect a moment on his/her answer to a problem. Ask:
✔ Did you check your computations for correctness? Double check!
✔ Have you kept an accurate and neat record of your work? Remember, your teacher will have to figure out your work.
✔ Did you reread the original problem to make sure your answer makes sense, is reasonable, and actually answers the
Barbara J. Hale, M.Ed., NBCT
Kingsbury Elementary School
825 Kingsbury Road
Sumter, SC 29154