Chapter 2
Why Teach Problem Solving Skills
We live in a world that utilizes mathematics. Think about it. When we determine which purchase to make, how much carpeting we need in the living room, choose car insurance or a health plan, we need to use our math skills. We can locate a vast assortment of mathematical information whenever we use the Internet, CD-ROMs, and other media. In the workplace, the level of mathematical thinking and problem solving has increased dramatically.
Those who understand and can implement mathematical skills correctly will have opportunities that others do not. The level of a person’s mathematical competence opens doors to productive futures. A lack of mathematical competence closes those same doors.
From what I have read and from my own experiences of teaching mathematics, I feel we need to teach our children how to solve word problems for several reasons. Read the list below and think about what each one means.
Children need to be able to solve word problems for the following reasons:
• To see why they need to learn new math skills
• To apply recently taught math skills independently
• To improve their willingness to try problems and gain determination in looking for solutions
• To independently apply math skills in solving real world problems that directly affect them
• To solve these problems all through adult life
• To pass entrance exams for the military, civil service, college, or vocational schools
• To be able to transfer this problem solving skill in other facets of life
• To reduce the chance of math anxiety
Seeing why they need to learn new math skills
How often have you heard your students or your own children ask, “Why do we need to learn this?” It is a valid question. Unfortunately, it often goes unanswered. When that happens, students tend to shut down or lose interest in the learning.
When you introduce a new math skill or a series of related math skills, you should show the students why they need to learn those skills by showing them a word problem or the big picture. Children tend to learn better when they realize why they need the skill or skills. They need a goal to work towards and the reason why skills and concepts are needed. That is the main reason why teachers are now required in so many school districts to include objectives in their daily schedules on the wall or chalkboard.
The math problem or case study could be placed on chart paper or somewhere on the chalkboard. It should be kept there as you teach the various related math skills. Then, when you finish teaching the series of skills, you have your class solve the problem.
Basically, you are giving the children the big picture or goal. Seeing the big picture motivates children.
Applying skills that were just taught
The question you need to ask yourself as you teach children math skills,
“Can they use the skills I just taught them?”
The best way to find out is to give children word problems after each set of new skills. You can diagnose any problems during such problem solving activities while giving them experiences with solving problems.
• Do they understand the math vocabulary?
• Can they perform the math skill?
• Can they orally explain how they solve the problem?
• Are they able to write about their solution?
Do your students understand and use the correct math terminology?
One of the reasons many children have difficulty with solving word problems is that they do not understand and use the correct math terminology. As soon as children begin to read, they begin to work on math. That is when you help them learn math vocabulary whether you are the parent or the teacher. More information on developing vocabulary for mathematics is further developed in Chapter 3.
If the math skill itself is still presenting some difficulty, then reteach that skill or review the skill periodically.
• You might need to use a different method of teaching the skill.
• Remember many children need hands-on activities for learning math concepts, even older students.
• You also need to keep in mind that you might have a class where some children might catch on to the new concepts more quickly than some of the others.
• Sometimes you can use the students who are doing well with the new concept as helpers and assign them to groups who need extra help.
• Be aware of each student’s learning style, strengths, and skills they already have. Use that knowledge to differentiate some lessons.
• Assign differentiated homework so the students who understood the concepts can do challenging projects while the other students can work on review activities.
Oral explanation on how students solve the problems
How often should you have the students explain orally?
Explaining orally how to solve a problem could be done when a new skill has been taught. Perhaps the students could explain aloud after having had some practice with a particular word problem skill.
Or you could have the class divided into small groups and assign each group a problem for the oral explanation time. This way, they get to hear other groups’ explanation for the solutions. This gives your students the opportunity to see their classmates’ viewpoints on why they solved the problem a certain way. Working together on oral explanations can help the students learn to understand and evaluate their classmates’ thinking.
You might even permit the students to choose which problem they want to explain aloud rather than assign them a certain problem out of the ones they are doing. Children like having choices.
Another time for explaining aloud would be when a particular student is having some difficulty with the work. Often, having the student explain aloud what they did to solve the problem can help you locate the difficulty. This student could orally explain to a classmate who has solved the problem successfully. The other classmate could share what he has done. The other student could orally explain to the teacher so the teacher can diagnose and pinpoint the area needing extra work or correction.
But don’t have your students explain aloud every single word problem you assign them. Besides being time consuming, this would cause overload and lost of interest in math.
Why is the oral explanation important, particularly with the younger children?
Oral explanation can give you an idea on how well the concepts being used are understood. Quite often children can solve an easy word problem and have no idea how they did it. They are simply mirroring what they have seen others do, not comprehending what is going on. Oral explanation from a child offers the teacher or parent the opportunity to diagnose any difficulty the child might be experiencing with problem solving.
When children can start explaining the whys and hows, then perhaps understanding is really setting in.
Also, when children share their solutions and reasons for choosing the strategy, learning is strengthened. They also develop a stronger mathematics vocabulary which is key for understanding the lessons.
Oral explanation is also important in leading children into writing an explanation.
Model oral explanations each time you
• Teach a different math skill
• Teach a different strategy for solving word problems
Whenever you teach a new math skill, you could be introducing new math terminology. When you introduce a different math strategy for solving word problems, you could be introducing new math vocabulary. For example, guess and test strategy involves different vocabulary than using the strategy, logic.
If explaining orally about solving the problem is presenting the class with some difficulty, then practice math talk. As you and your children are working on math skills, use the math vocabulary associated with the skills being taught. Let math talk be as natural as kicking the ball.
Modeling how to orally explain the solution to the problem
Mrs. Harris was teaching her son,