A few years ago while on a shuttle to speak at a math convention, I started talking to a young man next to me. When he found out I was involved in math, he said he could solve story problems as long as someone told him what operation to use. The young man didn’t realize that the essence of solving story problems isn’t performing calculations, but rather deciding what procedures to use.

The purpose of learning math is solving problems; calculations are only a part of the equation.

**General Considerations**

Keep in mind that a problem is not a problem if the solution is obvious. If I am making my favorite recipe and have all the ingredients, I have no problem. But if I am missing an essential ingredient, I have a problem.

Unfortunately, traditional textbooks had a part in promoting a misconception regarding story problems. Worksheets consisted of a group of exercises, followed by a few story problems. Invariably, the problems were solved by the same operation as the one practiced in the exercise. So, the student didn’t bother to read the problem, but merely performed the practiced operation on the numbers in the story.

Later, when these students attempted to solve a diverse set of problems, they often try in vain to remember the lesson where they learned how to solve that particular problem. The details of those long forgotten lessons are missing.

Katie was a victim of that type of math learning. In her early twenties, she decided to go to college, but was scared of taking of math courses. She told me that there was so much to memorize. She didn’t realize math is not about memorization, but understanding. Solving problems is about thinking, not trying to recall a particular specific procedure. No one could possibly remember how to solve every type of story problem.

Some people are under the impression there is only one way to solve any problem. Actually, solving a problem in a different way is a check on correctness, an important consideration in real life. Or, another way to look at it: if humans didn’t find new ways to solve problems, we would still be living in the Stone Age.

### Preschooler Problem Solving

Problem solving starts when a preschooler assembles a jigsaw puzzle. Through such work the child does the following:

- masters frustrations,
- acquires perseverance,
- learns there is more then one way to do the puzzle, and
- experiences the joy of success.

The role of the parent or teacher is:

- to provide the appropriate puzzle,
- prevent distractions,
- offer bits of encouragement, and
- rejoice at its completion.

### Elementary Problem Solving

For simple addition and subtraction problems, use part/part/whole circles. A larger circle, the whole, is drawn above two smaller circles, the parts, with lines connecting each part to the whole.

Let’s use the part/part/whole circles to solve this missing addend problem:

**Lee received 3 goldfish as a gift. Now Lee has 5. How many did Lee have to start with?**

Is the 3 a part or a whole? A part.

Is the 5 a part or a whole? A whole.

What is the missing part? 2.

It doesn’t matter if this problem is considered addition or subtraction, young children can solve the problem.

Another tip to help younger children solve problems is to change the problem by using their name and their circumstances. In other words, personalize the problem.

It’s also helpful for children to make up their own problems. Of course, everyday events frequently lend themselves to great story problems.

**Some Tips**

One thing to avoid is teaching the child to look for key words. That is, do NOT teach that “altogether” or “sum” means add or “times” and “of” means multiply. Do you look for key words when solving real-life problems? I like to write problems with the wrong key words.

Children should not expect to know how to solve every problem. Problems are sometimes used to teach a math concept. A Japanese teacher will give the class a problem to work on in pairs. Then the teacher asks the students to explain their solution to the class. The solutions are presented with the simplest first and the most sophisticated last. Everyone learns some math this way. Mistakes are treated as a normal part of learning.

Sometimes textbooks use the format of a story problem to ask a rote question. One such example is: “Percy has 342 pencils. How many tens does he have?” This is nonsense. The textbook wanted 4 as an answer, but actually Percy has 34.2 groups of ten pencils. In this case, t\he student is not learning to make sense of mathematics, but to satisfy the textbook.

Sadly, achievement tests often put a simple question into a story format. For example, to check whether the student can read an analog clock, the test might ask, “Sophia’s violin lesson starts at the time shown on the clock. What time is that?” This is unfair to the child who is struggling to learn to read or to master English as a second language. Asking for the time on a simple clock will do.

**More Tips**

Generally, math problems need to be read several times. I told a group of home schooled middle-schoolers that even mathematicians read problems more than once. They were astonished.

Often a simple sketch can make a problem seem clearer. Some textbooks do this unnecessarily for the students. The student learns more by making their own sketch.

When a child gets really stuck, tell them to leave the problem and go do something else. Their brain will continue working in the background. When they return, they will probably have new insights.

Who has ever completed a puzzle by always finding the wanted piece on the first try? What baby has learned to walk without frustrations and falls?

Studying math, or anything else for that matter, will be frustrating at times.

Sarah Dooley says

Thanks so much! My daughter is on book A but I really appreciate these insights not to mention the curriculum itself! I recently learned of a new math program designed for older kids to help them to

conceptualize math. My daughter, through RightStart, is learning it from the very beginning. We both love it!

I have really been enjoying these posts. Thank you. Reading the reasons and logic behind the method has helped me keep perspective on my overall goals in teaching mathematics. I’ve fought against the time-aspect of teaching mathematics logically and thouroughly for years, and have wandered around in other curricula, only to come back to RightStart. I’m now convinced that if I’m going to have my kids learn this discipline, I’m only going to have them learn it the “RightStart” way. If it’s worth doing, then it’s worth doing it “right.” I would see confusing and frustrating questions in other curricula, and did not think it was giving my child the tools to truly *understand* number theory/sense, which I is vital for the enjoyment of mathematics. Thanks again.

My daughter was required to take STAR testing as a 2nd grader in our homeschool/charter program yesterday. It was the first time EVER that she had a total breakdown attempting to do math. There were questions, such as those you mention, requiring unnecessary reading to conduct a simple math problem. Her results on the test will not demonstrate at all the depth to which she understands the concepts thanks to RSMath. Thanks again. Love your blog!

I just want to say that this is the very concept that brought me to RSMath in the first place. I could cry happy tears, because this is EXACTLY what I want for my children. And myself! By teaching these problem solving skills to my kids in math, I am actually learning the same things, both in teaching them to problem solve in math, and be okay with mistakes, but also in other areas of life! This literally applies to all things life, and I am grateful that RSMath exists.

Excellent exposition, thanks. I deeply appreciate RightStart Math, and an one of those who will always be a little sad that we didn’t find it sooner so all our children could view numbers this way. Could would, I know. But I’m now an educational assistant in the public schools assisting students with different abilities; the part/whole circles was a grateful reminder I can use to help these fantastic kiddos to better tackle their challenges.

Thanks so much for the brush up.

Thank you so much for your positive comments, Nancy!

I so appreciate your expertise in teaching me how to teach my children. As a child, I dreaded math, did not understand how to solve problems and felt that I was too stupid to learn. I am now 60 years old. I have used Right Start Mathematics since 1995 when my oldest was 5 years old. You taught me how to teach my children. In the process, you TAUGHT ME! I’m now working alongside my youngest daughter doing Geometry. I bought my own workbook so I can learn alongside her and learn as well. Some day I hope to be able to do calculus….💜 Thank you!

Hi, Roberta.

What a great testimony!

I did not dread math in school. Instead, I loved it. However, just like you, while I taught RightStart Math to my four children, I was learning right alongside them. What I was taught to just memorize in school – I was beginning to understand by learning the RightStart way.

Thank you for sharing and keep on learning!

Rachel