Doing Math with Your Child - Promoting Problem Solving; Suggestions for Parents
The best way to develop your children’s mathematical problem-solving abilities is to pose problems to your children and support them solve the problem using their own strategies. Here is an example of a dad posing a problem to his 7-year-old daughter in a manner that supports the development of problem solving:
Dad: I have a math problem that I have been thinking about. I am curious how you would solve the problem. Here is a sheet of paper and some pencils. You can write whatever you want on the paper that might help you solve the problem. I will say the problem as many times as you want to hear it. Let me know if you want me to write the problem on the paper. Here is the problem:
Angelina has 4 boxes of pennies with 6 pennies in each box. How many pennies does Angelina have?
Angelina: Is this one an add or subtract problem?
Dad: I want you to think about what is happening in the story, we can talk about if it is add or subtract after you solve it.
Angelina: I don’t know what to do.
Dad: That’s ok. Take a minute to think about it. It’s really important for all of to find ways to solve problems – especially problems that we don’t know how to solve right away. That happens to me all the time at work. Last week I went to fix someone’s sink and I just couldn’t figure out why it didn’t work. I didn’t want to leave without fixing the sink, so I had to think really hard about things I could do to fix it. After a while, I figured it out, and I was really happy that I was able to solve the problem. Let me tell you this math story again. As I say the word, try to picture what is happening in your mind or draw a picture on the paper about what is happening in the story.
Angelina has 4 boxes of pennies with 6 pennies in each box. How many pennies does Angelina have?
Angelina: I don’t really want to have pennies.
Dad: Ok, what do you want to have?
Angelina: I would like to have lots of kittens.
Dad: Ok, we can make the problem about kittens, but it will have to be pretend. Let’s try this:
Angelina has 4 baskets of kittens. There are 6 kittens in each basket. How many kittens does Angelina have?
Angelina starts draws 4 circles on her paper. Her Dad gets up and starts working on the dishes to support Angelina to continue working on her own. After 3 minutes, Angelina proudly calls out, “I got it Dad! I have 25 kittens!” and her Dad returns to the table.
Dad: Wow! I am so glad that you find a way to solve that problem. Could you tell me what you did?
Angelina shows her dad her paper:
Angelina: First, I made 4 circles. Those were the baskets. Then I started drawing kittens in the baskets, but that got a little hard and messy so I thought, I will just put little squares for the kittens.
Dad: That was a great idea to use squares. How did you figure out that you had 25 kittens?
Angelina: I counted them.
Dad: Could I hear and see how you counted?
Angelina points to the kittens (boxes) one-by-one and counts them. This time she has 24 kittens.
Angelina: That is odd, I got 24 this time. Which is right, 24 or 25?
Dad: Why don’t you count them again and see what you get?
Angelina counts and again gets 24.
Dad: So, which do you think it is 24 or 25?
Angelina: I want to count them again.
Dad: That’s a great idea.
Angelina: I got 24 again, so 24 kittens.
Dad: Thanks for sharing your math thinking with me. You did a great job figuring out how to solve that problem!
Angelina: Now, can I get those kittens?
Dad: No, remember I said that this was pretend.
The most important thing to remember when engaging your children in mathematical problem solving is to support them to solve problems using their own strategies. Since we all want to help our children learn math, it is often tempting to say, “The way you solved that problem was great, but now let me show you a faster way.” Unfortunately, this can give children the message that our strategies are better than theirs. They also might develop the belief that someone else has to show them how to solve problems. Believing that you are a person who understands mathematics and can generate ways to solve problems is essential to success in the mathematics one encounters throughout life. These beliefs are crucial outcomes of our children’s elementary school mathematics education.
The problem about 4 groups of 6 worked well for Angelina because it wasn’t a problem that she could immediately solve and it also wasn’t a problem that was so hard that she couldn’t solve it on her own with some work. Her dad supported her to solve the problem by changing the pennies to kittens and suggesting that she draw what was happening on the paper, but he didn’t tell her how to solve the problem.
It’s not easy to choose problems for your child. With some practice you will get better at it. Here are some problems that might work for your elementary school children. If you choose a problem is overwhelming your child, make the numbers smaller or move to an easier problem.
Leon had 8 cookies. He ate 3 of them, how many cookies does Leon have now? (This problem may be routine for some children – especially older elementary school children. For older children you could try 15 cookies, he eats 7; 35 cookies, he eats 12 or 50 cookies, he eats 21.)
Ms. Jones has 4 children. Each child has 2 stickers. How many stickers do they have altogether? (For older children try 6, 9, 26, 149, or 247 stickers for each child.)
Tyrone has 18 Yu-Gi-Oh! Cards. He wants to have 20 Yu-Gi-Oh! Cards. How many cards does he need to get to have 20 all together? (This problem will work best for children who are 7 or older. For an added challenge, try using these numbers, has 58 cards and wants 61, has 98 cards and wants 101, has 598 cards and wants 601, has 998 cards and wants 1001, has 3998 cards and wants 4002.)
Linda has 4 boxes of pencils with 3 pencils in each box. How many more pencils does she need to get to have 20 pencils all together? (This problem will work best for children who are 7 or older. For an additional challenge try 6 boxes with 12 pencils in each box and Linda wants a total of 100 pencils.)
More problems are available on the Mentor Teacher area of the site under Resources. Look under the teachers’ names for lists of problems.
A personal note from the author:
If you are reading this blog during the COVID-19 crisis, I want to encourage you to be gentle on yourself and your children when it comes to academics. I feel it is disrespectful to the teaching profession and unsympathetic to the realities of family life to expect parents to fulfill the role of a teacher at any time, but especially under times of stress. Parents who are working outside the home to provide vital services that our society needs should be especially gentle on themselves and their families. My children are now grown, but if they were in elementary school and I was able to be home with them, my goal would be to have them solve 2 or 3 problems a week. The number of minutes I would set aside for each problem would be roughly double their age - for example about 10 minutes for a 5-year-old, 20 minutes for a 10-year-old. If you aren’t able to set aside this time right now for any reason, please don’t worry about it.
This blog post was supported by the U.S. Department of Education, through grant award number U423A180115 to Florida State University. The opinions expressed are those of the authors and do not represent views of the U.S. Department of Education.
