**The father of 3-year-old Luke** shared a surprising story with Luke's preschool teacher. It seems that Luke watched his father unsuccessfully bat at a balloon. The balloon hugged the ceiling high over the lower step of a staircase. Luke finally suggested, "Dad, hit it over there (pointing to the landing overlooking the staircase) so you can get it when you go up the stairs."

In everyday life and in math, young children can be amazingly good problem solvers. If we recognize the strategies they use to solve problems, we can help them become even better thinkers.

**Using Problem-Solving Techniques**

Luke used "means-end" thinking. This strategy involves figuring out where you are and where you have to be and trying to "close the gap." Many children first use means-end thinking between 6 and 9 months, when they learn to pull on a blanket to bring a toy into their reach. Preschoolers asked to get 5 forks might get 2, count them, check whether they have 5, and if not, get another one, and repeat this process until they reach their goal. As they become more confident, encouraging them to "keep counting until you have 5" might encourage them to achieve the next level of math skill.

**Modeling Strategies**

Preschoolers and kindergartners can solve a wide variety of math problems if adults allow and encourage them to use another effective strategy, modeling. For example, a teacher might say, "Do you want more blocks? If you have 3 blocks, and I give you 2 more, how many will you have?" The child might model this situation by counting out 3 blocks, then 2 more blocks, and then counting all 5. What if the question were, "You have 5 blocks ... if you put 3 on the shelf, how many will you still have?" The child might put up 5 fingers on one hand, push 3 fingers down, and then count the 2 remaining fingers. Using objects to directly model the situation, this child has solved a problem often not introduced formally until first grade.

**Putting Strategies to Work**

Encouraging children to become powerful problem solvers is not difficult. The following four strategies are helpful:

**Help children see math problems around them**, in numbers, of course, but also in building, putting together puzzles, giving and following directions, measuring, and making patterns. Engage them in card and board games that involve spinners and dice, which introduce many mathematical problems.**Make sure that you have plenty of manipulatives**, such as small colored blocks or plastic shapes available for modeling different mathematical situations. As we saw, fingers are also great "manipulatives." Also, children older than 5 years should be encouraged to draw the problem.**Whether they use fingers, drawings, or mental strategies**, ask children how they solved the problem. Use questions such as, "How did you know?" "Can you show me that?" and "Why?"**Offer help as needed.**A good strategy, to keep from doing too much and limiting the child's opportunity to solve the problem, is to use prompts, hints, and giveaways. If a child struggles, start by offering a general prompt such as "What do you think you could do?" It's surprising how simple prompts such as this can motivate children. If a couple of prompts are ineffective, try a hint, such as, "What did you do the last time you figured out how many spoons we needed at snack time?" or "Do you think you could count the other number on your other hand?" If needed, move to "giveaways"-talk the problem through with the child, demonstrating a strategy as you and the child solve it together.

Recognizing the surprising problem-solving abilities of young children, and using the four strategies provided here, will help young children become powerful problem solvers. They'll learn math skills, math ideas, and problem-solving skills-three for the price of one! Best of all, children's thinking will delight you as you acknowledge their intelligence and creativity.