by Amanda Dobbins
My 4-year-old son, Charles, has waffles on his mind. He asks if he and his sister can each have two with the “slow” syrup (a.k.a. Aunt Jemima). I say, “Sure,” and then seize the teachable moment to ask him, “If you’re having two and Julia is having two, how many do you need?” He grins and declares, “Four!”
This is new for me, asking my kids to do quick mental calculations. In the past, I’ve felt a bit self-conscious asking them to answer the math questions that everyday life presents. Turns out, all the encouragement I needed was learning about a little theory. There is an essential area of knowledge called “number sense” that is developed through these informal math interactions. Number sense is what allows children to understand mathematical concepts and procedures through reasoning.
Early number sense, for example, is knowing that four waffles are represented by the number four. As children develop their number sense, this fundamental understanding grows into the ability to add, subtract, multiply, divide and perform increasingly complex operations.
The key to developing number sense is providing plenty of practice with skills such as mental calculation, sorting, estimating, numeral-to-object relationships and measurement. That’s not enough, though. We need to go a step further and ask children to explain their reasoning.
Marilyn Burns, a nationally renowned educator and founder of the math products and resources company Math Solutions (mathsolutions.com), says number sense is gradually acquired as we grapple with math questions and construct understanding in our own minds. Beginning in preschool, children do daily work that reinforces number sense, but we parents can play an important role in helping build this foundational knowledge.
So where do you start? We know that reading aloud with our kids will build literacy and help them learn to read independently. We know that seeing us read sets a good example and encourages kids to follow suit. Unlike reading, children have few opportunities to see adults using math unless we count apples into our grocery carts or explain how it is that four quarters make a dollar. It’s easy to get started if you think about number sense as math out loud – the mathematical equivalent of reading aloud.
Make It Part of the Routine
Our daily lives are full of ways to help kids sharpen their number sense. Martha Tassinari of Beverly finds that math learning opportunities abound in the kitchen. When filling a measuring cup, she asks 5-year-old twins Max and Ali, “Does that look like half to you?” to give them a sense of half and whole. Max and Ali enjoy any math questions that center around parties or family meals. Martha challenges them to do quick mental calculations by asking, “If there are five in our family and four more people coming for dinner, how many plates do we need?”
The critical step for developing number sense is following this up with, “How did you figure that out?” When children have a chance to explain their reasoning, it extends and reinforces their understanding.
Amy Monteiro, a kindergarten teacher at Sheehan Elementary School in Westwood, is always happy to talk with parents about ways to reinforce number sense. “Parents may think that because a child can count objects, he’s ready to move on to addition and subtraction. But there is actually a lot that he needs to hold in his head in order to perform these operations with accuracy and understanding,” she says.
We adults have already learned to get a visual on a group of objects and know how many there are without counting them individually. Looking at a die with six dots on it and knowing there are six is something that takes practice and is part of our number sense.
by Amanda Dobbins
Monteiro says games with dice are perfect for learning to recognize groups of objects without counting them; she encourages parents to play these games at home. She creates her own dice and places the dots in irregular patterns to challenge her students. Other number-sense teaching strategies include:
• Board games, such as High-Ho Cherry-O and Chutes and Ladders – Good for getting a visual on groups of objects, counting and quick mental calculation, High-Ho Cherry-O can be played by kids as young as age 3. Chutes and Ladders, also good for young children, reinforces counting skills up to 100.
• Recycling chores – Recycling offers a chance to practice counting, sorting and estimating. In her book Beyond Facts and Flashcards, author Jan Mokros suggests asking younger children to sort recyclables and then explain why we sort them the way that we do and which objects go together. Or have them look at an empty recycle bin and ask them to estimate how many bottles or cans would fit in it.
• Gardening –Mokros suggests using gardening to introduce “personal benchmarks” as concepts of measurement. Ask a very young child to plant seeds a finger-width apart, a hand-width apart or a foot-length apart, depending on what you’re planting. This is a chance to begin talking about inches and feet. Mokros suggests asking an older child, based on personal benchmarks or use of a measuring tape, how many seeds will fit in a whole row.
Ultimately, whether your math partner is age 3 or 13, the most important part of all this is keeping it fun. Kids can lose interest in math drills. Tassinari and her family know this and jump at the chance to engage in math conversations.
“It’s a way of connecting,” she explains, which is the best reason to engage our kids on any subject. n
Amanda Dobbins is a freelance writer and author of The Baby File: All the Lists, Forms, and Practical Information You Need Before and After Baby’s Arrival (Running Press, 2008). She lives with her husband and two children in Hamilton