Marilyn Burns one of the nation's most eminent math educators discusses in articles and lessons how to teach mathematics from early childhood to high school. Burns is the author of mathematics books, articles, and related materials.
- Arithmetic skills are necessary life tools that children must learn.
As adults, we use arithmetic daily. We add, subtract, multiply, or divide when we balance our check-books, calculate tips in restaurants, figure out how much wallpaper to buy, finance a car, keep score for games, and so on. A person who can't do arithmetic is handicapped in many situations.
Classroom strategies: To help children appreciate the importance of arithmetic, ask them to interview their families about when they use arithmetic. The question they should ask is: When do you have to add, subtract, multiply, or divide to find out something you need to know? Record what children report on a class chart. (For older children, sort the information into two groups: "at work" and "at home.") Afterward, discuss how the chart shows that arithmetic has many useful purposes.
- Arithmetic should prepare children for real world math.
Most of the daily situations that require arithmetic call for more than merely counting. For example, we need to problem-solve in order to decide on the numbers to use or which operation to choose.
Classroom strategies: Involve children in solving problems that relate to classroom routines, such as:
- When taking attendance, count children present, then ask the class to figure out how many are absent.
- Ask children, when lining up, to predict whether everyone will have a partner.
- When collecting milk money, involve students in making change and figuring out how much everyone spends on milk.
- Involve older students in figuring out how much classroom supplies cost, such as a year's supply of paper.
- For class parties, have the students figure out how much refreshments will cost.
- Learning to compute mentally is an essential skill.
We do many of our daily arithmetic calculations mentally, such as when we keep track of what we put in the supermarket cart so we don't go over the $20 we have, when we divide a check at a restaurant, or when we double a recipe that calls for 3/4 of a cup of broth. Usually we don't reach for paper and pencil, but figure in our heads.
Classroom strategies: Ask children to do mental math on a regular basis. Call it "hands-on-the-table" math and ask children not to reach for paper or pencil, but to reason in their heads. Try this:
- For younger students: Have two children take a handful of beans or tiles and count how many they have. Ask the class to figure out how many they have together. To verify, count the objects. Or ask each student to put two cubes in a jar and then have the class figure the total number of cubes in the jar. To verify, count the cubes by 2s, 5s, and 10s. (Not all young children know that you'll get the same result no matter how you count.)
- For older students: Scoop beans into a jar using a coffee scoop and have the students count how many scoops it takes to fill the jar. Then give pairs of students a scoop of beans to count, discuss with the class what might be the average number of beans in a scoop, and then have students calculate mentally how many beans are in the jar.
Students should have math facts at their fingertips before they leave elementary school, such as addition and subtraction combinations to 20, multiplication tables to 12 x 12, and related division facts. Students learn some of the facts easily, such as adding 1 to any number or doubling numbers. Still, memorization is necessary to learn all of the facts. Classroom strategies: While memorization is needed, it should follow, not precede, understanding. Before they're expected to memorize addition combinations, young children should have many experiences combining sets of objects and learning to record addition sentences. And even when memorizing, children should be encouraged to look for patterns and to reason. A child who can't recall how much 8 x 4 is, for example, should be encouraged first to think about something familiar, like 8 x 2 or 4 x 4, and then use that information to figure out 8 x 4.
When we balance our checkbooks or make change, accuracy is important. But in many situations, estimates will do, such as when we double the amount of broth for a recipe or measure fertilizer for the lawn. Sometimes estimates are the only answers possible, such as when contractors bid for jobs, business owners figure margins of profit, or school districts predict the next year's budget.
Classroom strategies: While knowing how to calculate accurate answers is important, students also need experience estimating and learning when estimates are appropriate. Have students review the list they compiled about when their families do arithmetic. Then talk about when accurate answers or estimates are needed. Also, provide opportunities for children to practice estimating. For example, give prices for several items and have them figure out the smallest bill they could use — a $5, $10, or $20. Or ask students to figure out about how much milk they drink in a week, a month, or a year.
Practically everyone today has a calculator. We use them when numbers are too complicated for us to do in our heads. Using a calculator is easier than resorting to paper and pencil, and valuable when we want to be sure we're correct. Calculators should not be viewed as arithmetic crutches, but as useful tools.
Classroom strategies: Calculators can help children think and reason numerically. For example, they're useful for introducing decimals. Third graders can explore equations like 5 x __= 24 or 3x __= 40 with the help of a calculator, and learn how decimals work.
Ask adults to double 38 in their heads, and you're sure to hear several different methods. Some add 30 and 30 and then add on 16. Some double 40 and subtract 4. Some double 35 and add 6. Some think about multiplying, not adding. There's no one best way.
Classroom strategies: Give students opportunities to discuss different ways to compute. With young children, for example, have them think about all the different ways they can add two numbers. Older students can talk about different ways to add or multiply two-digit numbers. Have all students who volunteer explain their reasoning aloud so students can learn from one another.
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Do the Math with Marilyn Burns