Math II (562417), страница 26
Текст из файла (страница 26)
Music and math seem to create a connection between the two hemispheres of the brain. Music is considered a rightbrain activity, while math is a left-brain activity. When combined, the whole child is engaged not only in the realm of thinking but in all the other domains of social-emotional, creative, language, and physical development. Music and math: Together they make a complete developmental package.
The melody of math
The next time your child is singing a song she learned at school, join in. Clap or tap a beat to go with it--even if you don't know the words. Rhythm is made up of patterns--just like math. By focusing on the beat, you will be making the structure of math audible. Tap the beat to a favorite song and see if your child can guess it. Clap the rhythm of her name.
Make up a rhythm for your child to echo back to you.
Take time to sing counting songs too. Remember "One Potato, Two Potato" or "10 Little Monkeys"? Songs like these help children learn about numbers by giving them a "hands-on" experience. Instead of counting by rote, children can count to a beat, a tune, a motion, or an object--or all of the above.
Math around the house
Besides making music, other "homegrown" activities can help your child understand matching, comparing, sorting, and making patterns and sequences and build a foundation for future math learning.
Match them up. Matching and comparing are essential skill activities in math development. Before your child can understand that 3 is more than 2, she needs to be able to recognize more than (bigger than), less than (smaller than), and same as (equal to) in the world around her.
• Invite your child to build a tower that is as tall as the coffee table (or the couch or the dining table). How many blocks did she use? Is her tower bigger or smaller than the table? By how many blocks? Is her "couch tower" bigger than, the same as, or shorter than her "table tower"? By how many blocks?
• Have a pizza party! Invite your child to match one piece to each person (one-to-one correspondence). You can extend the learning by asking, "How many slices will we need for everyone to have two?"
Patterns all around. One of the important skills in math is the ability to see (or "read") and verbalize a pattern.
• Look for the patterns in your environment. Is there a pattern on the wallpaper, the parking lot, even the stripes on your child's shirt? Point these out and invite your child to say or clap the pattern with you: "red, blue, red, blue, red, blue." What color comes next?
• Make patterns with the shells you collected at the beach this year, with the coins in her piggy bank, with socks--anything you have multiples of!
How big? How long? Measurement is a natural extension of matching and estimating. To measure, your child has to match a series of objects to the length or width of something. The first step in measuring is to create a standard of measure--but the item you use to measure with doesn't have to be standard at all.
• How many (clean!) socks long is the kitchen counter? Count them and see. Then measure the counter with soup spoons. Suggest another item--toy cars, cereal boxes, magazines--and ask your child to guess (estimate) how many of these will be equal to the length of the counter. (Just remember that all your "measuring items" should be around the same size.)
• Your child can use nonstandard measuring items for practical purposes too. How much room will the new picture take up on the wall? Why not measure around the frame with erasers? (And for comparison's sake, show your child the equivalent measurement in inches on a ruler.)
Exactly the opposite. The concept of opposites is important to math: For instance, in order for your child to understand low, she needs to experience high. When you use the comparative language of opposites, you are helping your child learn about proportion and number relationships.
• Ask your child: "Can you put this can on a low shelf and reach up to put the cereal box on a high shelf?."
• While you're taking a walk, say, "Can you take BIG steps? Now do the opposite."
Tally the score. Tally marks are up-and-down lines that are made in sets of four with the fifth mark made as a slash through the set of four. Children learn tally marks quickly because they are connected with an action or event.
• Show your child how to keep score in family games such as go fish or tic-tac-toe.
• For children over 3 who no longer put objects in their mouth, instead of tally marks, use objects such as buttons, beads, or coins and count five of each into egg carton sections.
• As your child becomes comfortable with tally marks or objects, you can introduce a "shopping cart tally." Use a child-size calculator to add up how much each item costs as it goes into the shopping cart. Your child may not really understand what the numbers mean, but she will see that they get larger and larger as the cart gets fuller and fuller.
• When you get home, play with the change that is left over. Your child may be becoming interested in money, and although she may not understand the value of each coin, she can begin to sort the pennies and other coins she is collecting. (This activity is for children age 4 years and older.) She can match them by size or color. Eventually your child will be able to match pennies to nickels and dimes just like she matched the tally marks to objects!
Numbers are everywhere in your child's world. You might find them on speed limit signs, route number signs, posters, and houses. Point out the numbers on household electronic devices. Set the timer together on the coffee machine, microwave, alarm clock, or VCR. It's through simple day-to-day activities--from singing songs to slicing pizza--that your child will have her first important math experiences.
PHOTO (COLOR): Rat-a-tat-tat, toot, toot. When playing musical instruments, children experiment with rhythmic patterns.
PHOTO (COLOR): "This tower is eight blocks higher than the coffee table." Parents can help children practice the language of math
PHOTO (COLOR): "The picture is five erasers wide." Your child can estimate and measure without using a ruler.
Great Books about numbers, size, and counting
Beep Beep, Vroom Vroom!
by Stuart J. Murphy, illustrated by Chris L. Demarest
HarperCollins, 2000; $4.95, paper. Ages 4-8.
Benny's Pennies
by Pat Brisson, illustrated by Bob Barner
Yearling, 1995; $5.99. Ages 4-8.
The Cheerios Counting Book: 1, 2, 3
by Barbara Barbieri McGrath, illustrated by Rob Bolster and
Frank Mazzola, Jr.
Scholastic Inc., 2000; $6.99. Ages 2-4.
Eating Fractions
by Bruce McMillan
Scholastic Inc., 1991; $15.95. Ages 4-8.
Learn to Count, Funny Bunnies
by Cyndy Szekeres
Scholastic Inc., 2000; $6.99. Ages 2-4.
More, Fewer, Less
by Tana Hoban
Greenwillow, 1998; $15. Ages 4-8.
The 1, 2, 3's of Math Learning
Your child's acquisition of math skills follows a developmental sequence just as children (most, anyway) crawl before they walk, they learn math relationships before they learn the names of numbers and how to use them. Children need to learn the structure of math before they can use (and, most important, understand) the vocabulary and symbols of math. Too often we present children with numbers before they have had the opportunity to understand what those number symbols or words mean. For instance, sometimes a young child can count to 10, but he doesn't really understand what he is doing. He is just saying a series of memorized words.
RUNNING BY THE NUMBERS
Source: Mathematics Teaching in the Middle School, Dec2000, Vol. 6 Issue 4, p262, 4p, 2 charts
Author(s): Milliken, Paul; Little, Catherine
In 490 B.C., the messenger Pheidippedes ran twenty-six miles to Athens carrying the news of Greek victory at the battle of Marathon. He delivered the news and dropped dead from the effort. Today, we celebrate that famous run with one of the most demanding events in human athletics, the marathon. Like Pheidippedes, the modern runner strives to complete the distance in as little time as possible. Unlike that early messenger, today's competitors undergo extensive training to ensure that they remain alive when they have finished the run. Kevin Smith uses mathematics to help runners prepare for marathons.
Marathon Dynamics, Inc., in Mississauga, Ontario, is Kevin Smith's company. He provides a variety of services for the running community, including hosting running clinics, conducting fitness and health presentations and seminars, managing and promoting local running events, coaching runners, and creating customized training plans for individual runners using software that he developed himself.
"Basically my days are filled with crunching numbers," Kevin says, "involving calculations of distances, times, paces, and heart rates." He works with runners at all levels, from "recreational joggers to competitive athletes." Each training plan is customized "in order for an individual to improve running performance." Kevin brings an essential "appreciation and understanding of the relationships" among all the variables in his number-crunching.
Kevin says that he has "had to, at one time or another, apply the skills, formulae, and thought processes learned in" a whole range of mathematics disciplines, including "calculus, probability, algebra, and tons of more basic percentage and exponential calculation, and unit conversions (miles to kilometers, miles per hour to kilometers per hour, or meters per second, and so on)." All this work, on top of the accounting, record keeping, and financial management of operating his own company, means that Kevin is always doing mathematics on the job.
Does that mean that Kevin studied mathematics in college to prepare for his career? No. "I had no idea," he says, "I would be using math in this way or to this extent. I created the job I do when we founded our company." The mathematics-related courses that have been most useful to him are the accounting and economics courses that he took as part of his business administration degree at the University of Western Ontario. "As co-manager of the business, my responsibilities include most of the financial management duties of any small business, but the entrepreneurial spirit and desire will only get one so far." He still has to do the bookkeeping.
"I suppose my attitude toward mathematics would have been a little different," he admits, "had I known how it would all end up." He always did well but looked on mathematics "as a chore. I was not a natural, so I had to work at it. If I had known how vitally essential a comfort level with numbers was going to be in my career, I might have had a little more pure motivation to excel in math."
Instead of a specific interest in mathematics, a technology connection spurred Kevin's career and got his company started. "I started to toy around with a simple Lotus spreadsheet idea I had six or seven years ago," he explains, "about a way to help runners of vastly different experience and ability" plan their training. The resulting software program helped runners calculate "how frequently, how much, and how fast to train." Kevin claims that he "had no idea it would turn into what our customized training software has become--a matrix of over sixty interrelated Microsoft Excel spreadsheets, each of which has hundreds of lines of code and formulae embedded in it. I created the job I do after university, so I had no preconceived notion of how math would be involved in my current career."
Mathematics can save your life only if you know how to apply it. The first marathoner, Pheidippedes, did not know how to pace himself and died as a result. With help from Kevin Smith and some number-crunching through his customized-training-plan software, the famous messenger might have lived to deliver more news.
Teacher Notes
Begin work on the activity sheet on page 265 by having students measure their heart rates. In pairs, have them take each other's pulses by having one person count and the other time the beats per minute. Record the beats per minute for each student. Graph the results, and look for trends. Have the students exert themselves by running in place, for one minute, and measure the rates again. Compare the results. This exercise prepares the students for question 1.
For the other questions, make sure to review conversion strategies. For example, when converting from kilometers per hour to meters per second, students must change units of both distance and time.
When calculating the amount of running done in one year for question 2, remember that every fifth day is a rest day.
See figure 1 for one student's solution to the activity sheet.
"Math at Work" explores how mathematics is used in the workplace. Each article will highlight a particular career and the mathematics specific to that discipline. Readers are encouraged to submit manuscripts for this department by sending them to "Math at Work," MTMS, NCTM, 1906 Association Drive, Reston, VA 20191-9988.
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