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Teacher Says:
Quilting and Other Math Fun
Hosted by Evelyn Vuko
Washington Post Education Columnist
Guest: Johnny Lott
President, National Council of Teachers of Mathematics
Tuesday, May 20, 2003; 2 p.m. ET
Even if you've hated math since way back in Mrs. Leftover's fifth grade, you can learn to confidently help your kids with math. You can restore math skills by sharing some of your favorite hobbies. For instance, quilting is a great way to teach kids about geometry.
Share your worries and learn ways to make math more interesting for your children.
Join Post Teacher Says columnist Evelyn Vuko and her guest Johnny Lott, president of the National Council of Teachers of Mathematics, on Tuesday, May 20 at 2 p.m. ET. Submit your questions and comments before or during the discussion.
Lott, a mathematics professor at the University of Montana, is also an avid quilter. Quilting and calculators are two of the ways he believes math can be made interesting and fun.
Below is the transcript.
Editor's Note: Washingtonpost.com moderators retain editorial control
over Live Online discussions and choose the most relevant questions for guests and hosts; guests and hosts can decline to answer questions.
Evelyn Vuko:
When kids have trouble or dislike math, parents and teachers have to get creative. Quilting, of all things, is one way to get kids of all ages interested in the intricacies of math. It's colorful and unique and just one of the many ways my guest, Johnny Lott, President of the National Council of Teachers of Mathematics, and I will help you light the math spark in your kids. Welcome!
Philadelphia, Pa.:
My eighth grade daughter is motivated about a lot of other things, but not about math. I like the quilting concept as a learning device, but do you have any suggestions about how to present the quilting idea to her so that she will think it's cool? To date, she has not shown much interest in sewing, knitting, etc.
C. E. Wadd washingtonpost.com:
The Geometric Appeal of Quilting (Post, May 20)
Johnny Lott: While there are no automatic answers to what will appeal to eighth graders, among the things that may help are having her look at things like wallpaper patterns, visit almost any large department store and see the numbers of quilts on display for use as bedspreads, etc. One thing to think about is what types of colors might look best in her room and on her bed. What are her favorite colors? How does the types of quilt patterns change the look and feel of a room? These are not so much mathematical ideas as affective statements.
New York, N.Y:
How young should kids start using calculators? Won't it hurt their ability to calculate on their own if they're always depending on a machine for answers?
Johnny Lott: A part of having young children think about calculators to learn math is thinking seriously about how they are being used. Few people want young children to simply add one digit numbers or multiply one digit numbers on a calculator. Certainly not the National Council of Teachers of Mathematics. However, by thinking about how students can learn with the tool, parents can help their children even from very young ages think about number patterns. These don't have to be done with a calculator but can be. For example, if one thinks about the number of teddy bears on a shelf and the number of paws on those bears, a calculator number pattern might help the child. Simply counting might also help the child.
No bears=no paws
One bear=four paws
Two bears=8 paws
three bears=12 paws
and so on. This might be an introduction to multiplication facts. It is a simple example.
The Nim type game that Evelyn and I have discussed using a calculator is a number strategy game and the calculator is very effective. Because this type of game is quite old, it was invented before calculators of the modern type and can be done in many ways.
Chevy Chase, Md.:
I was lousy at geometry and now my daughter is having a rough time with it. Is there any way I can help her even though I was never very good at it myself?
Johnny Lott: One of the things that will help your daughter is to think more positively about yourself and your abilities in math. When you say that you were "lousy at geometry," think about what you are saying. Would you tell your daughter that you were "lousy at reading?" I doubt it.
What were the things that you liked about geometry? If there was nothing, then think about the things that you do like that involve geometry. I chose quilting because I watched family members do it as a child.
If you like a particular wallpaper pattern or a style of wallpaper patterning, talk with your daughter about it. What does she like and why? Are there repeating patterns in the patterns that she likes?
Does she like stenciling? This is the way many geometric slides or translations are done.
What types of architecture does she like or do you like? Why? What are the geometric features that intrigue you and her?
Geometrically, how does one print a page on a large sheet of paper, fold and cut so that print and pages come out in the proper order? For example, take a regular piece of paper and think about how you could fold it in half and then in half again and again so that you could have a 16-page book. How can you fold so that there are the fewest number of cuts in making the book? How can you print letters and page numbers so that they are "right-side up" when the book is printed?
These are but a few questions, but think about things that you like that are geometric in nature. There are many things that I think you will find are around you that might surprise you.
Take any small cardboard box. Think abouthow it was made. It was cut out from a flat piece of cardboard. If many boxes were made at the same time, how was the original cardboard cut? How could the template for the boxes be placed in order to save cardboard and waste little?
Washington, D.C.:
I want to start my children off on the right foot to learning. Is two too young to start teaching math? If not, how and what can I do to start? We are having them count numbers by repeating them to us. Evelyn Vuko:
Two is not too young to teach math, because even little ones know that having a cookie for each hand is better than just one. When the kids are repeating after you, clap the number or hold up your fingers to give them some sensory reinforcment. You might even place toys on the floor in a line to show how it grows longer when you list one number after another. Find big wooden numbers or magnetic ones and let them handle the numbers as you say them. One of my favorite ways to introduce numbers, and letters to little ones, is to have them make and bake cookies in the different shapes. The learning experience is rewarding, and edible.
Johnny Lott: Among the things that you can do with your children is to find books that you will read to them that contain math. At two, the books will be pretty limited, and you will probably see mostly counting books, but some of Dr. Seuss's books have a mathematical nature. The children will like the rhyming of the poems and stories. Another thing along this line is to use the nursery rhymes and emphasize the ones with math concepts.
Centerville, Virginia:
Some would look at working with quilts and question why aren't we spending this time drilling facts or working with equations. How is it that quilts can be truely valuable in learning math?
Johnny Lott: Learning math through quilts is not intended to take-away from other concepts in math, but drilling facts is also not the only important part of math for children. When you think about what people in the world today are using in math, you have to think about data analysis, geometry, probability, measurement, and algebraic concepts as well as number concepts. American students do very well with computation.
Working with equations is an algebraic concept that students do need to know as well. However, the area and perimeter concepts and measurement concepts found in quilting certainly can be heavily involved with equations--depending on how one approaches it and what types of questions are asked.
Much of math can be learned in context of real problems and will be retained longer than if taught in isolation. Quilting is a rich context for teaching some concepts--not all.
Salem, NJ:
Quilting seems to deal with geometry. What kinds of geometry should kids be learning before the usual tenth grade course?
Johnny Lott: Many children come to school knowing about geometrical concepts. Is there a child around who could not tell you in some way why a ball will roll better than a block?
Spatial visualization is something that children start to learn really early and tend to lose that as they get older. Things like which clothes fit which paper dolls or three-dimensionally, which clothes fit which dolls are good spatial visualization problems.
Symmetry is another concept that students recognize early. Which objects are flip images of other objects? (Mirror images are basically the same thing.)
Size and proportionality are also important concepts that can be address early.
I could go on.
Centreville, Va.:
The middle school age kids I know are full of energy and often have a hard time focusing. Is it really possible to get the students to focus and learn the math rather than focusing on what might be seen as a art or crafts projects? Evelyn Vuko:
Yes! But that's depends on how you engineer the project. If the directions and tasks you give emphasize numbers and math, the arts and crafts will be just what they are: the hook and the vehicle.
Johnny Lott: I would defer here to Evelyn because I'm very biased. Interest can lead students to the math. The teacher or the parent working with the child also has to be focused to make sure that the math comes out in the process.
arlington, va:
my son is 4&half years old. he is doing additions and subtractions for 2 digit numbers quite well. like 18-9, 8+4 etc. but he is not well in the concepts more/less. he cannot tell correctly 18 is bigger then 9. (he guess answers) is it right to teach maths ahead of time. or i try to divert him to some other skills. Evelyn Vuko:
You can teach skills ahead of time if you use visual methods. Your son needs a visual image of the value of 18 before he can determine its relationship to another number. Try this idea: attach a piece of paper to a wall or doorway and mark off the inches until you reach 60 (because I'm sure he's not taller than five feet!) then place things against the wall and measure how tall they are. How many inches tall is he? How tall is a spoon? Give him an idea of the difference of numbers by showing him, clearly, what they look like.
Johnny Lott: This is a tough question without knowing the child. If the is doing subtractions like 18-9 and doesn't know which is bigger, then I suspect that the subtraction may be being done in a rote type of way. Maybe not, but this is a place where using blocks and having demonstrations of which number is bigger is important. Would your child attempt to do 9-18? If not, why not? Is it the words "more" and "less" that are confusing or is it a deeper question?
Does he understand one-to-one correspondence and a matching of the number of objects in two sets? You might want to start there.
Chicago, Ill.:
I want to do enriching, non pencil and paper/drill and kill math activities with a rising eigth grade boy this summer- who wouldn't touch quilting with a ten foot pole. Do you have any ideas or resources to recommend?
Johnny Lott: One place that you might think about looking is at www.figurethis.org. This site put together by the National Council of Teachers of Mathematics, the National Action Council for Minorities in Engineering, and the Widmeyer Corportation is a collection of problems for middle grades students. They are good mathematically and quite challenging.
If geometric notions are what you are thinking to do with the child, try some of the airplane books. There is great geometry and math in some of them. Designing a plane that will fly the farthest is really an engineering problem.
Kites are another source of paper folding and geometry that interest some students.
Arlington, Va.:
Not completely on topic, but I've long thought thast those who can design clothing and patterns for making it must be intuitively good at calculus.
Knitting would also be good for learning math, though maybe not as good as quilting.
Johnny Lott: Jhane Barnes is a clothing designer who use much mathematics in the design of fabric as well as in making clothes. You might want to do a googol search to see her web site. She spoke at the National Council of Teachers of Mathematics annual meeting in Minneapolis several years ago and was superb. She also uses fractals and computer design in the design process.
Arlington, Va.:
What advice do you have for teachers (and parents) in terms of acquiring materials for hands-on math, and also what tips and tricks do you have for managing large quantities of manipualtives? Evelyn Vuko:
For hands-on materials, go to the classic source: Cuisenaire, the makers of the famous counting rods used with generations of kids. Check out their website at www.cuisenaire.com Regarding managing large quantities of manipulatives: try clear plastic boxes, they stack easily and come in a wild variety of colors. You might even code the colors; like all the purple boxes have measuring materials in them; all the green ones have fractions materials, etc.
Johnny Lott: For managing large quantities of materials, try very large baggies, even gallon freezer bags, plastic containers of all types, some plastic stacking shoe boxes or even cardboard boxes with good labeling are effective.
For hands-on materials, in addition to the many commercial places, think about what is available around you.
For young children, old keys or buttons make great manipulatives.
For a good geometry manipulative and chore, what is the shape of the cardboard inside a paper towel roll?
Math Mom:
I always enjoyed math and did very well with it. My profession requires me to use and understand math. Yet, my 3rd grade daughter says she hates math. Her teacher says she is doing fine. Why the negative attitude? Should I try to change it and if so, how?
Johnny Lott: If your daugher is like my son was, one reason for not liking math was because he had a parent so involved with it. A very wise teacher told me to think very carefully about what I was doing with him and how I should not make everything a math problem! It was good advice though very hard to follow.
For third graders, think about checking out books from the library at her level that have math involved. The books do not have to be number drill books, but simply those that have math concepts somewhere. Have her see that even in her world, there are math things that are good to know.
Grandfather Tang's Story is a good one for shapes. One can start with tangrams and move from there.
Good luck.
Edgewood, Ky.:
My son is in third grade and having trouble remembering his multiplication tables. He seems better at some than others and he hates flash cards. Any suggestions? Evelyn Vuko:
Use a rectangular array. That's a boxed design made with a series of dots--four across and five down, for example. Make an array using brightly colored markers and have him block out 20 as the answer for 4X5. Use pennies to make an array and have him remove the correct answer. Make an array of jelly beans and he can eat the answer.
Johnny Lott: One relatively easy thing to think about is skip counting. Don't concentrate on the multiplication, but think as follows:
Can you count the legs of a large number of people? How would you start? Counting by ones takes for ever. Let's count by twos. 2, 4, 6, 8,
Could you count legs by 4s? How would that go? If not legs, then together how many legs and arms would the people have?
4,8,12, and so on.
How about corners on triominoes? (These are triangular shaped game pieces?)
Similarly think about tiles for the floor and the number of vertices (corners) on the tiles. Usually triangles, squares, hexagons and maybe octagons are available.
Fives, use fingers on hands.
Sevens are somewhat problematic, but skip counting by sevens can lead you to a calendar and the number of days in lots of weeks.
And the list goes on.
Johnny
Warren, Mich.:
I just wanted to comment on using crafts to teach kids math. My mom taught me to crochet when I was 5 and I learned how to sew not long after that. I always enjoyed making my own creations and I think I learned quite a bit of math that way because I was always measuring my projects and designing them on graph paper so that they would turn out the way I wanted them to. I'm now a college student majoring in math and I think part of the reason I've always liked math and have been good at it is because of my early exposure to projects like your quilt suggestion. Evelyn Vuko:
How nice to hear from a math student that crafts are a great way to teach math! It does my teacher's heart a world of good. Thanks for getting in touch today.
Johnny Lott: Thank you for a great statement!
Southern Maryland:
I am a middle-aged woman and have had a case of fear and loathing of anything mathematical since first grade. I could tell horror stories of the tearful homework battles with fractions and long division! I never learned the basic multiplication tables in 3rd grade. I had no hopes whatsoever of going to college, even though I was in the top 25% of my high school class (poor parents, no encouragement to do so). Subsequently, I only learned enough to squeak through public school with a general diploma. I would suggest to teachers if they want to instill even a basic interest in math, they'd better explain the thought processes in dealing with it. I had teachers who only put up problems and then supplied an answer. Not even a clue on how to go about solving the problems. If you want better students, hire better teachers.
Johnny Lott: As mentioned in the No Child Left Behind Act, we do certainly need highly qualified teachers. And we need teachers who know more than one way to approach a concept. Having a teacher who knows only one strategy to teach something is insufficient. Students do not all learn alike.
I'm sorry that you had an unhappy math childhood. Wish you could be in a class of mine. You might not like it but I would try to help you see why you do some things in math.
Athens, Ga.:
What role should parents take in introducing children to technology and mathematics- calculators, computer software, etc? At what age should this occur?
Johnny Lott: Personally, I allowed my son to use calculators and computers from the time he was curious about them. He used a Little Professor and was fascinated by the lights. He used a calculator to do patterns, and we had a rule that for every 30 minutes of play on the computer, he had to do a time on the typing tutor. As an adult, he is a very fast typist, is a financial analyst, and seems pretty comfortable with most math. It was never his favorite subject but he does use it.
Silver Spring, Md.:
My son will be joining kindergarten from september'03. he has been enroll to a school. now i came to know the school is not giving good results compared to other school and group of childern is not that which i want for my child to join. as i know, i can not violate the boundaries. what is the procedure to get the transfer. Evelyn Vuko:
Transfer rules vary greatly so you will need to go to the central administration office of your school district to see what you can do about transferring schools. If you are unable to transfer, talk to the teachers, visit the classroom and get a feel for the class where your son will be. Try to make the best of the situation and do not share your worries and concerns with your son. He might be happy and do well there. Give him a chance to form his own opinions.
Johnny Lott: I agree with Evelyn.
Getting Manipulatives:
I heard about a school where the children were asked to bring in those plastic tabs used to seal bread bags. You could amass large numbers of things and involve the children by getting them to pitch in. Evelyn Vuko:
This is a great suggestion. One of my first grade classes brought in old buttons. What great fun we had learning grouping and counting!
Johnny Lott: One of the big things is "how big is a million?" Students are fascinated with this and for good reason. Plastic tabs or aluminum tabs from soda cans are frequently used.
Arlington, Va.:
i asked the following question.
arlington, va: my son is 4&half years old. he is doing additions and subtractions for 2 digit numbers quite well. like 18-9, 8+4 etc. but he is not well in the concepts more/less. he cannot tell correctly 18 is bigger then 9. (he guess answers) is it right to teach maths ahead of time. or i try to divert him to some other skills.
i taught the method to add or subtract in the following manner.
initially i started with the fingers to add or subtract the numbers less then or equal to 5.
i work with some problems like if he has 5 apples and he eat one how many left. if he found 2 more apple how many total now.we made the story to do some additions and subtractions. but numbers always ranges between 1 to 10 so that he can use his fingers to count.
now he is doing in the following manner.
for 18-9 he draws the 18 lines then cut 9 lines and count the remaining.
similarly he dos for addition.
what is the efficient way for a 4-5 age group to teach add/subtract.
Evelyn Vuko:
I found with first graders that they had an easier time with addition and subtraction if I had them use not just their fingers, but their whole body to learn how numbers shrink and grow. This is why I suggested the tape measure on the wall. You could, however, put a tape measure on the floor and have him "walk" the equation.
Johnny Lott: I agree with Evelyn.
Laurel, Md.:
In my high school (late 70s) we were taught how to use a slide rule, even though scientific calculators had dropped to $15 by then. I couldn't help but remember my grandmother telling me that when she was in school, girls were taught how to churn butter.
Today I work in a heavily mathematical field and I would say 99% of what I do boils down to:
Figuring a math problem on paper
Programming a computer to do the calculations
Asking "does this make sense?" (checking results)
Explaining the results to others of various levels of understanding
Thinking back to my own education, from what I've seen of the new employees at my work, I infer that schools these days are pretty good at #1 and #2. But their "number sense" (#3) is not good and communications skills (#4) are atrocious. In school math classes, finished products were a bunch of calculations with an answer circled. What should parents and schools do to improve higher-level understanding of the context in which math problem exists in real-life experience?
Johnny Lott: Drawing the math out of the contexts does take work. Help from parents and teachers is much appreciated in doing this. John Paulos's book on innumeracy does have some good suggestions. Simply being aware of numerate issues is a place that parents can start to help their children. Estimating costs of groceries is a good thing to do.
Evelyn Vuko:
Quilts and crocheting teach math, who'd have thought? It was great to hear, from a math major even, that hand-crafts forge not only stronger math skills but the interest to make math work a career. Thanks to Johnny Lott, a great math teacher and avid quilter for making this chat unique and helpful. Join me liveonline again on June 3.
Evelyn Vuko:
That wraps up today's show. Thanks to everyone who joined the
discussion.
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