Faces are very important to my daughter Emma, because faces have feelings and stories to tell. Math, however, is not important to Emma, because to her, it is coldly impersonal and meaningless. Word problems are OK, but abstract equations – forget about it.
Knowing her “right-brain” nature, I tried to ease Emma into math gently, with lots of manipulatives, friendly math picture books, and hands-on Montessori type activities. She was fine with all of this and seemed to understand the concepts of quantity, comparisons, and even basic arithmetic (if I have 5 apples and give you 2 apples, how many do I have left?). When she was about six, we started the Miquon math books and she found the Cuisenaire rods mildly interesting, but she balked at any visual representation of equations. The plus, minus, and equal signs all looked the same to her and she could make no sense of it. This made her furious. She threw up a mental wall and refused to look at any of it.
Ordinarily, I would have just waited another six months to a year to approach this material, but I had made the mistake of joining a public charter school for homeschoolers and they were going to be checking up on her progress. So I really wanted to get her over the hurdle of recognizing simple symbols. I found a very interesting book by Mark Wahl called, Math for Humans, which helped me invent a technique to help Emma. Since her natural strengths were interpersonal and artistic, I decided that math symbols would be less threatening if I gave them faces and personalities.
I created little 5-inch tall paper dolls with bases that allowed them to stand up on a table. The plus and minus symbols became princesses with the appropriate symbol boldly displayed on their crowns. The equal sign became the queen, also with the equal sign on her crown. The two princesses each had a miniature basket (found at the craft store). The basic premise was that the plus princess liked to collect things and add them to her basket. The minus princess liked to give things away, subtracting them from her basket. The equal queen’s job was to count the objects in their basket at the end of a transaction.
Of course, I had to embellish each story somewhat. So when faced with an equation like “2 + 7 = ” the “plus princess” would take her basket, filled with two lentils, and go collecting seven more lentils from imaginary bushes. When she came home, the queen would check her basket and discover that she now had nine lentils. To reverse it, the “minus princess” would take nine lentils in her basket, then distribute seven of them to assorted small toys attending the story. Throughout the process, Emma would keep up a running dialogue between all the characters and I would do my best to contribute voices and personalities.
With the paper dolls, it didn’t take long for Emma to overcome her fear of the symbols and she was able to remember what each one represented, regardless of the way an equation was written (2 + 7 = 9 or 2 = 9 – 7). After the first week or so, we put away the paper dolls, but she still needed to draw dots or other objects to help her visualize the problems. She came up with some very imaginative pictures and faces to dress up the numbers in her workbooks. Her margins were works of art! It made math time last twice as long, but I didn’t mind because it was the only thing that made it bearable for her.
The problem was when she attended third grade at our public school. Her teacher would not allow doodling on any of the math homework, so Emma was at a disadvantage. She could not answer any problems without some sort of visual representation. At home, she could use her Cuisenaire rods or scratch paper, but at school or during test time, she was miserable. We finally decided to bring her back home during the spring semester.
Learning to multiply and divide was another odyssey. We took it slow, with lots of hands-on games and activities. I made another paper doll with a times symbol on her crown. Instead of lentils, she collected unit rods of equal length. So if the question was “2 X 3 =”, the multiplication princess would either collect two 3-unit rods or three 2-unit rods. We always did it both ways to show that the answer was the same. The division princess would reverse the work that the multiplication princess had done, taking the rods in her basket and dividing them amongst grateful small toys. Again, we only used the dolls for a week or so, until Emma could remember what the “X” and “÷” symbol meant. After that, we depended on the rods for all of her math work.
Memorizing the times tables was also a long process. I found some flash cards that presented each of the multiplication facts as a story and that helped a lot. We also quizzed each other on our weekly hikes. I would ask Emma, “What is 6 X 7?” and if she answered correctly, then she would ask me a question like, “What is one million times two million?” She was always amazed when I gave an answer – those numbers seemed so impossibly big to her. I was amazed that she didn’t mind this kind of verbal quizzing. She liked the social aspect of it.
When Emma was about twelve, math really started to come together for her. She still didn’t like it, but it became easier for her to think abstractly. We were able to move along at a much faster pace, although repetition was important. On her own, Emma realized that she had to constantly review old concepts while learning new things or else she tended to forget that she had ever learned it. Instant feedback also helped. In seventh grade, she used the interactive 7th grade math DVDs available from the Teaching Textbooks company. It was so helpful to know immediately if she was solving the problems correctly. Then she didn’t have a chance to learn the wrong method. Unfortunately, Teaching Textbooks doesn’t yet offer similar interactive DVDs for any of their other courses. However, a phenomenal resource called www.khanacademy.org does have interactive math videos where students can practice new concepts, and teachers (or parents) can track the student’s progress. Khan Academy is always adding new videos. Best of all is it’s free!
I don’t know how well Emma would have absorbed these math videos when she was little, although if I had access to them I certainly would have tried it. But if you have a child who struggles with the abstract symbols of arithmetic, try putting a face on them. It could be anything – princesses, dinosaurs, puppies, spiders or maybe superheroes. I can envision a similar game with toy trucks, gathering or delivering unit blocks depending on what symbol is pasted on the cab. Use your imagination! It might be just the thing for overcoming a child’s resistance to unfamiliar concepts.
Unfortunately, I threw away our original paper dolls many years ago. But Emma (now 15) was gracious enough to draw some new ones for you. If you have a child that might need a little help recognizing basic arithmetic symbols, just click here to download Emma’s paper dolls:
You may print them out on heavy cardstock and cut out (loosely – no need to get exact). Your daughter may even want to color them first. Be sure to accentuate the “+”, “-“, and “=” symbols!