Eugenia spent 15 years developing creative teaching materials. She taught both high school and university students (University of California at Irvine) and mentored other teachers. She received a B.A. and an M.A. in literature from Southern Methodist University and has done graduate work at UCI. Faced with the challenge of teaching her son the multiplication tables, she developed her own innovative method, discovering patterns and tricks to the multiplication tables. Eugenia resides in Irvine, California and is available for Teacher In-Service Training for schools in Orange County.
RADIO INTERVIEW can be found at: www.blogradio.com/Homeschooling101.
HOME EDUCATION MAGAZINE Guide to Resource News October 2006
Recently, Eugenia Francis, author of "Teach Your Child the Multiplication Tables, Fast, Fun & Easy with Dazzling Patterns, Grids and Tricks!", wrote to Home Education Magazine to tell us about her book and the methods she uses in it.
I learned from her website:
"Eugenia Francis has spent 15 years developing creative teaching materials. She has taught both high school and university students (University of California at Irvine) and mentored other teachers. Faced with the challenge of teaching her son the multiplication tables, she developed her own innovative method, discovering patterns and tricks to the multiplication tables."
I began by asking Eugenia to tell us more about how she came upon her method of teaching the multiplication tables.
Eugenia: When my son Scott was in the third grade, I was teaching at UC Irvine. My challenge there was to teach literary analysis and writing to freshman students, many of whom had poor writing and analytical skills. At home, my challenge was to get Scott through the third grade.
One afternoon, Scott came home with page after page of multiplication drills. He was overwhelmed! I knew there had to be a better way. So I drew a 100 square grid for tables 1 - 10 and asked him to fill in the tables he knew. Scott quickly filled in tables 1, 2, 5 & 10. I saw that these were the tables with a nice, easy pattern. But what of the other tables? I remembered a trick for table 9. I had Scott fill in the right side of the column 9 to 0 and to the left of these 0 to 9. "There you know the 9's!" I said. Scott was amazed by this trick. The 9’s, he decided, were super easy!
With one simple “trick” or pattern, Scott had mastered the 9's. Why not find patterns for the rest of the tables? Patterns are fun, fast and easy! Patterns enhance recall.
As Scott filled in the grid, we noticed that multiples of ODD numbers had a hopscotch ODD-EVEN pattern. On the grid which has 100 multiples, only 25 were ODD. Why was that?
Scott and I soon discovered that an ODD number multiplied by an ODD number produces an ODD multiple.
The Secret Code for ODDS was: ODD x ODD = ODD.
Whereas when an EVEN number multiplied ANY number the multiple was EVEN!
EVEN x EVEN = EVEN. EVEN x ODD = EVEN or ODD x EVEN = EVEN.
The Secret Code gave Scott a new-found confidence in math! With new tables, he could PREDICT whether the answer would be ODD or EVEN. The tables for EVEN numbers we found were remarkably easy to learn. Why? The multiples of tables 2, 4, 6 and 8 end in some combination of 2, 4, 6, 8 & 0. Soon the fridge was papered with patterns and tricks. Discovery made learning fun!
As a seven year old, Scott was developing analytical skills. He was finding patterns. He was making connections. He was seeing the big picture. Most of all he was intrigued by the times tables. Learning these became a game to him.
Mary: You mention that your workbook teaches a child to discern patterns among odd and even numbers and discover the secret codes of multiplication. Can you share a bit about how that is done?
Eugenia: In designing the workbook, I followed the sequence that I used with Scott. The workbook starts with patterns for EVEN numbers. Once these are mastered, the ODD numbers are introduced along with the Secret Code for ODD and EVEN numbers.
At 165 pages, my workbook has a variety of exercises. First, I explain the concept of multiplication and show that 2 x 3 is the same as 3 x 2. I explain how multiplication is a fast form of addition. There are grids and patterns and often tricks for every table, exercises on number sequencing, games, interpreting graphs, exercises on the ODD/EVEN rule, fill-in-the-blank multiplication problems, squaring numbers, word problems of increasing difficulty as well as division and two-digit multiplication. Each page has artwork. The original artwork we found was extremely important. The artwork is in shades of gray rather than color. However, I found that this worked well as children can color in the circus animals as they learn the tables.
The key to my method is patterns. Why not divide the tables among ODD and EVEN since each has DISTINCT PATTERNS rather than learning them the standard way -- 1 through 10? Two months ago, I sent a copy of my workbook to Laura Bush. Her office forwarded it to the U.S. Secretary of Education. Their response to my workbook:
“The recognition of patterns is a creative way to have students develop understanding for the concept of multiplication. Pattern analysis should be part of the elementary study in mathematics as it is also viewed as foundational skills for algebraic reasoning.”
Algebraic reasoning . . . wow! Why not develop these skills at an early age? Why not teach analytical skills to young children? Analysis needs to start in the early grades.
Mary: You also mention that the book may be helpful to a child with special needs. Can you explain why?
Eugenia: Soon after publication, a teacher emailed me saying the workbook would immensely benefit children with special needs. A mom of a dyslexic child reported that her son took to my book “like a duck to water.” A parent of an autistic child wanted a copy. I needed to learn more. In Sandra Rief’s How to Reach and Teach Children with ADD/ADHD, I learned the following:
Patterns provide structure. Children with ADD/ADHD need structure. These children have a difficulty memorizing the times tables. The visual-spatial method of patterns and grids works better. Patterns also help dyslexic children as they strictly order number sequence. Special needs children can better visualize and recall where a number is placed if they see a pattern. My son too was a visual/spatial learner.
Special needs children (this is true of ALL children) respond best to methods that are interesting, innovative and motivating. I believe my method based on distinct patterns for ODD and EVEN numbers is that. I wanted to motivate children through an encouraging tone. The “you-can-do-it” approach. My workbook was designed for collaboration between parent and child. I came up with the circus motif to engage young children. The artwork and the story had to be appealing, interesting and relevant. There had to be visual cues that make solving word problems so much easier. I had to have a variety of strategies that engaged a child’s attention. I had to appeal to a child’s affective senses – his feelings, his emotions. Can you imagine my workbook without the story or artwork?
I was pleased to learn that a spatial learner is often “art smart.” Had I known this, I would not have been surprised that special needs children love the art exercises in my workbook -- the “Can you copy Rudy on the grid?” pages. I use the grid for fun as well as instruction. If you look closely, you will see that all grids have “watermark” figures in them that a child can trace. Why not reinforce the relationship between art and math?
Also important are the differences between children who are left-hemisphere dominant and those who are right-hemisphere dominant. Whereas the left-hemisphere dominant child learns from parts to the whole, the right dominant prefers the big picture, seeing patterns and making connections. The right side is the creative and emotional side of the brain. Special needs children are often right-brain dominant. That is why I believe my method works so well with them. My method presents left-brained learning through both left and right-brained strategies. Both sides of the brain are needed for learning.
Mary: Can you share a couple of tips that will help a child learn their multiplication tables?
Eugenia: I endorse hands-on techniques of teaching math. Make a double batch of your favorite brownies and have your child do the measuring. Take an egg carton and trim it to 10. Ask your child to divide 12 beans or beads equally into 4 egg cups. Then ask: “How many go in each? That’s right, 3 x 4 is 12!” Division reinforces multiplication. It is the inverse of multiplication.
Mary: The website states your book is designed for a child who is in 2nd or 3rd grade, but many homeschoolers do not go by a system of grade levels. Would this method be helpful to anyone learning their multiplication tables or would an older child find it designed for a younger child?
Eugenia: On the first edition, I had “Grades 2 – 3” on the cover of the workbook. However, I deleted this as grade level is arbitrary. One child might be ready for the workbook at a much younger age. Another might be a bit older. The illustrations in the workbook were designed to appeal to a young child. I am considering a second version for an older child. One high school math teacher told me that 30% of her Algebra 1 students did not know their times tables! I imagine homeschool moms aren’t shocked but I was! I need to consider the older child with special needs. I also want children in other countries to benefit as well. I have been reaching out to homeschool communities overseas. My workbook will be available in Spanish in December. It is currently listed on Amazon in Canada, the United Kingdom, France and Japan. I want to reach children there as well.
My goal is to reduce the time it takes to learn the times tables, eliminate frustration and develop analytical skills.
Mary: Do you have any other tips you would like to share for children once they have learned their multiplication tables?
Eugenia: Once children have mastered the times tables through patterns and the Secret Code for ODD and EVEN numbers, they are ready for complex word problems such as those found in the last pages of my workbook. You’ll notice I simplified these by giving visual cues such as tickets to the circus or the circus menu and then I broke the problem into parts. Have children quickly sketch their own visual cues and then break the problem into parts. This is an effective learning strategy. Also teach them to decipher math word problems: “How many in total?” is very different from “How many were left?” Have your child be fluent in the language of math. I am not a math teacher nor have I taught elementary school. My forte is literature. I urge parents to integrate literature and math. Sandra Reif (page 297) lists stories for children that integrate math concepts. Math should be fun. It should engage your child’s imagination.
I hope that my workbook instills in your child a love of numbers and confidence in math.
Mary: Eugenia, thank you so much for taking the time to share your method and book with our readers. If our readers would like to learn more, they can visit: http://www.teachildmath.com/.