Kara D. Lubin

SDC Teacher, McKinley School

Corona, CA

As a Special Day Class teacher, my job consists of modifying the general education curriculum to meet the specific individual needs of my students. Disabilities in the class range from students with mild autism to students with specific learning disabilities who are transitioning back to a general education classroom. Needless to say, there is an extremely wide range of abilities in the class I teach. The one area in which the entire class struggles, however, is the mastery of multiplication facts.

Dina, a student with Williams Syndrome, came to my class in 1998 as a 4^th grader. After extensive reading about WS, conversations with Dina’s parents, and my first-hand experiences with Dina, I became aware that mathematics was clearly NOT a strength of individuals with WS. Armed with this knowledge, and fully aware that it might be quite a frustrating task, I was determined to give Dina, at the very least, a functional knowledge of mathematics. My ultimate goal was to keep her with her same-age classmates during math instruction. I know that this was Dina’s goal, too, for she wanted nothing more than to be able to participate successfully in class.

Dina mastered strategies for solving her addition and subtraction facts with the aide of Touch Math concepts. Touch Math involves placing imaginary touch points on each number 1-9. The number of touch points on each number corresponds to the number itself. The student simply counts forward or backward while touching the points on the given number first with a finger, and later with a pencil point. If a student can count from 0-19 and back, all addition and subtraction problems are accessible.

Because Dina must see and touch addition or subtraction problems she is given, transfer of this knowledge outside a structured setting has been a problem for her. In class and other structured settings though, she is able to carry, borrow, and solve simple word problems. Frequent reteach and review is constantly necessary. Nevertheless, we were all quite proud of Dina as she ended her 4^th grade year…Now it was time for us to teach Dina multiplication and division facts. Uh-oh!

I decided to use "Memory Joggers" to teach Dina her multiplication and division facts. That program was developed by Donnalyn Yates, a 3^rd grade teacher from Irvine, California. It is based on the idea that most children learn visually, and need associations in order to facilitate long term recall of information. According to Yates, the Memory Jogger system uses numbers and words, which rhyme or are shape-related in order to stimulate memorization. Each number 0-9 has a corresponding visual object. For example, zero looks like a mouth which "eats" all other numbers, three is a tree (rhyming), eight is a snowman (shape-related), and so on.

There are approximately 25 stories to read, visualize and recall using the 0-9 visual objects as characters. The stories teach the student a fact family, such as 9, 7, and 63. The family is permanently associated in the child’s mind. For example, if the child is given 9 x 7=?, then the missing number is 63. These stories also teach division facts. If the child were given 63 divided by 7, the missing number would be 9. Once the fact family is learned, the student is able to remember both multiplication and division facts simply by recalling the missing number from the fact family.

The Memory Joggers stories are for the threes, fours, sixes, sevens, eights, and nines multiplication facts. These are the facts that tend to give students (and teachers!) the most trouble. The answers to the multiplication facts also have a "sound alike" tie-in (63 sounds like "sticky tree"), or a "play on words" (81 = "ate one"). I give a sample Memory Jogger story for 7 x 9 at the end of this essay.

The zero, ones, twos, and fives are taught as a group of facts. Zero is visualized as a mouth that "eats" all other numbers, one is gum that "sticks" to other numbers, two is "shoe" which always comes in groups of two, and fives are associated with a clock face. The student is taught to count by 2s and 5s. By using the visualization stories along with the Os, 1s, 2s, and 5s strategies, all multiplication and division facts 0 –9s are taught simultaneously.

I began using this method of teaching multiplication facts with all of my students in Winter Quarter of 1998. I immediately saw results with my students with learning disabilities. The entire set of facts (0-9s) took approximately 4 weeks to completely master, and to this day, I have not seen a student use (or ask to use) a multiplication chart in my classroom. It is simply not necessary.

I knew that Dina would be able to benefit from the Memory Joggers program as we finished this unit. Before she had any knowledge of the concepts of multiplication and division, she had memorized the stories and answers to some of the most difficult multiplication facts simply by overhearing students and teachers review the stories and facts. She was so interested in fact, that we often had to move her out of earshot of these groups so she could finish her own assignments!

Dina began the Memory Joggers program in September of this year, and is keeping up very well with her same age peers in class. She is simultaneously memorizing her multiplication and division facts using the Memory Joggers program. Her visual and auditory memory is a strength, so this system has been wonderful for her. Her self-esteem is high, she enjoys math, and can’t wait for the next story. There is frequent reteach and review necessary for all of the students in her group, so she keeps up beautifully! I am also finding that Dina does not need to see the multiplication or division problem on paper in order to solve it, and there has been transfer of this knowledge outside of the classroom setting. Dina is also able to successfully participate in classroom activities and games involving mathematical concepts up through division facts. For further practice and review, Dina’s parents have been taught the program, and have been given copies of all of the stories "just in case" she needs her memory "jogged" at home. The Memory Joggers program has made these previously inaccessible concepts and facts accessible to Dina. It has been a joy watching her learn.

I am still unsure whether or not Dina truly understands the concepts she is being taught with the Memory Joggers multiplication and division learning system. She is, however, successfully memorizing her multiplication and division facts, and can solve them without having to see or touch the numbers on paper. I will use the new Memory Joggers addition and subtraction system (soon to be released) with Dina next, and hopefully eliminate the need for Dina to see and touch her addition and subtraction facts in order to solve them. Math is still a struggle for Dina. She still would much rather be in music class, and we must constantly review previously learned mathematical concepts. She sometimes becomes frustrated, and just needs to take a break. That need is always respected. After she rests, Dina returns to her group fully refreshed and ready to learn again. I am confident that Dina is putting forth 100% effort in all subjects at school. As a teacher, that is all I can ask for.