There are some questions I am asked frequently. This one is no different. Comes often.
"How do you get children to master multiplication facts?"
The question is usually followed by a great sigh of, "I've tried everything."
Multiplication is a common frustration for parents. Mike and I hear concerns at evaluation time. I read worries on Facebook. Parents inquire while visiting my booth at conventions. And, I find the question in my inbox.
And, we are walking the journey with you!
We have personally faced this problem, several times.
Others have, too. YOU are not alone!
Developmentally, children must understand the concept of multiplication before they will understand what the symbolic (the number and signs) equation means. After understanding the concept and hence what the symbolic equation represents, children can begin mastering the facts. In other words, children must understand the language " ____ groups of ______" and the corresponding numerals before mastery will make sense (unless, of course, the goal is to simply master the facts).
Based on our experience and the experiences of those whom we have coached through the process, the answer to the question about mastering multiplication depends on the child. In other words, every child has a unique developmental time table and there is no one right answer as to how to master facts (there are however, many opinions). In addition, some who once mastered the facts forget over a year's time and need review.
Though we all hope for an easy answer, one that works for every child, over time. It's just not so.
At least it hasn't been for us or the folks we know.
Thankfully, however there are many options and ideas from which to choose when working with children to master facts.
Start with the concept. Go back and review it when needed whether several times in a lesson, several times a year or once every year. The learner must innately understand (even see a picture in the mind, for visual learners). Remember, the wording to internalize is "(a number) groups of (a number)". For example, a dozen eggs can be 2 groups of 6 OR 6 groups of 2.
Draw a picture. Drawing a picture is a great help, especially for visual learners, though it can be beneficial for other learners as well.
Find it in life. Look for examples of multiplication in real life where math can be taken off the page and made relevant, meaningful. This is especially important for kinesthetic learners. Examples are a box of 16 crayons divided in 2 rows, 3 four-legged animals, 2 tricycles, etc. This strategy was helpful for all of our children.
Make a visual or model. Outlining arrays (rows and columns of squares) on a piece of graph paper, drawing a picture for a math problem in a lesson, counting objects to represent an equation, really anything a child can relate to and then save as a picture in the mind.
Skip Counting. In our twenty-one years of home education experience (as well as experience with hundreds of homeschoolers through mentoring and annual evaluations), skip counting does not always equate to understanding the concept multiplication. The child must be able to have the memory and the processing abilities to convert and apply the information. Skip counting worked for one of our learners.
Turn Math into an Art Project. For our creative learner who likes to cut and paste, math is palatable when accompanied by color and flare. Last Thanksgiving we enjoyed making multiplication turkeys. Placing the 8 facts on colored feathers not only added festivity to our day but allowed quick access to troublesome, hard to remember facts.
Read about Math. We have had great success finding math-related books in the non-fiction section of the library. In fact, I have shown my children where the math books are shelved to give them greater independence as they dig deeper into math concepts introduced at home or in their math program.
Triangle Flash Cards. For one of our learners loved this idea, probably because it presented as more of a game than flash cards. Regardless, we were pleased with the results. Sherri Seligson explains her version of DIY Triangle Flash Cards on her blog, Just Extraordinary.
Whole Equation, Including the Answer. "Are you kidding me?" That was my reaction to this method. For some learners we know, writing the fact (the whole equation factors and product) on flash cards and then verbalizing the equation aloud was the only technique which yielded mastery.This approached worked for one of our learners.
No matter which strategy or technique you choose, there is an easy, natural sequence which helps learners feel successful, almost immediately. Mastering the facts in this order is helpful in terms of ease and building confidence: 1s (and number times one remains the same), 2s, 3s, 5s (perfectly illustrated with nickels), 4s, 10s (pull out the dimes), 6s, 7s, 8s, and 9s.
For example, if using flash cards with answers (full equation), write all the 2s on 3x5 cards. Mix up the cards. Set a timer for two minutes. have the child go through the stack verbalizing the full equation on the card and moving the card to the back of the stack. Repeat through the deck until the timer rings. Repeat the activity once or twice a day for one week. To evaluate whether mastery is emerging, give an oral drill. If all the facts were mastered, move to the next fact grouping.
Check Off List. Using a check off list, learners can cross out mastered facts. A dry erase check off list has worked well in our home. Once we practice drilling the facts with verbal and visual cues (using cards mentioned above) twice or three times a day for several days, we do an oral drill. Sometimes we do this while driving to a field trip or while enjoying shade outside under a tree. If the leaner knows the answer to the fact I give, we exchange high fives (if I am not driving!) and I tell the child they can cross the fact off the list. If we drill in the car, we high five and mark off facts when we arrive home. Checking off facts is always a CELEBRATION!
I must add, I was not a fan of flash cards UNTIL I had a child who could only learn multiplication with this strategy. Though I was hesitant, I wanted my child to learn as desired. And, at the child's request, I tried and was pleasantly surprised. We did, however have to review for several years.
You may be on the mountain (as it seems) to mastery. Take courage! You are not alone.
We are walking the journey together.
Preschool to high school and every stage in between.
A handy tool offering learners a visual picture of mastered facts. When a fact is mastered, the child uses a dry erase marker to cross out the fact.
Master the fact, cross it out!