I have never been good at memorizing facts and my students aren't either. Drilling multiplication facts was an awful experience for me because even if I managed to remember them after some time of drilling, when I came back to it the next day, it was like starting all over again. I just couldn't hold onto these facts in my brain because they had no real meaning to me. They, to me then, were just random, meaningless facts. I later found out that I had dyscalculia and that was why I struggled so, and had such a hard time with math. I didn't want my children to hate math like I had, so I sought out another method. Then I found The Center for Innovation in Education, Inc.'s Mathematics, A Way of Thinking by Bob Baratta-Lorton.
"The teacher should post a large multiplication matrix where it visible to all students; access to this is the vest way for students to learn individual math facts. Each student should also keep one in his or her desk. The ready availability and frequent use of the matrix causes most students to effortlessly commit all or most of the multiplication facts to memory."
That somehow felt like cheating. Yet, when you think about it, it is not cheating, if you use it, not as a tool for testing, but a tool for practice. Students can use other tools, too, and practice with tool after tool they will eventually learn not only the time table facts but the concepts of what they mean behind it. By the way, I find it much easier for students who are beginning to use the multiplication table to use two pieces of paper to make a rectangle for the answer that is being sought. I help them further see how the matrix works by having them in the beginning count the number of squares within that rectangle, and they see that the answer in the lower right hand corner (in the case of the photo above, 24) and the number of squares is equal. It turns the table from being a chart of random, meaningless numbers to a manipulative.
I then have them work with tiles, and then cups and beans. For cups and beans, I begin with two cups and a stockpile of beans. I first tell them to start with putting 1 bean in each cup, and I begin recording while they count the beans. 2 (cups)x 1 (bean in each cup) = 2
Then I ask them to put 1 more bean in each cup and I record while they count.
2 x 2 = 4
We continue on like this for a few minutes.
Somewhere along the way, I just give them 1 instead of a set of two beans and ask them what do we do about this?At this point we talk about some numbers not coming out evenly, and then we add 1 more to make a set he can add to the cups, and continue on from there. We can add more beans or more cups as long as there is interest in this activity. In this way, young children can bridge the gap between addition and multiplication seamlessly.