Before I begin today’s post, I must thank my brother, Doug Perry, for his generous gift to my GoFundMe campaign. I wish I were the one helping my younger brother, but life has a way of flipping things around on us some times.
Now, I know there are many people out there that will read today’s headline and immediately say something to the effect of, “Well, that’s the way I learned it and that ought to be good enough for kids today.” Well, children used to have to suffer through scarlet fever, mumps, and polio too, but nobody uses the same logic in relation to taking their kids for their immunizations.
The fact is that children should not have to suffer through the boring, archaic ritual of the multiplication table. And while we are at it, it is called a multiplication table and not a times table. One part of the Common Core Standards is to promote accurate and precise language regarding mathematics. One can multiply numbers, but they do not times them. Every time I hear a teacher or parent say that, it makes me cringe.
While I know many of you used the multiplication table, you probably also remember how much you dreaded it when the teacher laid it in front of you. Math should not be a tedious, nightmare inducing endeavor. Besides, the multiplication table does not really help students memorize multiplication facts, it merely helps them remember them in a very specific order. That is why many adults today can fill out the table in a matter of 30 seconds, but when asked what 9 x 7 is, they take more than 20 seconds to remember that one fact. The multiplication table does not make multiplication automatic, merely formulaic. The other issue with the multiplication table is that if a student writes down a wrong answer and it is not caught right away, they continue to practice it that way and then they have remembered the wrong answer for life.
What can be done instead? I have used two others methods with great success:
Taped Problems: This technique uses a piece of paper with anywhere from 25 to 144 facts on it. The teacher pre-records an audio file (mp3) that reads each fact, pauses for 1-2 seconds and then reads the answer to that fact. This method offers a couple of benefits. First, if students do not immediately know the answer, they can wait for the recording to tell it to them. This prevents students from learning incorrect answers and prevents them from feeling the anxiety of not knowing the answer. Additionally, if a student knows the answer and can write it before the recording, they are given a sense of victory, which boosts their confidence. Secondly, the mp3 file can be emailed home with extra answer sheets. A few minutes of practice each night is easy for both parents and students and no one has to hear complaints about the dreaded multiplication table. As students’ skills improve, the teacher can re-record the audio with less time for each answer. I know, I know. That is cheating. You gave them the answer. I want them to have the answer. Having the answer allows them to learn the answer and remember it forever. Before I started this intervention with a 5th grade class, my students averaged 68% accuracy for 100 problems and it took them an average of 9 minutes to complete all the problems. Now, these students had all had the multiplication table the year before and had supposedly “mastered” multiplication, but all they had mastered was a chart. After using taped problems for 2 minutes per day in class, and 4 minutes per day at home, the average accuracy rose to 98% and the average time to complete was 2 minutes and 11 seconds. The students’ confidence level shot up, their test scores increased dramatically, and they didn’t dread multiplication like many students do.
Cover, Copy, and Compare: This method uses a piece of paper folded in half lengthwise. The multiplication facts or problems are written on the front half of the sheet and students go down the column filling out their answers. If they are unsure or just want to double check that they are right, they merely need to flip up the folded paper to reveal the problems with answers below. Again, this prevents anxiety for students and ensures that facts are not erroneously recorded on paper to be committed to memory. Also, students love this because they have the answers and it seems almost too easy. Yet, before they know it, they have learned all their facts and many can answer any multiplication fact more quickly than their parents. It was always so thrilling for me to hear students tell me they had challenged one of their parents or older siblings to a multiplication race and won rather easily.
Many times, in education and in life, we do something because that’s the way it has always been done. However, just because something appears to be tried and true, does not mean that it is the best way. So, the next time you think about using the multiplication table, don’t. Throw it out or burn it. Taped problems and cover, copy, compare will take more initial work on the teacher’s part, but it will pay huge dividends in the long run. Your students will thank you for it.
I recently completed my PhD in Education (Curriculum and Instruction) at the University of Wyoming. I have published multiple articles in peer reviewed journals and have a book chapter coming early next year. I aim to explore issues of privilege and equity of education, especially as they pertain to STEM education.