“To attain knowledge, add things everyday. To attain wisdom, remove things every day.” ― Lao Tse.
I know, if you just completed your teacher qualification or if you are fairly new to the profession (less than 2 years) your answer would likely be a very strong “NO! Students should be taught the concept of multiplication and not just recalling facts!” Am I right?
Well, this was me in my first three years or so of teaching. But when I started teaching 14-year olds who did not know their 3-times table much less the entire 12-times table, I took a sharp U-Turn and here is my reasoning:
There are many good literature on educators suggesting that students should or should not memorise their multiplication table. Those who are against it seem to suggest that this limits students understanding of the concept of multiplication and that learning by rote may do more harm than good (I agree to some extent example when learning about area and perimeter). Whereas, those in favour of students memorising their multiplication table explains that this ability is fundamental to future success in mathematics. This I agree with 100%. I think some things, you can learn the facts first, then understand the whys and hows later. So, perhaps now, during this period of school closure, students can learn or recall their times table?
In the book I am currently reading, How To Teach For Mastery by Dr Helen Drury, Dr Drury compares the teaching strategies of countries in the East vs those in the West, countries such as China vs United Kingdom and what the data from PISA tells about high performing students. On page 119 her extensive research summarizes why memorising facts can be particularly helpful:
“Quick recall of number bonds, tables and key formulas is vital for problem solving. Students need to spot links, patterns and have an idea of what could be done to tackle a problem. We need students to have rapid recall of certain key number facts, and to be able to use these to calculate efficiently. Speed and memorisation are therefore essential for high-level mathematics but they are not the only very important skill.”
In my 7+ experience of teaching, the students who know their times-table usually progress so much faster that those who had to stop to draw circles or who had to write 3 × 9 as 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 or on the good days as 9 + 9 + 9. Now, while these were mainly acts of low ability sets, they were significant enough to spot the huge gaps in attainment. Gaps that will continue to widen among disadvantage children if they leave primary education without such a vital skill as knowing their multiplication table.
Consequently, both breadth and depth of teaching would often have to be put on the back seat while you addressed the basic prerequisites. So what do you do in these scenarios? How do you teach a lesson on factorising to a year 9 or a year 10 class when there is an issue with students not knowing or recalling their times table?
1. Secretly (if it is a mixed ability class) give that student a multiplication table to ’study’ at home? (Just to let you know, the student may still be embarrassed even when this is done discreetly)
2. Give all the students a multiplication table to ‘study’ at home? (In the case where it is a low ability class and majority of them struggle with this skill).
3. Ensure that you have the multiplication table mounted in your classroom….and hope they will ‘cheat’ or actually look up at the chart and tell you the correct answer?
4. Teach them the concept of repeated addition and hope that they will apply it to other situations?
I am not telling you what to do? After all, I am but one teacher who simply read and experiment in my classroom. But, teachers of years 6 and secondary school, I am genuinely interested in what you actually do when faced with this problem.
Needless to say, my husband has been teaching our 3 year old daughter her multiplication table and even I could not have convinced him otherwise (not that I want to).
As always, I look forward to hearing and learning from you as I aim to #bettermybest.