There can be no progress in arithmetic without a sound grasp of the basic multiplication facts. Waldorf methods enliven their teaching, help learners at every level of ability, and can make regular practice quite enjoyable.
Much repetition is necessary to learn essential multiplication facts successfully. This is done in brief, focused practice sessions across the Lower School years.
REGULAR PRACTICE
In the first three classes, such practice can be integrated in the Morning Circle; not in every Main Lesson, but from time to time, as appropriate.
In the Middle School years, pupils are expected to spend time at home rehearsing multiplication facts they feel uncertain about – usually the middle regions of the 7-, 8- and 9-times table.
But it is a rare child who takes this homework practice seriously. Mostly they “forget”, finding it hard and unappealing. As a result, progress in arithmetic is hampered, confidence plummets and dislike of the subject grows.
To counteract this negative trend, class teachers use exercises that involve the whole group in rote learning. Changing form in step with child development, these exercises aim to imprint the basic multiplication facts on everyone’s mind.
Memory is strengthened through repeated chanting, accompanied by some form of activity. The senses of hearing, movement and balance are addressed, avoiding intellectual strain.
Note: This non-visual approach can be particularly helpful to those with special learning needs.
Hearing a multiplication table recited by the strong class chorus while participating in a familiar sequence of movement takes the weakest members of the group along. It gives the support they need without an embarrassing focus on their slow learning.
Class 1
In the second half of the year, after the four basic operations have been introduced, the multiplication facts of 2, 3, 4, 5 and 10 can be introduced and explored in various ways:
- Holding hands as a circle, chant in unison and hop with both feet on the numbers of the table.
- Facing forward as a circle, chant in unison and step with a stamp on the numbers of the table: “One times 2 is 2, two times 2 is 4, three times 2 is 6 …” etc.
- Then walk backwards, stamping, clapping and chanting the same sequence in reverse.
- Clap only the even numbers, but chant and stamp them all, forwards and backwards.
- Stamp every number as before, but say only the even numbers out loud.
- Hop on one leg for odd numbers, and on both legs for even numbers (like hopscotch).
- Two groups hop alternately, chanting their odd or even numbers.
Since Class 1 children absorb things so easily through chanting, movement and imitation, these rhythmic circle exercises prepare the ground for the following year’s multiplication work in an enjoyable way and are successfully recalled in Class 2.
Note: From the start, every table is learnt not to 10, but to 12 times the number.
Class 2
The multiplication tables of Class 1 are recalled and rehearsed in turn. Practise the 2- and 4-times table one week, the 3- and 6-times table a week later, and then the 5- and 10-times table.
Grouping them in this way reveals their connection and logical pattern. These patterns can be studied in a corresponding Maths Main Lesson on the Number Grid, where the 11- and 12-times table are introduced.
THE MULTIPLICATION CIRCLE
This highly effective practice method has everyone facing a partner, chanting, for example, “One times 4 is 4!” and clapping hands together on the product.
Moving on with a small curve to the right, all meet their next partner. They chant and clap, “Two times 4 is 8!” – Moving on, all chant and clap, “Three times 4 is 12!” – Moving on, etc. … up to 12 x 4.
Then all turn to face the opposite direction and do the same sequence in reverse.
A multiplication table is practised several days in a row at increasing speed. Then, for variation, only the main numbers are chanted and clapped around the circle: “4 … 8 … 12 … 16 …” etc., and in reverse.
Note: Doing things in reverse is essential for strengthening the life forces connected to memory.
Class 3
Familiar multiplication facts are recalled in turn, and established patterns of practice are applied to the more challenging 6-, 7-, 8- and 9-times table.
At some point during the year, a new exercise brings an enjoyable challenge:
THE JUMPING ROWS
Standing at their desk, each row of children in turn chants the next number in unison while doing a 180-degree jump-turn to face the row behind them, or – in the case of the back row – the back wall. The front row, calling the next number, jump-turns to face forward once more, and each row in turn follows suit. Again, this is done to 12 times the number, and then in reverse.
The aim is to unite chanting and jump-turns in an unbroken flow across each row and across the class, going a bit more swiftly each day. The same table is rehearsed several days in a row before moving on to the next one, but it is good to move the starting point randomly between the rows.
The children want to belong to the group that knows all ‘their’ numbers really well. Those who don’t are carried along by the vigorous chorus and thus learn the sequence more easily, whereas the most able individuals enjoy displaying their knowledge in a strong voice that is helpful to their group.
After several days of repetition, a new challenge is added: One capable volunteer from each row is chosen, and together they perform the exercise as before, but this time as solo voices, observed and admired by the group.
A couple of days later, the teacher points to a child in the first row to begin the chanting for all those who sit directly behind her – the ‘vertical’ row – who are now to perform the sequence solo.
Note: This puts the necessary gentle pressure on dreamers who like to leave the work to others, and also on those who need to rehearse the multiplication facts more diligently.
End the exercise by asking the class a few random questions, for example, “Six times 7 is …? – Nine times 7 is …? – Three times 7 is …?” etc., consolidating what was rehearsed.
Class 4
Now a new element is added to the Jumping Rows exercise as multiplication tables are practised in groups to the power of 10. As before, this is done forwards and backwards, first in unison and then individually.
The 2-, 20-, 200- and 2000-times tables are rehearsed together for a couple of days. 3, 30, 300 and 3000 follow … continuing across several weeks to 9, 90, 900 and 9000.
Your random questions at the end are also getting more challenging: “Twelve times 4 is …?” – “Eight times 40 is …?” – “Three times 400 is …?” – “Five times 4000 is …?”
Those who know raise a hand, and someone is called on to answer.
Note: This is practice, not a test, and yet it shows reliably who knows the multiplication facts.
Daily repetition soon sees a notable increase in raised hands and confident answers. In this way, the same multiplication table can be repeated several times daily across the week without getting boring.
And at this ‘Viking’ age, the activity is carried by an enthusiastic energy that naturally wanes towards puberty. Even so, the Jumping Rows can be used in later years to rouse sleepy teenagers.
Note: I had the parents try this exercise at a Parents’ Evening. It was slow going, felt heavy and uncoordinated, without any uplift. When they saw the class perform the same exercise at an Open Classroom event soon after, the parents were blown away by the smooth flow, joyful energy and perfect synchronicity which they had failed to achieve.
A Number Study Main Lesson block leads quite naturally to bookwork on the multiplication facts, in connection with the resulting sequence of square numbers.
This is the perfect moment to let each pupil produce two personal multiplication charts that are laminated. One is kept in the desk for use at school, the other is taken home to help with future Maths homework:
Class 5
By Class 5, all multiplication facts up to 12 x 12 ought to be known by heart. The ongoing work with fractions and decimals demands a good grasp of the basic times tables.
But despite regular practice in class, it is seen that not every member of the group has them at their fingertips. How to fit a bit of extra practice into the timetable? … In the weekly Maths lesson, for example, because it no longer fits into your densely packed Main Lesson.
Class 6 & Class 7
Pupils who joined the class in recent years from other schools usually struggle with arithmetic in general, and multiplication tables in particular.
To reinforce the message that knowing the essential multiplication facts is to be taken seriously, one can now introduce an age-appropriate challenge:
THE MULTIPLICATION SPEED TEST
- On two consecutive days each week, at a suitable point of the morning, hand out loose paper and let the class number a list from 1) to 10).
- Then dictate ten random multiplications, pausing no longer than is needed to write down each result in turn. Just the product, nothing else!
- The first five multiplications are fairly simple. For example: “Twenty times 3 … Five times 7 … Four times 8 … Two times 9 … Ten times 11.”
- The next five are more challenging and address the known weak spots: “Seven times 8 … Six times 7 … Eight times 9 … Eight times 12 … Eleven times 11.”
Important: No time is given for working it out. The answer must be known instantly.
Then the desk neighbours exchange their sheets. As you announce the correct results in turn, or let volunteers contribute them, all mark each other’s work, write down the total score out of ten and convert it to a percentage. (My class added encouraging written comments, unprompted.)
Those with a score below 90% write their name on a whiteboard you keep for such administrative matters. They will be staying in for 15 minutes of supervised rehearsing at lunch break, since they clearly did not put in the requested homework practice.
The result of this speed test is that the scores improve rapidly across the class. On the other hand, lapses show when someone is resting on their laurels or has been absent.
Important: Keep a class list of dates and scores to assess progress, to present factual evidence to doubtful members of the class or concerned parents, and for your end-of-year reports.
A welcome side effect is that arriving pupils voluntarily take out their multiplication chart for a bit of focused revision before school starts, quizzing each other to get 100% on the next speed test.
All are pleased to see that the fruits of this eager practice are instantly noticeable, and your lunchtime ‘practice group’ melts away like snow in March.
Comments are welcome, so don’t hesitate to share experiences, questions and feedback below.
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