We must recognize it: learning the tables is one of the educational challenges that frightens more children and parents in primary school. Almost as much as reaching the erect station or starting to eat solid foods
There are many ways for Teach the tablesfrom the most fun to the more demanding and complex ones. Any technique is chosen for children, the most difficult rock remains: to learn them by heart.
Most of the scholars on the subject agree in recognizing theimportance of the tablesfundamental both to speed up arithmetic procedures and as a basis for higher order mathematical learning. But the tables are not just for this; they can in fact be very useful in the daily life: from activities in the kitchen, to shopping, from spending to the supermarket, to calculating the house budget. In the western world, moreover, they are requested in numerous tests for the transition to subsequent school levels or to access university courses with limited number.
Certainly, as the professor and mathematician Giuseppe Rosolini reminds us: “A good with the tables is not necessarily good in mathematics, and vice versa (…) but the tables serve as the alphabet is needed”. That’s why their importance should always be recognized. So let’s see what are the Better methods to make children learn the tables.
How to teach children’s tables?
The Traditional method to do Learn the tables It provides for the mnemonic repetition of the same by the child for a number that is not well identified in times. This type of method requires considerable commitment and effort from the baby and often leads to modest results.
Among the methods for teaching the most used tables Today we find those who, responding to the neuroscientific discoveries on the link between movement and mind, foresee the involvement of the body and hands in learning processes.
In Steinerian schoolsfor example, the tables are learned at a wheelbase or beating their hands in pace. The psychomotor method, also used in some Montessorian schools, instead provides for the association of a scoreboard with a specific gesture. According to these approaches, children find their own rhythm of movement and, thanks to repetition and body involvement, acquire safety in the operations.
Among the techniques to learn the tables we find the one used in Asian countrieswhere a table is studied similar to the Pythagorean one (or table table), but containing half of the numbers. In the Chinese table, 0 and 1 are eliminated (it is given as awarded that each number multiplied by 1 remains equal to itself and that each number multiplied by 0 is equal to 0) and all the redundant calculations of the Pythagorean table. Thus, taking advantage of the commutative propertyimmediately teaching children who, for example, 3 × 5 = 5 × 3; In this way they do not study it 2 times and the mnemonic load goes from 81 to 36 data.
Others Tricks to learn the tablesquite used in Italian schools, are:
- The analog method of Camillo Bortolatowhich provides for the use of specially prepared tools and which, thanks to associative learning, images and hook sounds, accompanies children along the path of storing the tables, helping them to create a mental image of the same even before memorizing them.
- The Indian method. More than a real method, it is a trick to learn the tables faster than Leonardo Fibonacci (Italian mathematical of the XII century), which resumed it in turn by vendic mathematics texts. It plans to learn the tables Until 5while for calculating the subsequent ones there is the use of the following strategy … Suppose we want to calculate 7 × 8. Five units are removed from both factors (7-5 = 2 and 8-5 = 3), then two fingers rise on the left (i.e. 7-5), on the right hand three (8-5). They add up the fingers raised and you have the tens: 5. Then the fingers that have remained lowered, then three in the left hand and two on the right are multiply: 2 × 3 = 6; This is the second figure that must be added to the dozens. Result: 56. This trick can be used for all tablets after 5.
Is there a Montessori method to learn the tables?
Teach the tables with the Montessori method It provides for a long journey that begins at the children’s house, where pupils learn to know the operation of multiplication using special materials that allow you to concretely understand the process of repeated addition.
In primary school students continue to work on the multiplication process using multiple materials, since the goal of Maria Montessori was to provide the child different visions of the same phenomenon or concept. In this way, learning the tables becomes something more complex than mnemonic repetition alone.
Next to the material aimed at acquiring the “sense of number”, As the mathematics Jo Boaler would say, we find other faces to storing products. Among these, the best known is the storage table: A square tablet with a hundred grooves, in each of which can be placed a pearl. Above, above each pearl column, the numbers from 1 to 10 are printed. In the middle of the left side of the tablet there is a hole where you can insert a cardboard with printed on one of these numbers. This cardboard represents the multiplying and must be changed as you proceed in the calculation. At the top left of the tablet there is a hole that contains a token to be placed on the numbers. The tokens will change from time to time placed following the scoreboard in action. There is also a wooden box containing 100 loose pearlsnecessary for the exercise. Let’s do a example …
If the child has to multiply 3 by 1, he will place the red token above the number 1 and then will have 3 pearls in the first three vertical grooves of the 1 column. To multiply 3 by 2, the child will move the token above 2 and place 3 more pearls below 2. He will proceed in this way until he concluded the 3. Special modulesalready marked with the operation. In this way, all will have to do is report only the result of multiplication.
Each child has Ten modules for each scoreboard. There Table of multiplication It is just one of the many materials designed for multiplication; The children, working simultaneously with each of them, have the opportunity to analyze, reflect, compare and memorize the proposed mathematical concepts, creating in the mind, as Stanislas Dehane believes, “a rich library of mental models of arithmetic”.
Learn the tables with the Montessori method It is not something boring or terrifyingbecause children almost don’t notice that they are studying them, and instead they are at work with materials which favor, in different ways, the repetition of the sequences of the tables: from the material of the decanomial (graphic representation of the Pythagorean table), to that of short chains and cubes, to the most specific tables of multiplication.
Games to learn the tables
Can you learn the tables by playing? Among the games to teach the tables To the children we find the classic card games, but also real motor games: from the treasure hunts that use the tables instead of the riddles, to the relays, to the obstacles routes that plan to find and pair the operation to the correct result.
Among the static games we find the Tombola of multiplicationwhere multiplications and not single numbers are extracted, or The naval battle with the tables as coordinates.
It is also possible to propose nursery rhymes, cantilene and stories. In this case, however, it would be good to verify that the child understood the process that leads to the scoreboard and does not store the simple nursery rhyme without understanding the underlying mathematical calculations.
Another game is the Mandala of the tablesa material inspired by the Montessori method and also used in Steinerian schools. It is a circle with ten pegs that can also be made at home with cardboard, wood or polystyrene. Each Piolo is marked by a number that goes from 0 to 9. Equipped with string and starting from zero, you start repeating the scoreboard, placing string in the numbers in succession.
For example If you are doing the score of the 2 from 0 from 0 counts up to 2 and pass the string, from 2 counts again adding 2, you will arrive at 4 and pass the string, then add 2 again and you will get to 6 and so on until 20. You will get a different geometric shape depending on the studied scoreboard. The mandala of the tables is an attempt to materialize Abstract concepts, anchoring numbers to the geometric shapes made.
