The mental representation of concepts: interview with Giacomo Stella

The mental representation of concepts: interview with Giacomo Stella

The number line function, multiplication table and interactive equivalence bar? “Operationalize concepts”.

We asked Professor Giacomo Stella, creator and scientific director of the SOS Dyslexia Centers, about the function of interactive tools such as the Number Line, the Multiplication Table and the Equivalence Bar. The goal of these tools? “Operationalize the concepts”. has developed in collaboration with Giacomo Stella three interactive voice-guided tools to support children in learning operations (addition, subtraction, multiplication and division) and equivalences: the Line of Numbers, the Multiplication Table and the Equivalence Bar interactive.

In interactive and printed versions, they are an essential support for learning not only for students with SLD (Specific Learning Disorders). In the words of the professor, “these compensatory tools provide fundamental support in the process of operationalization of concepts”.

Doing operations and counting backwards with the Line of numbers

The number line is a linear graphical representation of the numbers from 0 to 20 that allows you to carry out the operations of addition and subtraction in a simple and fun way and also helps in counting backwards.

Thanks to the number line, children can rely on a mental representation of the numerical sequence, which "becomes fundamental in processes that require greater application and that do not end in routine processes or automatic blocked series or sequences learned by heart (eg . nursery rhymes, days of the week, months of the year). The line of numbers is a tool that allows you to build the concept, that is the representation: the child constructs a mental representation of the sequence of numbers after making access to the sequence of the numbers automatic. The child is able to count backwards and replicate a sequence because he "looks" into the mind and resorts to a mental representation of the number line. If a 6-year-old child is unable to count backwards from 10, it means that the sequence of numbers has not become a stable mental representation and therefore the line of numbers drawn on the sheet supports this weakness in the representation ".

The Multiplication Table as a matrix representation of numbers

The multiplication table allows you to carry out multiplications and divisions, both with operations proposed by the computer and for free consultation. Thanks to the multiplication table, the matrix display of numbers is immediate.

"Today, the tables are learned as sequences independent of each other, but this is not the case, as they are not independent. This involves a "parenthesized" learning, that is, children learn the sequence without contact with everything around it ".

Here is an example of the professor: "If I ask a child for the 4 times table, he answers 4, 8, 12, 16, …., 28. If I ask a child for the 7 times table, he answers 7, 14, 21, 28…. However, the child is often unable to recognize the relationship between the different sequences (he does not understand why the number 28 is present in both the 4 and 7 times table). This happens because the tables are learned as independent columns, as encapsulated and distinct neuronal tubules ”.

“The tool of the multiplication table therefore allows the visualization and matrix representation of numbers. The table is an important support as it integrates procedural memorization and favors semantic memorization which helps to develop the concept ".

The Equivalence Bar to operationalize the concept

The equivalence bar is the latest interactive compensatory tool introduced on the Redooc platform to understand the mechanism underlying the equivalences. Thanks to immediate feedback and help with repeated errors, students are able to understand the steps.

The goal is to ensure that children can "have a support in working memory and the representation of concepts. This approach is in fact fundamental to operationalize and make visible a concept that is not yet well fixed in the mind ".

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