Abstract:

In his constructionist theory, Papert pointed out how learning is most effective if we resort to the construction and manipulative use of cognitive artifacts. The latter can be defined as those objects we create that are intended to support, reinforce or enhance cognition (Hutchins 1999, 126) and, as stated by (Heersmink 2013, p. 465), “they make us more powerful and versatile thinkers, but also because they shape and transform our cognitive system and cognitive practices”.

This paper describes the construction of a simple cognitive artifact, a paper calculator, that can support primary school children in performing multiplication and understanding the properties of this operation. The calculator is made by folding a square sheet of side 10 cm and becomes a dynamic object that can be manipulated by students. The material used and the ease of construction makes this tool feasible in any school.

This cognitive artifact has numerous potentials. First, it is a visual and tangible tool that is personally constructed by each student, who also gets to use rows and columns of the arrays oriented according to his or her learning style. Its use is based on the ability to quickly change its shape in relation to the calculation to be performed, and the immediate construction and visualization of the result make it extremely effective in use.

The artifact also makes it possible to visualize "geometrically" the classical properties of multiplication and the properties related to the multiplication of odd and even numbers. These properties can be "discovered" in a hands-on way by learners who have the opportunity to work collaboratively. The paper calculator, through the possibility of manipulation and direct verification of results and properties, is a practical aid in the transition to abstraction. In addition, like other folded paper objects, handling reduces anxiety while performing tasks.

Finally, the calculator can be used as a dispensatory, inclusive tool (not a substitute) in the case of students with non-severe dyscalculia, avoiding heavy use of the electronic calculator, and taking advantage of their expertise in memorizing particular products.

The paper calculator has recently been successfully proposed during some training courses for elementary school teachers and is being tested in classrooms.

Keywords:

Math learning, cognitive artifact, hands-on activities.