## To do is to know mathematics

**Dor Abrahamson**, Ph.D., A member of the Matific Academic Board, Professor of Learning Sciences & Human Development in the Graduate School of Education, at the University of California, Berkeley.

Children learn by doing. It is an active part in the acquisition of their own mathematical knowledge. In this article, Prof. Dor discusses one of Matific's pedagogical principles that focuses on providing a nurturing and engaging environment for children to build conceptual understanding in a guided self-discovery process.

What do kids do, when they do mathematics? They often write numbers and other signs on paper. They also use various methods they’ve learned to work these symbols and get the information they need. But is that all?

Many researchers in the field of cognitive developmental psychology believe that children’s conceptual learning begins the moment they interact with objects, whether material or virtual. As they manipulate the objects, children keep adapting how they perceive the objects. Doing that, in turn, enables them to manipulate the objects even better, and so on. These interactions form in the mind new patterns called sensorimotor schemes, which are reactivated when the children encounter similar enough situations in the future.

That’s why it’s so important that interactive mathematics modules are designed to foster sensorimotor schemes that both capture the essence of a concept and will apply in future encounters with new situations that require the same mathematical principle. Matific activities are created with this principle in mind. For example, "Save the Ball" activity demonstrates the idea in the context of basic arithmetic.

**Save the Ball Missing Addends: Totals Within 10**

Children use a number line model to find the missing addend in order to make a given total. Each spring is labeled with a number that shows the distance and direction the ball will travel. Children select the correct spring so that the ball makes it into the hole with the net.