# Fraction Skittles

Like many Montessori demonstrations, this one is generally given in a one-on-one situation.  One-on-one teaching is possible because most activities are designed so that children can do them on their own (after a demonstration by the teacher).

The fraction skittles are set of four six-inch skittles-a whole skittle, and skittle divided into two, three, and four pieces.  The skittle divided in half makes one skittle when put the red sides together.  The skittle divided in three pieces makes one when you put the orange sides together.  The skittle divided into fourths has matching green sides.

This lesson assumes that the child has been given the lesson with the apple.  The child that is given this lesson is generally four to six years old.

With the skittle materials, the child masters the names "whole", "half", "third" and "fourth".  The teacher supports this mastery with the three period lesson, which Montessori took from Seguin.  The purpose of the three period lesson is to teach children the names of things.  Below is Montessori's description of the three period lesson using the color tablets described above:

"First Period.  The association of the sensory perception with the name.

For example, we present to the child, two colours, red and blue.  Presenting the red, we say simply, 'This is red,' and presenting the blue, 'This is blue.'  Then, we lay the [tablets] upon the table under the eyes of the child.

Second Period.  Recognition of the object corresponding to the name.  We say to the child 'Give me the red,' and then, 'Give me the blue.'

Third Period.  The remembering of the name corresponding to the object.  We ask the child, showing him the object, 'What is this?' and he should respond 'Red.'" (Montessori, 1964, pp. 177-178)

Further, "there exists a period preceding the Three Periods of Seguin-a period which contains the real sense education." (Montessori, 1964, p. 178) Through the matching activities, the child learns to distiguish red from blue.  It is only after this that the names of the colors should be introduced.

### Design Implications

Make sure the child recognizes a thing before you try to teach the name of that thing.

Provide support for autoeducation.  Nowadays, this support is generally called "scaffolding".  Montessori called it "control of error".  The skittles are color-coded (halves red, thirds orange, fourths green).  This is actually a pretty lame version of control of error compared to lots of other Montessori materials.

There is a whole class of materials that can be introduced with this approach.  Here are some feedback ideas that can be taken from this them:

The idea behind scaffolding is to provide a temporary support.  After some initial period, the scaffolding should then fade.  Here are the kinds of fading that do or could take place in Montessori environments:

• From reliance on cues to reliance on memory.
• From having representation provided (this is.) to selecting representation (which one is.) to generating representation (what is this?)
• From control of possible moves (i.e., can't proceed or complete activity without required moves) to guidance through sensory feedback
• From direct sensory feedback to indirect feedback.  For example, from manipulation of the golden beads and numerical cards (https://www.ux1.eiu.edu/~cfsjy/mts/math/4-6.htm) to working only with cards or pencil and paper.
• From teacher demonstrating task to teacher supplying means (resources, plans) and ends for completion of task to teacher supplying ends (goals) only to child pursuing self-selected goals with independently obtained resources

Golden rule of fading: There must be some payoff for the child to let go of the scaffold.

When the child is given the opportunity to engage in autoeducation, the cost of mistakes is reduced because they are private.  When the exercises are short exercises that involve direct manipulation of objects, costs of mistakes are further reduced because it is easy to reverse or take back moves in order to recover from mistakes.

When the child is allowed to select an activity on her own, the reward for participation in the activity is increased because she is doing an activity that is personally meaningful.