PROBLEM SOLVING ACTIVITIES
WITH KNOBBLESS CYLINDERS
Kathy Carey, MAT
Charlotte Wood-Wilson, M.Ed.
Kim Quinn, MAT
• Original presentation by Bee Pape
• Former Director and Professor at Oklahoma
City University Montessori TEP
• Bee developed these activities with other staff
while teaching 3-6 year olds at Casady School
and as a Professor at Oklahoma City University
Maria Montessori (1964) quotes
Seguin
• “. . . To lead the child from the education of
the senses to ideas.”
Piaget
• Piaget identified the knowledge that the child
gains from sensations and observations
Physical Knowledge (cited by Kamii, 1985)
• Piaget labeled the kind of knowledge that
leads the child from sensations to ideas
Logico-Mathematical (cited by Kamii 1985)
• He also suggested that children should be able
to experiment and construct their own
knowledge
Levels the child moves through
from sensation to ideas
In order to follow Montessori’s directive to lead the
child from sensations to ideas we need to provide
appropriate activities and let the child engage in
• Exploration
• Imitation
• Initiation
• Pattern Completion
• (4 levels outlined by Marlene Barron, 1983)
Open Ended aspects of Sensorial
Materials
• In our program we have always felt it was
important to incorporate two ways of building
or using the sensorial materials (when
possible) in the initial presentation.
• Decoding activities occur as the child uses
pattern cards to recreate a construction.
Encoding activities include copying a pattern
the child has built with the concrete materials
in another medium.
Designs
• Patterns such as this do not
involve problem solving.
This is simply one to one
matching.
Matching Activity
Designs
• Patterns such as the next
slide do involve problem
solving. There is more than
one way to solve this
pattern.
The student has several
patterns and can find
different ways to solve the
problem
Many different designs or
patterns can be made. The
student will find several
different ways to match the
pattern.
The children can use the
knobbed cylinders to draw
around and create their own
designs. This is a Train.
Lotto Game
• The child will use 8 of the 10 cylinders. Make
the diameters on each card as different as
possible. Place the 10 cylinders in a mystery
bag or box. Each child reaches in the bag/box
and tries to find a cylinder matching a
diameter on his/her card.
Lotto Game with and without
a grid
Pattern Cards
The child finds the correct green cylinder,
places it on the card below and then finds
the red cylinder that is placed on top of
the green cylinder
Pattern Card and Pattern
completed
Child working with several
Pattern Cards
Completed and Content
Mystery Box
Diameter and Height Cards with
the Mystery Box
Matrix
Matrix
USING COLOR OR
Domino Game
What Am I? Cards
What Am I? Cards
Attribute Games with Knobless
Cylinders
• Many of the games outlined in attribute game
manuals can be used with the cylinders. The
Cylinders have three attributes:
• Height
• Color
• Diameter
Venn Diagrams
•
•
•
•
•
Begin with one set ring
Place height card in the ring and make a set
Place diameter card in ring and make a set
Place color card in ring and make a set
Use two cards, one for each category, then
cards from all 3 categories
Venn Diagrams continued
Two set rings-The rings will overlap forming an
intersection. Place a card from 2 categories,
one in each ring. Now there will be an
intersection where the rings overlap.
Three set rings-Now there will be 6 subsets
and 1 intersection. After the rings have been
laid out and the cards from each category
selected, ask the children to predict how many
pieces, if any, will be in each subset. This could
be done with one, two, or three ring sets.
References
Barron, M. (1983), Sensorial Ideas, New York:
Cloice Fannin Graphics
Kamii, C. (1985), Young Children Reinvent
Arithmetic, New York: Teachers college
Montessori, M. (1964), The Montessori
Method, New York: Schocken Books
Paiget, J. (1972), Some Aspects of Operations,
A paper presented to a symposium on Play and
Development at Loyola University of Chicago,
published in Play and Development, edited by
M.W. Piers
Pape, B. (2010), Sensorial Extensions for the
Colored Cylinders: Montessori Research &
Development