The Montessori Knobbed Cylinders: Introducing the Young Child to Changes in Dimension
The Montessori sensorial materials are a central component of the Early Childhood (EC) classroom, and are designed to help the child develop and refine their sense of sight, hearing, smell, touch, and taste. The materials for visual discrimination are varied—some focus on color, some on shape, and others on dimension. Those in the latter category include the Pink Tower, the Brown Stair, and the Red Rods. The Knobbed Cylinders, also known as the Solid Cylinders and Solid Insets, are the first materials presented to the child in this sequence, the ones that set in motion thinking about changes in dimension. As a sensorial material, the Knobbed Cylinders engage both the child's sense of vision and touch.
Physical Properties of the Knobbed Cylinders
The material consists of four sets of ten wooden cylinders. Each set includes a block of wood with a hole for each cylinder. The cylinders are topped with a small knob, which facilitates the removal and replacement of the cylinders within their corresponding holes. Descriptions of the material vary slightly between sources (material makers and training programs), with the most commonly used descriptors of the differences and sequence as follows:
- Block 1: Cylinders increase in height and diameter
- Block 2: Cylinders increase in diameter as height remains constant
- Block 3: Cylinders increase in diameter as they decrease in height
- Block 4: Cylinders increase in height, diameter remains constant
Considerations Regarding Block 3
Interesting to note is that Montessori's original description of the material (1914) only includes three of the four blocks described above, as addressed in her own handbook (p 29):
In the box of materials the first three objects which are likely to attract the attention of a little child from two and a half to three years old are three solid pieces of wood, in each of which is inserted a row of ten small cylinders …
Montessori also presents the three blocks in a different order from the sequence above. Her description of “the first case” is equivalent to Block 2; “the second” is equivalent to Block 1; and “the third case” to Block 4. Most noteworthy, she does not describe Block 3 in her 1914 handbook, raising the question of whether she or someone else added this set later.
Considering the sequence of materials for discriminating dimension that follow the Knobbed Cylinders, recall that the challenge level increases with fewer changing dimensions. For example, the pieces of the Pink Tower change in three dimensions; those of the Brown Stair change in two dimensions; and the pieces of Red Rods change in one dimension—from least challenging to most challenging, respectively.
In the sequence above, we notice that in Block 1, the pieces vary in two dimensions, and the pieces of Blocks 2 and 4 vary in one dimension. We would expect, therefore, Blocks 2 and 4 to be more challenging than Block 1. But Block 3 is a special case. The pieces change in two dimensions, like those of Block 1, but whereas the dimensions of the pieces in Block 1 change in the same direction (diameter and height both increase in each piece), the diameter increases while the height decreases in the pieces of Block 3.
One might suppose that Block 3 creates a more challenging task than Block 4, and indeed, it is sometimes described as the most challenging, given that “one variable grows while the other shrinks.” Given that Montessori did not describe Block 3, and given discrepancies about where it fits in the sequence of the four blocks, an interesting empirical question is how challenging children find it with respect to the other three sets.
Trial, Error, Retrial, Success, and Repetition
Once the child has been presented with the steps for removing and replacing the cylinders in sequence, the guide places the pieces randomly on the table. This way, the child has to more actively apply their skills of visual discrimination, together with their sense of touch, in order to find the correct aperture for each cylinder. This occurs, initially, through trial and error. Montessori's own words from her 1914 handbook describe the process. While the passage is lengthy, it give us a glimpse into the child's experience as observed by Montessori time and again (31-32):
But how is the child to find the right place for each of the little cylinders which lie mixed upon the table? He first makes trials; it often happens that he places a cylinder which is too large for the empty hole over which he puts it. Then, changing its place, he tries others until the cylinder goes in. Again, the contrary may happen; that is to say, the cylinder may slip too easily into a hole too big for it. In that case it has taken a place that does not belong to it at all, but to a larger cylinder. In this way one cylinder at the end will be left out without a place, and it will not be possible to find one that fits. Here the child cannot help seeing his mistake in concrete form. He is perplexed, his little mind is faced with a problem which interests him intensely. Before, all the cylinders fitted, now there is one that will not fit. The little one stops, frowning, deep in thought. He begins to feel the little buttons and finds that some cylinders have too much room. He thinks that perhaps they are out of their right place and tries to place them correctly. He repeats the process again and again, and finally he succeeds. Then it is that he breaks into a smile of triumph. The exercise arouses the intelligence of the child; he wants to repeat it right from the beginning and, having learned by experience, he makes another attempt. Little children from three to three and a half years old have repeated the exercise up to forty times without losing their interest in it [emphasis added].
As the second, third, and fourth sets are presented, Montessori writes that “the change of shape strikes the child and reawakens his interest.” As the child gains mastery of each set, the challenge can be increased by mixing the pieces of two, three, or all four sets. Finally, the child can try the exercises while blindfolded, fully engaging their haptic perception (how we see with our hands).
Knobbed Cylinders as Indirect Preparation for Writing
Unlike the Pink Tower, Brown Stair, and Red Rods, the child works with the Knobbed Cylinders at a table rather than on a rug or work mat. Sitting “in a comfortable position at a little table” is one aspect of indirect preparation for writing. Additionally, the child uses a pincer grasp (a two- or three-finger grip) on the knobs of the cylinders, which is indirect preparation for holding a pencil. Montessori describes how the Knobbed Cylinders, together with other sensorial materials, prepare the hand for writing (1914, 85):
Our children have long been preparing the hand for writing. Throughout all the sensory experiences the hand, whilst cooperating with the mind in its attainments and in its work of formation, was preparing its own future. When the hand learned to hold itself lightly suspended over a horizontal surface in order to touch rough and smooth, when it took the cylinders of the solid insets and placed them in their apertures, when with two fingers it touched the outline of the geometric forms, it was coordinating movements, and the child is now ready—almost impatient to use them in the fascinating “synthesis” of writing.
Montessori goes on to distinguish these exercises from those meant as direct preparation for writing, specifically, “exercises for the management of the instrument of writing.”
The Knobless Cylinders
A second set of cylinders, the Knobless Cylinders, have many of the same physical properties, but without the knobs. Unlike the Knobbed Cylinders, therefore, they are not placed into holes in wooden blocks, but are lined up or stacked sequentially. This material also consists of four sets of ten pieces, ranging in height and diameter from .5 cm to 5 cm. Each piece in a given set increases (or decreases) in size by increments of .5 cm, either in height, diameter, or both (according to Montessori's own descriptions from the 17th edition of The Montessori Didactic Material):
- Set A – Red: uniform 5 cms in height, but varying in diameter from .5 cm to 5 cms
- Set B – Blue: uniform 2.5 cms in diameter, but varying in height from .5 cm to 5 cms
- Set C – Yellow: varying in both height and diameter, from .5 cm to 5 cms
- Set D – Green: varying in both height and diameter, but in the reverse way to Set C, i.e. from 5 cms in height by .5 cm diameter and .5 cm in height to 5 cms diameter
The Knobless Cylinders, as described by Montessori, correspond to the Knobbed Cylinders as follows:
- Set A – Red = Block 2
- Set B – Blue = Block 4
- Set C – Yellow = Block 1
- Set D – Green = Block 3
Again, we note the discrepancy in the sequencing. We know from the source above that Montessori created all four sets of the Knobless Cylinders, and she does in fact place the Green set at the end of the sequence, leading one to believe that she considered this one to be the most challenging. Montessori states in this source that “these cylinders can be correlated with the Solid Wooden Insets [the Knobbed Cylinders].” Perhaps Block 3 of the Knobbed Cylinders was added later so that the two sets would be identical? If so, the question remains why it is most often found third in the sequence, rather than fourth, where Montessori seems to have placed it.
As with the Knobbed Cylinders, the child gains awareness that different dimensions determine an object's size. Moreover, they practice concentration and dexterity as they sequence the cylinders in ascending or descending order, or stack them.
Additional Benefits of the Knobbed and Knobless Cylinders
Like the materials that follow the cylinders, the additional benefits from working with the cylinders include the development of:
- Skills in visual discrimination
- Sequencing and seriation skills
- New vocabulary
But perhaps Montessori described it best, when she wrote (1914, 33):
The aim is not an external one, that is to say, it is not the object that the child should learn how to place the cylinders, and that he should know how to perform an exercise. The aim is an inner one, namely, that the child trains himself to observe; that he be led to make comparisons among objects, to form judgments, to reason and decide; and it is in the indefinite repetition of this exercise of attention and of intelligence that a real development ensues.
As with all the Montessori materials, there is much more going on with the child’s work than might appear to the casual observer. Among the first in the sensorial materials, the Knobbed and Knobless Cylinders set the stage for a progression of exercises that train the senses, encourage attention, and develop intelligence; in short, exercises that indirectly prepare the child for later work in language, mathematics, and all future academic endeavors.
About the Author
Cynthia Brunold-Conesa, MEd, is an educator of adult learners at two AMS teacher education programs. She has 23 years experience as a lead guide at the Elementary and middle school levels. Cynthia also publishes on a variety of Montessori topics. She is AMS credentialed (Elementary I – II). Contact her at email@example.com .