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Manipulatives in Education

My mother loves to recall my first day at Merryhaven Montessori, the elementary school I attended through the sixth grade. I recall her asking, “What did you learn today?” I also remember noticing her curiosity at my response: “I didn’t learn anything — we just played!”

Of course “playing” consisted of tracing sandpaper letters, cutting a cheese slice into equal parts, and (my favorite) counting beads; I could count with single beads, rods consisting of 10 beads, the flat squares of 100 beads (or 10 rods, I suppose), and the mammoth of them all: a giant cube of 1000 beads! (See Figure 5-3.) These “manipulatives” are core to the Montessori method of education, and all examples — dating back to the late 1800s — of learning through tangible interactions. Playing is learning, and these “technologies” (in the anthropological sense) make otherwise abstract concepts quite, concrete.

But why is this so?

Jean Piaget, the influential Swiss developmental psychologist, talks about stages of development, and how learning is — at the earliest ages — physical (sensorimotor). As babies, we grasp for things and make sense of the world through our developing senses. At this stage, we learn through physical interactions with our environment. This psychological theory, first proposed in the 1960s, is supported by recent advances in cognitive neuroscience and theories about the mind and body.

Montessori beads—

Figure 5-3. Montessori beads[]

Essentially, we all start off understanding the world only through physical (embodied) interactions. As infants, even before we can see, we are grasping at things and seeking tactile comforts. We learn through our physical interactions with our environment.

Contrast this with the workbooks and photocopied assignments common in most public schools. These pages represent “what” students should be learning, but ignore the cognitive aspects of “how” we learn, namely through interactions. Much of learning is cause and effect. Think of the young child who learns not to touch a hot stove either through her own painful experience or that of a sibling. It is through interactions and experimentation (or observing others) that we begin to recognize patterns and build internal representations of otherwise abstract ideas.

Learning is recognizing or adding to our collection of patterns.

In this regard, computers can be wonderful tools for exploring possibilities. This is true of young children playing with math concepts, to geneticists looking for patterns in DNA strands. Interactive models and simulations are some of the most effective means of sensemaking. Video games also make for powerful learning tools because they create possibility spaces where players can explore potential outcomes. Stories such as EnderS Game (in which young children use virtual games to explore military tactics) are a poignant testimony to the natural risk-taking built into simulations. “What happens if I push this?” “Can we mix it with...?” “Let’s change the perspective.” Computers make it possible for us to explore possibilities much more quickly in a playful, risk-free manner.

In this regard, physical models are crude and limiting. Software, by nature of being virtual, is limited only by what can be conveyed on a screen.

But, what of the mind-body connection? What about the means by which we explore patterns through a mouse or through our fingertips sliding across glass? Could this be improved? What about wood splinters and silky sheets and hot burners and stinky socks and the way some objects want to float in water — could we introduce sensations like these into our interactions? For all the brilliance of virtual screens, they lack the rich sensory associations inherent in the physical world.

 
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