
The Parents View

Parents want their child to have as much personal attention as
possible. But how much is possible? This is easy to figure. On the
average personal attention must be split among all the students
in the class.
The best we can hope for is a fair part for everybody. On the graph
we can see the maximum minutes each hour that a child can expect
personal attention.
Notice that by the time we reach 12 children, personal attention
is down to 5 minutes. This is why tutoring is best with less that
5 children. It is also why nature has designed human families to
be less than six.

The Teachers View
Teachers have long suggested that the addition of a few more students
has a big impact on manageability. This can be understood when we realize
that teachers are managing the interactions between students not just
individual students. This, no doubt, is a reason why most offices are
designed to minimize human interaction.

In this diagram, the dots represent students in the class and the
connecting lines represent interactions that can occur between students.
Interactions may include distractions such as talking during lessons,
reinforcing another's behavior, emulating another's behavior, playing,
picking on another, or any other way that students are interacting
with students rather than with the lesson.

Notice, one more child produces many more interactions. Adding
a new child involves adding all of that child's behaviors, plus
all the other students responses to his behaviors, plus all of his
responses to the behavior of other students.
So how many interactions must a teacher manage to have a successful
classroom? This graph shows how student interactions increase with
class size. A class of 16 constitutes about 100 potential interactions,
a class of 20 almost 200, and a class of 24 roughly 300. For class
around 20 students, the addition of six more students will roughly
double the interactions that must be managed.


The Students View
Researchers have observed that students spend much of their time waiting.
Waiting instead of learning, but waiting for what? Waiting for personal
attention, waiting for other students to catch up or correct their behavior,
waiting for an opportunity to be involved.
If all of the students behave perfectly, the the waiting increases
linearly with the class size.
This graph shows how long a student would wait for three minutes
of personal attention.
Even in a question answer sequence that moves much faster than
three minutes per student, a student spends most of her time waiting
for her turn.


What if the students behave like humans by letting their attention
drift and distracting each other. This results in more waiting.
The increase in waiting depends on the increase in distractions.
As shown above, distractions increase with the number of students.

Conclusion:
The challenges to managing a classroom increase rapidly as the population
increases. Class size has a major impact on the potential learning for
the students.

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