4-Block Stalagmite

Sample Stalagmite is an interactive computer-based model. The model is a part of the ProLab curriculum designed by Dor Abrahamson initially at Uri Wilensky’s Center for Connected Learning and Computer-Based Modeling (CCL) at Northwestern University and later at UC Berkeley. The EDRL website features some of these latter models as relevant to our publications. We are grateful to the CCL for continued technological support and version updates.

This interactive computer-based model is a part of the ProbLab curriculum designed by Dor Abrahamson initially at Uri Wilensky’s Center for Connected Learning and Computer-Based Modeling (CCL) at Northwestern University and later at UC Berkeley. The EDRL website features some of these latter models as relevant to our publications. We are grateful to the CCL for continued technological support and version updates.

Sample Stalagmite is an interactive simulation for the study of binomial distribution. The model connects between, on the one hand, combinatorics and sample space (theoretical probability), and on the other hand, actual experimental outcome distributions (empirical probability). These connections are made vivid by representing the experimental results not in histograms with stark columns but as the aggregated samples themselves (you can see and count up each of the outcomes, not only get a sense of overall frequency by category).

This image features the interface of Sample Stalagmite. The image is not interactive. An interactive NetLogo Web version is here. For best interaction with the model, please free-download NetLogo.

The randomness object in this simulation varies. For example, it can be set to be 4-block, a 2-by-2 array in which each of the 4 squares can be either green or blue. The model generates random 4-block samples one after another and assigns each of these samples to its respective column by number of green squares. For example, a randomly generated 4-block with exactly one green square will descend down the “1” chute. This creates a picto-graph histogram that grows bottom-up like a stalagmite. When the probability in the model is set at 0.5, this stalagmite will grow to 1:4:6:4:1 proportions. For other p values, the stalagmite will be tailed.

In related curricular material, we have worked with 9-Blocks (3-by-3 array). Students use crayons and paper to build the Combinations Tower. The Combinations Tower is a giant bell-shaped histogram of all the 512 different combinations of a 3-by-3 array of squares that can each be either green or blue. In the tower, these combinations are grouped in columns according to how many green squares there are in each. 9-Block Stalagmite accompanies these curricular activities. When the probability in the model is set at .5, the shape of this histogram resembles the combinations tower. If all repeating samples are removed from this histogram as it grows up, the model eventually exhausts the sample space at each run of the experiment, providing the view allows the tower to grow tall enough.