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INTERACTIVE SIMULATIONS TO MAKE SAMPLING MAKE SENSE

Sebahat Gok

Northwestern University &

Indiana University

Rob Goldstone

Indiana University

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Designing Pedagogical Simulations with Human Perception in Mind

Leveraging perception to understand difficult concepts (Franconeri, Padilla, Shah, Zacks, & Hullman, 2021)

Perceptual systems come with powerful capabilities (e.g. ensemble perception, spatial and feature-based attention, grouping) but also biases
Perceptual processes are not always superficial, but rather can be flexible and general (Barsalou, 1998; Nathan, 2021)

Our difficult concept: statistical sampling

Statistics and sampling are increasingly important in a world driven by information (Tishkovskaya & Lancaster, 2012)
Students have many misconceptions about sampling and statistical inference (Kahneman & Tversky, 1972)

Cats

Dogs

Pet Owned

Neuroticism

>1

1

Ensemble Perception

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Designing Pedagogical Simulations with Human Perception in Mind

Leveraging perception to understand difficult concepts (Franconeri, Padilla, Shah, Zacks, & Hullman, 2021)

Perceptual systems come with powerful capabilities (e.g. ensemble perception, spatial and feature-based attention, grouping) but also biases
Perceptual processes are not always superficial, but rather can be flexible and general (Barsalou, 1998; Nathan, 2021)

Our difficult concept: statistical sampling

Statistics and sampling are increasingly important in a world driven by information (Tishkovskaya & Lancaster, 2012)
Students have many misconceptions about sampling and statistical inference (Kahneman & Tversky, 1972)

Cats

Dogs

Pet Owned

Neuroticism

>1

1

Ensemble Perception

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A Typical Sampling Simulation

OnlineStatBook.com

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Our Sampling Simulation

Concept	Visualization
A population distribution is made up of individuals	Stacks of individually colored, animal tokens
Variable of interest	A visual dimension (number of stripes) belonging to each token
Random sampling	Randomly selected tokens are highlighted and dropped down
Individual versus aggregate characterizations	Shift from animal to rectangular tokens
Mean of sample	Animation of tokens converging to their center of gravity
Variability of sampling distribution decreases as sample size increases	Sequential comparisons of 3 sample sizes
Larger sample sizes permit stronger inferences	Movable hands show probability of a value in both distributions
Population distribution ≠ Sampling distribution	Sampling distribution tokens are gray. Alignment of two distributions

Conceptual-Perceptual Alignments

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Review Work

SAMPLER, Netlogo

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Rossman & Chance Apps

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Tinkerplots

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First, I want to make a point about our broad approach here. I figure this workshop is about learning and education. And education is of course a very complex thing and you could focus on many different dimensions of student experience to try to improve it. And if you look at things we focused on, perceptual features such as color, they are quite small things. And you could ask, does something as small as this even matter for improving education? The answer is we don’t know. But before us, we noticed that statistics education community had noticed the role of leveraging perceptual experiences to solve some of the practical problems they observed in the classes. So there was some ecological evidence that it would matter. And we were closely engaged with this literature when we were developing our experiments in our lab and added a bit more of a psychological approach, our own design, and randomization to it.

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Empirical Work

Iteration 1 (2021)

Iteration 2 (2022)

Iteration 3 (2023)

Iteration 4 (2024)

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Empirical Work (Iteration 1)

The simulation hurt students’ ‘good’ intuitions about the law of large numbers.

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People assume if things are perceptually similar, they are conceptually similar, too.

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Empirical Work (Iteration 3)

Predict-test-explain

Prediction scores

Student drawings

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Empirical Work (Iteration 4)

A third “Concreteness Fading condition” added

A desirable difficulty?