Meeting 3: Case and Jacobbe (2018)
Learning sampling distributions vs learning derivatives
Capacity to use modus tollens
How do changes in representation or the exposure to multiple representations affect learning?
How much of the observed challenges can be attenuated with changes in the curriculum and simulation user interface/experience?
Why are students not able to envision the multi-level nature of inference without having an applet open in front of them?
How can we get students to a place where they must face their own contradictions in reasoning/recognize their reasoning contains contradictions?
Real-world | Hypothetical | |
---|---|---|
Population | Actual population or true relationship | Hypothetical population or relationship |
Sample | Empirical distribution | Distribution of one simulated sample |
Sampling distribution | Distribution of statistics produced through replication | Distribution of statistics produced through simulation |
Real-world | Hypothetical | |
---|---|---|
Population | Actual population or true relationship | Hypothetical population or relationship |
Sample | Empirical distribution | Distribution of one simulated sample |
Sampling distribution | Distribution of statistics produced through replication | Distribution of statistics produced through simulation |
Real-world | Hypothetical | |
---|---|---|
Population | Actual population or true relationship | Hypothetical population or relationship |
Sample | Empirical distribution | Distribution of one simulated sample |
Sampling distribution | Distribution of statistics produced through replication | Distribution of statistics produced through simulation |
Real-world | ||
---|---|---|
Population | Actual population or true relationship | |
Sample | Empirical distribution | Distribution of one simulated sample |
Sampling distribution | Distribution of statistics produced through replication | Distribution of statistics produced through simulation |
Real-world | Hypothetical | |
---|---|---|
Population | A very long sequence of coin tosses of length \(N\) | A very long sequence of fair coin tosses of length \(N\) |
Sample | One actual sequence of coin tosses with length \(n\) | One artificially generated sequence of fair coin tosses with length \(n\) |
Sampling distribution | Literally tossing a coin \(n\) times repeatedly | Use the computer to toss a fair coin \(n\) times repeatedly |
Role-playing as a chance skeptic
Introduction to probability in an intro-stats course
Change the language used
Is the software layer the problem?