# Probability Development / Rubric

Kind of reasoning Kind of task |
Transductive | Transitional | Generative | Relational thinking |
---|---|---|---|---|

Thinking and reasoning |
Uses irrelevant reasoning (Because I like red, 7 is my favorite number, 6 because it did 7 last time and it's going down, maybe it takes turns). |
Uses concrete symbolic reasoning, generally along one aspect. When pressed will revert to transductive reasoning |
Lists outcomes experimentally and with combination strategies that are coordinated and quantifiable. Reasons with the recognition of more than one feature. |
Makes precise connections between sample space, outcomes, and their probabilities. Use valid numerical patterns to describe the probabilities of events and conditional events |

Identification of possible outcomes |
An incomplete set of outcomes for simple problems. Simple problems include experiments of one task with one set (one die, one spinner, choosing marbles from one sock). |
Lists a complete set of outcomes for a one task one set experiment and sometimes lists a complete set of outcomes for a two task experiment (sum of two dies, sum of two spinners) with limited and unsystematic strategies. |
Consistently lists the outcomes of a two task experiment using a partially generative strategy. |
Uses a systematic generative strategy that enables a complete listing of the outcomes for multiple task cases. |

Statements of probability |
Makes predictive statements with wording of most and least likely for events with subjective reasoning. Recognizes certain and impossible events. |
Makes predictive statements with wording of most and least likely for events based on quantitative reasoning, but may revert to subjective reasoning. Recognizes certain and impossible events. |
Makes predictive statements with wording of most and least likely for events based on quantitative reasoning including situations involving noncontiguous outcomes. Uses numbers informally to compare probabilities. Distinguishes certain, impossible, and possible events, and justifies choice quantitatively. |
Makes predictive statements with wording of most and least likely for events based on quantitative reasoning for single task experiments. Assigns a numerical probability to an event as either a real probability or a form of odds. |

Comparing probabilities |
Compares probability of an event in two different sample spaces using subjective or numeric reasoning. Can not distinguish "fair" probability situation from "unfair". |
Makes probability comparisons on the basis of quantitative reasoning (may not quantify correctly and may have limitations where noncontiguous events are involved) Begins to distinguish fair probability situations from unfair. |
Makes probability comparisons on the basis of consistent quantitative reasoning. Justifies with valid quantitative reasoning, but may have limitations when non - contiguous events are involved. Distinguishes fair and unfair probability generators on the basis of valid numerical reasoning. |
Assigns numerical probability measures and compares events. Incorporates noncontiguous and contiguous outcomes in determining probabilities Assigns equal numerical probabilities to equally likely events Probability comparisons are the ordering of the possibility of events happening. |

Identify conditional probability |
Does not give a complete list of outcomes even if a complete list was given prior to the first trial. Recognizes when certain impossible events arise in nonreplacement situations. |
Recognizes probabilities of some events change in a nonreplacement situation (as marbles are taken from a sock and not replaced before next draw) however, recognition is incomplete and is usually limited to events that have previously happened. |
Can determine changing probability measures in a nonreplacement event. Recognizes that the probability of all events change in a nonreplacement event. |
Assigns numerical probabilities in replacement and nonreplacement situations. Distinguishes dependent and independent events. Conditional probability is the possibility of an event based on certain conditions. |