proposing a viable research association: question for investigation categorical variables: contingency tables — clustered, stacked bar charts designing a study to explore a quantitative variables: scatterplots research question correlation and causation refers to creative and innovative models: mathematical thinking rather than to binomial distribution: representing math in a creative way, When is it appropriate? such as through art or music What does it model? curiosity and wonder: What assumptions can be made? asking questions to further understanding or to open other Shape of distribution affected by avenues of investigation n and p. inquiry: normal (Gaussian) distribution: includes structured, guided, and open when it is useful inquiry roles of the mean and standard noticing and wondering deviation, 68-95-99.7 rule determining what is appropriate to central limit theorem: describing the explore in a research question variation of a sample mean Visualize: use of simulation software to explore create and use mental images to sampling distributions support understanding inferential concepts: Visualization can be supported using making intuitive inferences based on dynamic materials (e.g., graphical a large number of simulations relationships and simulations), intuition on interval, estimation of concrete materials, drawings, and means and proportions via simulation diagrams. inference for proportion via flexible and strategic approaches: simulation deciding which statistical ideas are (randomization/permutation tests) useful in addressing a research inference for a mean via simulation question or hypothesis (randomization/permutation tests) choosing an effective strategy to two-sample questions via simulation address a research question (e.g., (randomization/permutation tests) observational or experimental study, software and technology: choice of variable[s] to measure, Software can assist us in exploring display method, inferential and summarizing data.
proposing a viable research question for investigation designing a study to explore a research question refers to creative and innovative mathematical thinking rather than to representing math in a creative way, such as through art or music curiosity and wonder: asking questions to further understanding or to open other avenues of investigation inquiry: includes structured, guided, and open inquiry noticing and wondering determining what is appropriate to explore in a research question Visualize: create and use mental images to support understanding Visualization can be supported using dynamic materials (e.g., graphical relationships and simulations), concrete materials, drawings, and diagrams. flexible and strategic approaches: deciding which statistical ideas are useful in addressing a research question or hypothesis choosing an effective strategy to address a research question (e.g., observational or experimental study, choice of variable[s] to measure, display method, inferential association: categorical variables: contingency tables — clustered, stacked bar charts quantitative variables: scatterplots correlation and causation models: binomial distribution: When is it appropriate? What does it model? What assumptions can be made? Shape of distribution affected by n and p. normal (Gaussian) distribution: when it is useful roles of the mean and standard deviation, 68-95-99.7 rule central limit theorem: describing the variation of a sample mean use of simulation software to explore sampling distributions inferential concepts: making intuitive inferences based on a large number of simulations intuition on interval, estimation of means and proportions via simulation inference for proportion via simulation (randomization/permutation tests) inference for a mean via simulation (randomization/permutation tests) two-sample questions via simulation (randomization/permutation tests) software and technology: Software can assist us in exploring and summarizing data.