GAISEing into the Common Core Standards A Professional Development Seminar sponsored by the Ann Arbor Chapter of the ASA

 Name  School  Interesting Personal Statistic Introductions

 A Framework for Teaching Statistics Within the PreK- 12 Mathematics Curriculum and for the College Introductory Course  Guidelines for Assessment and Instruction in Statistics Education  Strategic initiative of ASA; published in 2007  What is this document and why is it needed? GAISE

The goal of the K-12 document is to provide a basic framework for informed K- 12 stakeholders that describes what is meant by a statistically literate high school graduate and to provide steps to achieve this goal. GAISE

Writers:Advisors:  Christine Franklin Peter Holmes  Richard ScheafferCliff Konold  Roxy PeckMike Perry  Denise MewbornSusan Friel  Gary KaderBrad Hartlaub  Jerry MorenoLandy Godbold PreK-12 GAISE Writers and Advisors

 This Framework fleshes out the NCTM Data Analysis and Probability strand with guidance and clarity on the content that NCTM is recommending at the elementary, middle and high school grades, focusing on a connected curriculum that will allow a high school graduate to have a working knowledge of an appreciation for the basic ideas of statistics.  It also provides guidance on methods that are accepted as effective in teaching statistical concepts to students with wide varieties of learning styles. Based on the NCTM 2000 Standards

 The main content of the K-12 Framework is divided into three levels, A, B, and C that roughly parallel the PreK-5, 6-8, and 9-12 grade bands of the NCTM Standards.  The framework levels are based on experience not age. Levels in PreK-12 GAISE

At Level A the learning is more teacher driven, but transitions toward student centered work at Level B and becomes highly student driven at Level C. Hands-on, active learning is a predominant feature throughout. Distinction of Levels

Statistical analysis is an investigatory process that turns often loosely formed ideas into scientific studies by:  refining the question to one (or more) that can be answered with data  designing a plan to collect appropriate data  analyzing the collected data by graphical and numerical methods,  interpreting the analysis so as to reflect light on the original question. Statistical Investigatory Process

 Level A: Summarize frequencies in table or bar graph  Level B: Transition to relative frequencies – leap to proportional reasoning  Level C: Transition to sampling distributions for a sample proportion and role of probability in finding a margin of error which provides information about max. likely distance between sample proportion and population proportion being estimated. What type of music is most popular among their peers in school? (rock, country, rap)

 Both conceptual understanding and procedural skill should be developed deliberately, but conceptual understanding should not be sacrificed for procedural proficiency.  Active learning is key to the development of conceptual understanding.  Real world data must be used wherever possible in statistics education.  Appropriate technology is essential in order to emphasize concepts over calculations GAISE Basic Principles

 Writers of the GAISE report were on the writing and advisory teams for the CCSS-M  Statistical investigatory process  Developmental progression  Expectations of students at the varying levels  Conceptual understanding  Real world data Influence of GAISE on the CCSS-M

 Each day of the seminar we will focus on a series of standards and explore them using a GAISE perspective  Statistical investigatory process  Actively engaged in activities  Conceptual as well as procedural understanding  Real world data  Appropriate use of technology CCSS of the Day

 CCSS.Math.Content.6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. CCSS.Math.Content.6.SP.B.4  CCSS.Math.Content.6.SP.B.5 Summarize numerical data sets in relation to their context, such as by: CCSS.Math.Content.6.SP.B.5  CCSS.Math.Content.6.SP.B.5a Reporting the number of observations. CCSS.Math.Content.6.SP.B.5a  CCSS.Math.Content.6.SP.B.5b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. CCSS.Math.Content.6.SP.B.5b  CCSS.Math.Content.6.SP.B.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. CCSS.Math.Content.6.SP.B.5c  CCSS.Math.Content.6.SP.B.5d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. CCSS.Math.Content.6.SP.B.5d Summarize and describe distributions

 CCSS.Math.Content.HSS-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). CCSS.Math.Content.HSS-ID.A.1  CCSS.Math.Content.HSS-ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. CCSS.Math.Content.HSS-ID.A.2  CCSS.Math.Content.HSS-ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). CCSS.Math.Content.HSS-ID.A.3  CCSS.Math.Content.HSS-ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. CCSS.Math.Content.HSS-ID.A.4 Summarize, represent, and interpret data on a single count or measurement variable

 CCSS.Math.Content.7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. CCSS.Math.Content.7.SP.B.3  CCSS.Math.Content.7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. CCSS.Math.Content.7.SP.B.4  CCSS.Math.Content.HSS-IC.B.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. CCSS.Math.Content.HSS-IC.B.5 Draw informal comparative inferences about two populations.