A special thank you! Way! Christine Franklin University of - PDF document

5/20/15 ¡ Statistics and K-12 in the United States: We’ve Come a Long A ¡special ¡thank ¡you! ¡ Way! Christine Franklin University of Georgia Athens, GA USA Data Scientist: Sexiest MAA – 1923: Junior high should include Job of the 21st Century statistics and a stat course in high school • Harvard Business Review 1968: Joint ASA/NCTM 1990’s AP Statistics becomes Committee for K-12 Statistics Reality • Mosteller reached out as President of ASA to NCTM to form this committee • Early publication of committee was Statistics: A Guide to the Unknown • Now in 4 th edition 1 ¡

5/20/15 ¡ 2005/2007 Pre-K-12 GAISE 2000 NCTM Standards: Includes the sponsored by ASA Probability and Data Analysis Strand Statistics in the 2012 Common Core and Common Core Statistics • The presence of statistics in elementary school is important but is limited • Main topics in middle school include • Statistical investigative process introduced • Statistical variability • Distributions • Drawing inference about populations using samples • Simulations • Bivariate data analysis • Main topics in high school include • Categorical and quantitative data analysis • Inference using randomization tests and simulation • Conditional probability and probability rules • Probability for decision making The Statistical Education of Teachers The S tatistics T eacher ASA American (SET) N etwork Statistical AMERICAN STATISTICAL ASSOCIATION Association www.amstat.org/education/stn/index.html • The report emphasizes that teachers of all grade Number 68 ASA/NCTM Joint Committee on the Curriculum in Statistics and Probability Winter 2006 A Sequence of Activities for levels need to understand the “statistical process” Developing Statistical Concepts Christine Franklin & Gary Kader • Formulate questions Introduction The Board of Directors of the American Statistical Association (ASA) at its May 2005 meet- • Collect data ing endorsed the report, “A Curriculum Framework for Pre K-12 Statistics Education.” The develop- ment of this Framework was supported by the ASA though funding of a Strategic Initiative Grant pro- posed by the ASA Advisory Committee on Teacher • Analyze data Enhancement. The Framework is designed to give between a question that anticipates a deterministic educators guidance towards developing statistical- answer and a question that anticipates an answer ly literate citizens. The writers of the Framework were Christine Franklin, Gary Kader, Denise based on data that vary. The anticipation of variability • Interpret results is the basis for understanding this distinction. Data Mewborn, Jerry Moreno, Mike Perry, Roxy Peck, collection designs must acknowledge variability in and Richard Scheaffer. data and frequently are intended to reduce variabil- ity. An understanding of data collection designs that The Framework Model acknowledge variability is required for effective collec- Statistical Problem Solving and the Evolution of tion of data. The main purpose of statistical analysis Statistical Concepts is to give an accounting of the variability in the data. Accounting for variability with the use of distributions The Framework presents statistical problem is the key idea in the analysis of data. Statistical inter- solving as an investigative process that involves four components: pretations are made in the presence of variability and must allow for it. Looking beyond the data to make (1) Question formulation, generalizations must allow for variability in the data. (2) Data collection, Understanding the role of variability in the statisti- cal problem solving process requires maturation in (3) Data analysis, statistical thinking. The beginning student cannot be (4) Interpretation. expected to make all of these linkages. Statistical edu- • The statistical process components are the The Framework stresses the importance of cation should be viewed as a developmental process, understanding variability in the practice of this and this report provides a framework for statistical education over three developmental levels, A, B, and process. The formulation of a statistics ques- tion requires an understanding of the difference C. Although these three levels may parallel grade common headings in the three chapters levels, they are based on development in statistical thinking, not age. Thus, a middle school student who Also In This Issue… has had no prior experience with statistics will need to begin with Level A concepts and activities before mov- (elementary, middle, and high) of SET ing to Level B. This holds true for a secondary student Letter from the Editor ...................................... 12 as well. If a student hasn’t had Level A and B experi- 2 ¡

5/20/15 ¡ Distinction of Levels: Distributions Distinction of Levels: Questions and Type of Survey All four steps of the statistical process are used at all three levels A, B, C. What type of music is most popular among their peers The depth of understanding and sophistication of methods used increases in school? (rock, country, rap) across the levels. Level A Statistical questions at each level and data collection: Summarize frequencies in table or bar graph Level A: What type of music is most popular among students in our class (rock, country, rap)? [A census] Level B: What type of music is most popular among students at our school? How does music preference differ among classes? [Use sampling and consider random sample] Level C: Is there an association between liking rock and rap music at all the school district high schools? [Use simple random sample] Level B 
 Level B Comparison Relative Frequencies ¡ Level B 
 Level C 
 Association between 2 variables Association between 2 variables ! • Dotplot showing simulated sampling distribution of the difference in proportions using a randomization test to observe what happens due to chance variation – find a simulated P-value ¡ ¡ ¡ ¡ ¡ Like Rock Music? 25/31 = 0.81 4/19 = 0.21 Yes No Row Totals 0.81 – 0.21 = 0.60 Yes 25 4 29 Like Rap Music? No 6 15 21 Column Totals 31 19 50 3 ¡

5/20/15 ¡ Standards ¡for ¡MP ¡ The Statistical Education of Teachers (SET) 2. Reason abstractly and quantitatively. 1. Make sense of problems and Reasoning and 3. Construct viable arguments and persevere in solving them. • Writers: Explaining critique the reasoning of others. • Christine Franklin (Chair) 6. Attend to precision. • Anna Bargagliotti 4. Model with mathematics. Modeling and • Catherine Case Using Tools • Gary Kader 5. Use appropriate tools strategically. • Richard Schaeffer • Denise Spangler 7. Look for and make use of structure. ¡ 8. Look for and express regularity Seeing Structure and Generalizing in repeated reasoning. 1.19 William McCallum, University of Arizona Joint ASA – NCTM Committee Appendix • 12 scenarios focused around the themes: • Question/Design Alignment • Connections between Data type, Numerical Summaries, and Graphical Displays • Proportional Reasoning in Statistics • The Role of Randomness in Statistics • Common misconceptions are discussed ASA K-12Resources 4 ¡

5/20/15 ¡ Traditional ¡Statistics ¡ ASSESSMENT TIME Assessment ¡Item ¡ A.1.1.3 ¡ LOCUS NSF Project Students are trying to choose new school colors. Which is the most appropriate statistical question to be investigated for a study of school colors preference? ¡ A. What colors are the colors of 4% your main rival school? B. What colors were the old colors of your school? 7% C. Which colors are most popular 59% in your school? D. Which colors do you like best? 30% C.1.1.8 ¡ C.2.1.3 ¡ A. Randomly select 50 students from the high school and A. Are ¡coffee ¡drinkers ¡more ¡likely ¡to ¡smoke ¡than ¡ ask them if they intend to take a foreign language class adults ¡who ¡do ¡not ¡drink ¡coffee? ¡29% ¡ next year. 20% B. Randomly select half of the foreign language teachers B. Does ¡coffee ¡consumption ¡cause ¡a ¡reduction ¡ in the high school and ask them how many students in ¡the ¡incidence ¡of ¡stroke? ¡19% ¡ ¡ are taking their classes this year. 8% C. Randomly select half of the sophomores taking C. Do ¡coffee ¡drinkers ¡have ¡fewer ¡strokes ¡than ¡ Spanish this year and ask them if they intend to take Spanish next year. 10% adults ¡who ¡do ¡not ¡drink ¡coffee? ¡11% ¡ D. Randomly select 40 sophomores from the high school D. What ¡percentage ¡of ¡the ¡population ¡are ¡coffee ¡ and ask them if they intend to take a foreign language course next year. 62% drinkers? ¡40% ¡ 5 ¡

5/20/15 ¡ A.3.2.2 ¡ A.3.2.2 ¡ • In which grade level did the responses vary the most? • Grade 6 1% • Grade 7 13% • Grade 8 85% • Grade 9 2% 6 ¡