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The Statistical Education of Teachers (SET): An American

Statistical Association Policy Document!

Christine Franklin!University of Georgia!

Data Scientist: Sexiest Job of the 21st Century!• Harvard

Business Review!

MAA – 1923: Junior high should include

statistics and a stat course in high school !

2000 NCTM Standards: Includes the

Probability and Data Analysis Strand!

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2005/2007 GAISE sponsored by ASA!

A Sequence of Activities for Developing Statistical Concepts

Christine Franklin & Gary Kader

IntroductionThe Board of Directors of the American

Statistical Association (ASA) at its May 2005 meet-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 Enhancement. The Framework is designed to give educators guidance towards developing statistical-ly literate citizens. The writers of the Framework were Christine Franklin, Gary Kader, Denise Mewborn, Jerry Moreno, Mike Perry, Roxy Peck, and Richard Scheaffer.

The Framework ModelStatistical Problem Solving and the Evolution of Statistical Concepts

The Framework presents statistical problem solving as an investigative process that involves four components:

(1) Question formulation,

(2) Data collection,

(3) Data analysis,

(4) Interpretation.

The Framework stresses the importance of understanding variability in the practice of this process. The formulation of a statistics ques-tion requires an understanding of the difference

Number 68 ASA/NCTM Joint Committee on the Curriculum in Statistics and Probability Winter 2006

S tatisticsT eacherN etwork

The

www.amstat.org/education/stn/index.html

between a question that anticipates a deterministic answer and a question that anticipates an answer based on data that vary. The anticipation of variability is the basis for understanding this distinction. Data collection designs must acknowledge variability in data and frequently are intended to reduce variabil-ity. An understanding of data collection designs that acknowledge variability is required for effective collec-tion of data. The main purpose of statistical analysis is to give an accounting of the variability in the data. Accounting for variability with the use of distributions is the key idea in the analysis of data. Statistical inter-pretations are made in the presence of variability and must allow for it. Looking beyond the data to make generalizations must allow for variability in the data.

Understanding the role of variability in the statisti-cal problem solving process requires maturation in statistical thinking. The beginning student cannot be expected to make all of these linkages. Statistical edu-cation should be viewed as a developmental process, and this report provides a framework for statistical education over three developmental levels, A, B, and C. Although these three levels may parallel grade levels, they are based on development in statistical thinking, not age. Thus, a middle school student who has had no prior experience with statistics will need to begin with Level A concepts and activities before mov-ing to Level B. This holds true for a secondary student as well. If a student hasn’t had Level A and B experi-

Also In This Issue…

ASAAMERICAN STATISTICAL

ASSOCIATION

AmericanStatisticalAssociation

Letter from the Editor ...................................... 12

Distinction of Levels: Questions and Type of Survey!

All four steps of the statistical process are used at all three levels A, B, C. The depth of understanding and sophistication of methods used increases across the levels.!

Statistical questions at each level and data collection: !!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]!

Distinction of Levels: Distributions !What type of music is most popular among their peers in school? (rock, country, rap)!

Level A!

Summarize frequencies in table or bar graph !

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Level BRelative Frequencies!

 

Level B Comparison!

Level B Association between 2 variables!

25/31  =  0.81      4/19  =  0.21      0.81  –  0.21  =  0.60  

Level CAssociation 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.!  

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2012 Common Core and Statistics!

Statistics in the Common Core!

•  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!

Huge Opportunities!

• Statistical Literacy for All!!

• Rethink College Course!

Huge Challenges!• Rethinking the college intro course and the

second course in statistics!

• Are colleges prepared for the increased number of students wanting to major and minor in Statistics?!

• Preparing K-12 teachers to deliver the statistical content in the CCSS – both pre-service and in-service teachers!

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MET 2!• Recommends a statistic course beyond intro

statistics for middle school !

•  Recommends for high school a modern day one or two intro course sequence !

• Emphasizing concepts!

• Utilizing activities and technology!

The Statistical Education of Teachers (SET)!

•  Writers: !•  Christine Franklin!•  Anna Bargagliotti!•  Catherine Case!•  Tim Jacobbe!•  Gary Kader!•  Richard Schaeffer!•  Denise Spangler!

 

Format  of  SET  Report  •  Chapter  1:  School  Statistics  and  Teachers’  Statistics  

•  Chapter  2:  General  Recommendations  and  Program  recommendations  

•  Chapter  3:  Mathematical  Practices  through  a  Statistical  Lens  

•  Chapters  4  -­‐6:  Grade  level  content  chapters  

•  Chapter  7:  Assessment  

•  Chapter  8:  Research  

•  Chapter  9:  History  

•  Appendix  of  Examples  

Research  and  History    

• Chapter  8  discusses  important  research  in  statistics  education  

• Chapter  9  presents  a  more  detailed  history  of  statistics  at  K-­‐12  (a  taste  was  given  at  beginning  of  presentation)  

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Preliminary Recommendations for Elementary Teacher Preparation!

• SET recommends that elementary teachers take!•  A special section of an intro course!OR!•  An entire course in statistics content for teachers!OR!•  A reconfiguration of an existing content course for

teachers to include at least 6 weeks of study of statistics and related ideas in probability!

Preliminary Recommendations for Middle Teacher Preparation!

•  SET recommends that middle school teachers take!•  A special section of an intro course!AND!•  A course focused on the statistical content they

will be teaching using the GAISE framework as a model!•  This course should also help teaches understand

connections across grade bands as well as between statistics and other areas of study in middle grades (mathematics, science, social science, etc.)!

!

Preliminary Recommendations for High School Teacher Preparation!

•  SET recommends that high school teachers take:!•  An introductory course that emphasizes modern data

analysis, simulation approaches to inference using the appropriate technologies!

•  A second course in statistical methods that builds on first course including randomization and classical procedures for inference [for example comparing two parameters, ANOVA, and tests for categorical data]!

•  A statistical modeling course based on multiple regression, including the use of both categorical and numerical explanatory variables and the fitting of exponential and power models!

Summary of “Courses”!•  Elementary!

•  6 weeks to 1 course!

•  Middle !•  2 courses!

•  High!•  3 courses!

•  These recommendations are consistent with the MET II report. Want courses taught with pedagogical component demonstrating how best to deliver subtle reasoning of Statistics to students. !

 

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The Intro Course!•  The standard college level intro stat course is not

adequate for teacher preparation!

•  SET recommends a modern day intro course emphasizing!•  data analysis and simulation approaches to understanding

inference, !•  more on modeling, and !•  statistical theory that ties in with probability theory (e.g., the

use of conditional probability in contingency tables and the chi-squared test)!•  The current typical standard course tends to be formula-

based, going through the list of hypothesis tests and probability theory somewhat removed from the statistical concepts being covered!

What Should Math, Math Ed, and Statistics Departments Do?!

• Carefully examine the intro stat course to see how it can be reconfigured to meet the needs of teacher preparation possibly opening up a specific section of the course for all K-12 teachers!

• Additional teacher coursework can be tailored to the grade levels a teacher will be teaching!

• Work collaboratively with statisticians who have experience in statistics education to design courses!

 

The  Mathematical  Practices  

• Through  a  statistical  lens  

Standards  for  MP  

1. M

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pro

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s an

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olvi

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6. A

ttend

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2. Reason abstractly and quantitatively. 3. Construct viable arguments and

critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Reasoning and Explaining

Modeling and Using Tools

Seeing Structure and Generalizing

1.28 William McCallum, University of Arizona

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The Statistical Education of Teachers (SET)!

• The report emphasizes that teachers of all grade levels need to understand the “statistical process” !•  Formulate questions!•  Collect data!•  Analyze data!•  Interpret results!

!

• The statistical process components are the common headings in the three chapters (elementary, middle, and high) of SET!

Connections!•  We want teacher preparation in statistics to be

connected throughout the grade bands!•  Elementary à Middle à High!

•  We want content at each grade band that will progress teachers through the statistical investigative process!

•  Let’s explore an example that can be used in each grade band differently to develop the appropriate skills of student appropriate for their grade level!

Bottle  and  Tap  Water  

• Demonstrating  connections  across  grade  bands  

ASA K-12 Resources !

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ASA K-12Resources! Exciting NSF Projects !

LOCUS    

• The  ‘A’  of  GAISE  and  the  basis  for  the  assessment  chapter  of  SET