The Question Formulation Unit 1 Data and Variability

The Question Formulation Unit 1 – Data and Variability 2/5/2022 Algebra 1 Institute 1

What is Statistics? • Groups of 4 • Write down your thoughts • Share the group results 2/5/2022 Algebra 1 Institute 2

Statistics is a Solving-Problem Process The investigative process of a statistical consists of four fundamental stages or steps: (1) (2) (3) (4) Formulating a question that can be address with data Designing and employing a plan for collecting data Analyzing and summarizing the data Interpreting the results for the analysis, and answering the question on the basis of the data. Principles and Standards and the American Statistical Association’s report Guidelines for Assessment and Instruction in Statistics Education (GAISE) (Franklin et al. 2007) Definition: A statistic is a function of data 2/5/2022 Algebra 1 Institute 3

The Case for Statistics Education In our increasingly data-intensive world, statistics is one of the most important areas of the mathematical sciences for helping students succeed in dealing with the requirements of citizenship, employment, and continuing education (Franklin et al. 2007; College Board 2006, 2007; American Diploma Project 2004). 2/5/2022 Algebra 1 Institute 4

Formulate Question • What would you like to know about the other participants? 2/5/2022 Algebra 1 Institute 5

Difference Between a Question and a Statistical Question • Question: deterministic answer – How tall am I? • Statistical Question: anticipates an answer based on data that vary – How tall are adult men in the USA? The anticipation of variability is the basis for understanding the statistics question distinction 2/5/2022 Algebra 1 Institute 6

GAISE: Statistics Education is a Developmental Process • Three developmental levels: A, B, and C. • Based on development in statistical literacy, not age. • If a student does not have statistical experience at level A, then it is not appropriate for that student to jump into level C. 2/5/2022 Algebra 1 Institute 7

(1) Formulate Questions Level A Level B Level C Beginning awareness of the statistics question distinction Teachers pose questions of interest Questions restricted to the classroom Increased awareness of the statistics question distinction Students begin to pose their own questions of interest Questions not restricted to the classroom Students can make the statistics question distinction Students pose their own questions of interest Questions seek generalization 2/5/2022 Algebra 1 Institute 8

(1) Examples of Questions Level A How long are the words on this page? 2/5/2022 Level B Are the words in a chapter in a fifthgrade book longer than the words in a chapter of a sixthgrade book? Algebra 1 Institute Level C Do sixth-grade books use longer words than a fifthgrade book? 9