GAISEGuidelines for Assessment and Instruction

in Statistics EducationPre-K -- 12 Report

Christine FranklinUniversity of Georgia

Department of Statisticschris@stat.uga.edu

What’s Happening in Statistics Education, PreK-12

• Everyone – students, teachers, parents, employers – interested in data

• Data analysis has become a key component of modern PreK-12 mathematics curriculum

• NCTM, NAEP, State guidelines

Current efforts

• Curriculum Standards (PSSM) of the National Council of Teachers of Mathematics (NCTM)

• One of the 5 strands, Data Analysis and Probability, which runs throughout the curriculum

Data Analysis and Probability Strand

Instructional programs from Pre-K through grade 12 should enable all students to—

• formulate questions that can be addressed with data and

• collect, organize, and display relevant data to answer them;

• select and use appropriate statistical methods to analyze data;

• develop and evaluate inferences and predictions that are based on data;

• understand and apply basic concepts of probability.

Current efforts

Advanced Placement Statistics

• First exam in 1997 – 7500 exams

• In 2003 – 60,000 exams

Science Education and Quantitative Literacy (SEAQL)

Series of workshops for science teachers and materials on how to improve science instruction by using QL techniques

What’s needed for the future

• Taken together, these programs and efforts, and many others such as NAEP and state guidelines, have produced an enormous need for better statistics education among the mathematics teachers of the country

• Mathematics Education of Teachers (MET) Report

• Sees statistics as the topic in which current and prospective teachers need the most help with content and pedagogy

• Quotes from the report:

Quotes from MET Report• Statistics is the science of data, and the daily display of data by

the media notwithstanding, most elementary teachers have little or no experience in this vitally important field.”

• “Of all the mathematical topics now appearing in the middle grades curricula, teachers are least prepared to teach statistics and probability.”

• “Statistics is now widely acknowledged to be an extremely valuable set of tools for problem solving and decision making. But, despite the production of interesting statistics materials for the schools, it has been hard to find room for the subject in (high school) curricula dominated by preparation for calculus.”

What’s Needed for the Future

• It is this goal – helping teachers to teach statistics – that must dominate the interest, energy, and resources of the statistics education community in the years ahead if the information age is to reach its full potential of informed decision-making based on rational thought and quantitative evidence

ASA Response to the MET Report: TEAMS

• A leadership conference entitled “Stat/Math TEAMS (Teacher Education: Assessment, Methods, and Strategies)

• Held at University of Georgia, October 30 – November 2, 2003

• Major support from ASA and NSF

TEAMSGoals of the conference

• To create awareness among teacher educators of what’s needed to better prepare K-12 teachers to give instruction in probability and statistics

• To build a team of statistics and math educators that can examine issues and provide guidance in methods to improve teacher preparation

• To draft guidelines for the statistics education of teachers and formulate a plan to have these adopted by the lead organizations involved with teacher education and statistics education

• To develop mechanisms for materials review and development, pedagogical improvements, and the implementation of research findings related to how students learn statistics and probability

What’s Needed for the Future

• Statistics is a relatively new science that is still developing

• Many teachers have not had any opportunity to develop sound knowledge of the principles and practices of data analysis they are now called upon to teach

• “Fleshing out” of the “Standards” is more essential for the statistics strand than for others

GAISE

• A Framework for Teaching Statistic Within the PreK-12 Mathematics Curriculum and for the College Introductory Course

• Guidelines for Assessment and Instruction in Statistics Education

• Strategic initiative of ASA

• What is this document and why is it needed?

GAISE

• The goals of the K-12 document are 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.

PreK-12 Writers and Advisors

Writers: Advisors:

• Christine Franklin Peter Holmes

• Richard Scheaffer Cliff Konold

• Roxy Peck Mike Perry

• Denise Mewborn Susan Friel

• Gary Kader Brad Hartlaub

• Jerry Moreno Landy Godbold

GAISE

The foundation for the K-12 Framework rests on the NCTM Standards.

• 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.

Levels in PreK-12 GAISE

• 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.

Distinction of Levels

• 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.

GAISE

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.

Distinction of Levels

• All four steps of this process are used at all three levels, but the depth of understanding and sophistication of methods used increases across the levels.

• For example, an elementary class may collect data to answer questions about their classroom, a middle school class may collect data to answer questions about the school, and a high school class may collect data to answer questions about the community and model the relationship between, say, housing prices and geographic variables such as the location of schools.

Distinction of Levels

Example of clarity of concepts at each level:Use of probability:

• Level A: Chance/uncertainty; impossible----certain; equally likely

concept; compare experimental and theoretical probability for coins and spinners

• Level B: concept of not equally likely; simple binomial distribution

• Level C: use simulation for sampling distributions to examine simulated p-values

Distinction of Levels

Example of clarity of concepts at each level:Mean:

• Level A: Idea of fair share – foreshadow the balance point

• Level B: Mean as a balancing point• Level C: Mean as an estimate from a

sample that will be used to make an inference about a population – understanding the concept of using a sampling distribution to take a sample mean to estimate the population mean.

Distinction of Levels

Example of clarity of concepts at each level:• What type of music is most popular among their

peers in school? (rock, country, rap)• 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.

GAISE

Basic principles around which the Framework revolves can be summarized as:

• 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

Conclusion

• Ultimate goal of the framework is to lay out a foundation for educational programs designed to help students achieve the noble goal of being a sound statistically literate citizen.

• Principles and goals of the PreK-12 GAISE document parallel the goals and guidelines of the college report.