Journey in Developing Statistical Reasoning in Elementary and Middle School Teacher Leaders DeAnn Huinker & Janis Freckmann Milwaukee Mathematics Partnership University of Wisconsin–Milwaukee Association of Teachers of Mathematics (AMTE) Annual Meeting February 5, 2009, Orlando, Florida This material is based upon work supported by the National Science Foundation under Grant No Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation (NSF).

Session Goals  Summarize the GAISE report Framework Model and key concepts (ASA, 2005).  Review a year-long sequence of activities used to strengthen statistical reasoning of teacher leaders.  Report impact on teachers’ statistics and probability content knowledge and knowledge for teaching (University of Louisville).

Ponder and Discuss… As you reflect on your work with preservice and inservice teachers, what are some concepts and ideas in statistical reasoning that challenge their understanding? Turn to the person next to you, share and explain your responses.

Statements from the 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.” (p. 23)  “Of all the mathematical topics now appearing in the middle grades curricula, teachers are least prepared to teach statistics and probability.” (p. 114)  “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 curricula dominated by preparation for calculus.” (p. 137)

Statements from Teacher Leaders  It was good to revisit some content that I had not used since high school or college. I enjoyed analyzing the data and deepening my understanding of probability. It is an area that scares people a bit (myself included) and therefore teachers may not teach it well because of the lack of understanding.  Statistics, probability, and data analysis has always been an area of weakness for me, but the content sessions have really allowed me to expand my knowledge. They have also given me the opportunity to see a continuum of thinking across grade levels that I didn't have before.

GAISE Guidelines for Assessment and Instruction in Statistics Education A Pre-K–12 Curriculum Framework American Statistical Association (2005)

The Nature of Variability  A major objective of statistics education is to help students develop statistical thinking. Statistical thinking must deal with the omnipresence of variability.  Statistical problem solving and decision making depend on understanding, explaining, and quantifying the variability in the data.  It is this focus on variability in data that sets apart statistics from mathematics. (GAISE report, p. 6)

The Role of Context  Statistics requires a different kind of thinking, because data are not just numbers, they are numbers with a context.  In mathematics, context obscures structure. In data analysis, context provides meaning. (GAISE report, p. 7)

The GAISE Framework I. Formulate Questions II. Collect Data III. Analyze Data IV. Interpret Results Nature of Variability Focus on Variability

Three Developmental Levels Level A  Level B  Level C  Articulates development in an orderly way.  Builds on previous concepts.  Increases in complexity.  Progression is based on experience, not age.

Collect Data Level ALevel BLevel C Do not yet design for differences Census of classroom Simple experiment Beginning awareness of design for differences Sample surveys; begin to use random selection Comparative experiment begin to use random allocation Students make design for differences Sampling designs with random selection Experimental designs with randomization

District & Participants  Milwaukee Public Schools, 90,000 students  127 Elementary Schools (K-5, K-8)  17 Middle Schools  58 High Schools, 11 Combined M/H Schools  Math Teacher Leaders (MTL)  Grades K–7  Grades 8–9

PD Sequence AugLikely and Unlikely Events; Simple Experiments SeptExperimental and Theoretical Probability OctRole of Questions in Statistical Investigations DecCollecting Data: Sampling, Bias, Randomness Jan Analyzing Variability in Data FebInterpreting Data: Measures of Central Tendency MarInterpreting Data: Stem and Leaf Plots, Box Plots AprInterpreting Data: Revisiting Box Plots JuneFair and Unfair Games www4.uwm.edu/Org/mmp/_resources/math_content.htm

Green Fields Golf 18 th Hole The math group went golfing as a way of celebrating the 5 th year of the grant. Which team did better on this hole? Team A Scores Team B Scores 4, 5, 5, 18 6, 7, 8

Ritzy & Normal Counties In Ritzy County, the average annual household income is $100,000. In neighboring Normal County, the average annual household income is $30,000. Sally thinks the average income of the two counties is $65,000.  Do you agree with Sally or not?  If so, explain why; if not, explain why not What other information would you need in order to calculate the average annual household income in the two-county area?

Are You Typical? In MPS there are: 4,793 teachers with 58,414 combined years of teaching experience Mean years Mode 5 years Median 10 years

Same Median, Different Mean Nine teachers reported their years of experience as follows: 7, 5, 5, 4, 6, 8, 7, 6, 6 Draw cubes to represent this data set. What is the median? the mean? Rearrange the cubes in your drawing to represent possible data sets for the following. You may add or remove cubes. Record each data set and its mean.  Sample of 9 teachers with a median of 6 years experience, but a mean less than 6.  Sample of 9 teachers with a median of 6 years experience, but a mean greater than 6.

Consolidate ideas What changes occurred in the data set that allowed you to keep the median but change the mean?  To lower the mean…  To increase the mean…

Big Ideas: Analyzing Data  When analyzing data, key features of the data are measures of center, spread, and shape.  The question affects the choice of measure of central tendency.  The median is a more robust measure of central tendency.  The mean is more influenced by outliers.

Clarity of Concepts: “Mean” Level A: Mean as an idea of fair share or redistribution and leveling. Level B: Mean as a balancing point. Level C: Mean as an estimate from a sample to make an inference about a population.

Procedures Pretest: September items on Statistics and Probability School Year: Monthly PD sessions 16 hours Grades K–7 Math Teacher Leaders 12 hours Grades 8–9 Math Teacher Leaders About 200 Teacher Leaders Posttest: May/June items on Statistics and Probability

Diagnostic Mathematics Assessments for Middle School Teachers  Level 1. Declarative Knowledge  Level 2. Conceptual Knowledge  Level 3. Problem Solving and Reasoning  Level 4. Mathematical Knowledge for Teaching URL: louisville.edu/education/research/centers/crmstd University of Louisville, Center for Research in Mathematics and Science Teacher Development

Instruments  Statistics and Probability Pretest & Posttest  Form A (v2.3), Form B (v5.3) (Reliability 0.90)  20 items: 10 multiple choice, 10 open response  Open response items score up to 3 points  Each Level I–IV has a possible score of 10  Statistics sub-score (20 points)  Probability sub-score (20 points)

K-7: n=62; Gr 8-9: n=32 Test Results by Strand

Types of Knowledge  Level 1. Declarative Knowledge  Level 2. Conceptual Knowledge  Level 3. Problem Solving and Reasoning  Level 4. Mathematical Knowledge for Teaching

Test Results by Type of Knowledge

Using the GAISE Report How Can I Use the GAISE Report?  As a quick reference for the components of the framework.  As a resource for explanations of each component in practice—and as a series of examples by which we can teach each component. Focus Questions  Considering the three levels, where would you place the majority of the lessons that are taught in your school?  How might you use the GAISE Report for professional development at your school?

MTL comment: Variability  I have a better understanding of variability. I realize that statistics is centered more on the main term "variability" than it is on mean, median, and mode. Usually when statistics is mentioned, someone automatically talks about mean, median, and mode. Now I understand that these "m” terms are used to help describe variability.

MTL comments: Formulate Questions  We had grade level discussions about formulating good questions and the implications of teachers always giving students the questions rather than having students develop them, too.  I have seen some of the teachers applying this idea to questioning in several different subject areas. For example, the Kindergarten teachers were having students ask questions that they thought they might be able to answer from data they were planning to graph.

MTL comment: Sampling  I took back to my students the idea of collecting data. We designed surveys about favorite foods. I think that the learning was deeper because I better understood the importance of formulating a good question and identifying the sample population.  Several students asked for my answer, so we had to discuss whether or not I was included in “the class.” We were able to talk about how this impacts the results and accuracy of our data.

MTL comment: Role of Context  The GAISE Report clearly outlined the major parts of statistics. Many teachers create graphing projects without knowing how to make them appropriate for their grade levels.  I found that I could push my students to make some statements that were more precise than saying "pink has more than yellow.” They were able to connect their representations back to their questions and the context, and say "more children in our class like pink than yellow.”  It's just a small step, but it's the kind of tweaking that could make our students more successful with statistics.

MTL comments: Development  Because some of the content presented in these meetings was challenging for me at the K–5 level, it helped me reach beyond what I might have done in the past with my students, giving me the enrichment I needed as a teacher to thoroughly teach concepts at deeper levels.

Thank You! MMP website PD Resources www4.uwm.edu/Org/mmp/_resources/math_content.htm DeAnn Huinker, Janis Freckmann,