journey in developing statistical reasoning in elementary and middle school teacher leaders deann...
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Journey in Developing Statistical Reasoning in Elementary and Middle School Teacher LeadersDeAnn Huinker & Janis FreckmannMilwaukee Mathematics PartnershipUniversity of Wisconsin–[email protected], [email protected]
Association of Teachers of Mathematics (AMTE) Annual MeetingFebruary 5, 2009, Orlando, Florida
www.mmp.uwm.edu
This material is based upon work supported by the National Science Foundation under Grant No. 0314898. 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)
www.cbmsweb.org/MET_Document/
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.
GAISEGuidelines for
Assessment and Instruction in Statistics
EducationA Pre-K–12 Curriculum
Framework
American Statistical Association (2005)
www.amstat.org/education/gaise/
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 QuestionsII. Collect DataIII. Analyze DataIV. Interpret Results------------------------------------Nature of VariabilityFocus 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 A Level B Level 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
Aug Likely and Unlikely Events; Simple ExperimentsSept Experimental and Theoretical Probability Oct Role of Questions in Statistical InvestigationsDec Collecting Data: Sampling, Bias, RandomnessJan Analyzing Variability in DataFeb Interpreting Data: Measures of Central
TendencyMar Interpreting Data: Stem and Leaf Plots, Box
PlotsApr Interpreting Data: Revisiting Box Plots June Fair and Unfair Games
www4.uwm.edu/Org/mmp/_resources/math_content.htm
Green Fields Golf 18th Hole
The math group went golfing as a way of celebrating the 5th year of the grant. Which team did better on this hole?
Team A Scores Team B Scores4, 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 12.19 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, 6Draw 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 2007
20 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 200820 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 websitewww.mmp.uwm.edu
PD Resourceswww4.uwm.edu/Org/mmp/_resources/math_content.htm
DeAnn Huinker, [email protected] Freckmann, [email protected]