Download Statistics and Probability

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Progressions through the Common Core
Angelina Morelli
Mary Velez
Chance Nalley
Mandy Lenham
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Overview of the past
In the past, Statistics and Probability took a back-stage to
Algebra and Geometry in the secondary school. Units on
Statistics and Probability were relegated to the end of the
year either for educational enrichment after standardized
testing or crammed in for the question or two that appear on
state tests.
In elementary and middle school, students learned to
calculate the mean, median and mode from contrived data
sets. Students were given data and taught how to construct
representations such as bar charts and circle graphs. Little, if
any, coverage was given to the why a particular data
representation was preferable; and little opportunity was
given to generate data.
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Overview of the Past
The high school level was pretty much more of the same. In
Algebra 1, students reviewed methods for calculating
measures of center, constructing representations such as box
plots and histograms, and rote application of some of the
basic rules of probability. In Algebra 2, students received an
introduction to standard deviation to facilitate coverage of
the Normal Distribution and exposed to formulas for
combinations and permutations.
At every level, little or superficial emphasis was placed on
analysis and interpretation of the results of statistical
processes. Only students taking AP Statistics, were expected
to articulate true understanding of data representations,
generate data and draw conclusions based on data.
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A kindergarten through 12 look…
K-3:
Categorical Data Progression
4-5:
Measurement Progression
Prior to grade six the students are exposed to statistics
through the Measurement and Data Strand. At age
appropriate levels they have measured, collected, and
interpreted data with line, bar, and picture graphs. They
have formulated and answered questions with respect to
data; designed and used a plan to collect data; analyzed it;
and interpreted the results to draw age-appropriate
conclusions.
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6:
A kindergarten through 12 look…
• Increase understanding of variability
• Describe data distributions with respect to center and spread
• Organize data into histograms and box plots FOR interpretation and
comparison
7:
• Move from analysis to production of data and introduce probability
• Differentiate between variability in a sample and variability in a
statistic computed from a sample
• Create and interpret sampling distributions
8:
• Transition to interpretation of bivariate data
• Link coordinate plane to analysis of bivariate data
• Scatterplots, regression lines, and describing the shape and center of
bivariate data
• Analysis of Two-way tables; looking for patterns and associations
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9-12:
A kindergarten through 12 look…
Interpreting Categorical and Quantitative Data
• Summarize, represent, and interpret data on a single variable
• Summarize, represent, and interpret data on two variables
• Interpret linear models
Making Inferences and Justifying Conclusions
• Understand and evaluate random processes of statistical experiments
• Make inferences and justify conclusions from sample surveys,
experiments, and observational studies
Conditional Probability and the Rules of Probability
• Understand independence and conditional probability and use them to
interpret data
• Use the rules of probability to compute the probabilities of compound
events in a uniform probability model
Using Probability to Make Decisions
• Calculate expected values and use to solve problems
• Use probability to evaluate outcomes of decisions
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How the Thinking of Teachers and Teaching will Change
Gone are the days of statistics and probability as an optional
topic—progression in a six-through-twelve curriculum
creates a dependence on completion of each objective in
due course.
Teachers will need to consider where and when these topics
should be taught because they MUST be taught—and deeply
within context.
At the beginning stages (k-5) students must be able to
describe and articulate comparisons between data
representations—even before being technically competent.
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How the Thinking of Teachers and Teaching will Change
In middle school students are asked to interpret data representations in
context, which many AP Statistics teachers can say is a challenge for
high school students. This will require students to build an appropriate
lexicon to call upon in discussing statistics.
Within this context measures of central tendency (mean, median, and
mode) will be supplanted by SHAPE, CENTER, and SPREAD qualitatively
and, to an extent, technically.
Teachers will need to be story tellers and discussion leaders, setting a
stage for students to delve deep with both technical skills and
qualitative skills.
High school teacher will need to adjust in the awareness that the
students coming to them have in fact seen statistics and articulated
conclusions and made observations.
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Surprising
Our Take on The Stat(e) of the Stat
It was extremely surprising (especially as an AP Stat teacher)
to realize the extent of the content that is taught in the middle
school—even before middle school students should have an
understanding of dotplots.
In grade 6, the concepts of variability and describing data are
taught, including center and spread. Grade 7 delves into probability
by using tree diagrams and 2-way tables; and students are
introduced to the idea of random sampling (Yay!). In grade 8,
bivariate data, both categorical, with marginal and conditional
probabilities, and quantitative (finding the least squares regression
line and correlation coefficient) are introduced (whoa!).
These topics are essentially the first month or so of many AP
Statistics courses. Students often come in with very little knowledge
of any statistics, but this will change.
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Our Take on The Stat(e) of the Stat
Implications
With the common core standards, students are exposed to
statistical concepts early. Statistics has always been present in
standards, but was usually brushed aside due to time constraints or
lack of connection to future topics.
Statistics is now valued more at ALL grade levels. Not only
will this increase students’ preparedness for both an AP Statistics
class and an undergraduate level statistics courses (which is the
most common math class that college students take for their GE
math requirement), but it will also increase the level of statistical
reasoning of the next generation of adults.
In our technological world a multitude of career options are
available that utilize statistics; and now weight is given to the
importance that all students have the opportunity to explore this
branch of mathematics thoroughly.