Transcript Level A - People Server at UNCW

Notes on Statistics Education
(loosely based on C. Franklin's ppt at the ASA website)
• Curriculum Standards (PSSM) of the
National Council of Teachers of
Mathematics (NCTM)
• One of the 5 strands, Data Analysis and
Probability, runs throughout the
curriculum, from Pre-K to grade 12…
Data Analysis & 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.
Statistics and Data Analysis –
PCAI
Pose the
question(s)
Collect the
data
Process of
Statistical
Investigation
Interpret the
results
Analyze the
distribution(s)
• Many teachers have not had any opportunity to
develop sound knowledge of the principles and
practices of statistics, data analysis, and
probability they are now called upon to teach
• The GAISE report helps by giving a structure to
teaching this strand in K-12:
– Guidelines for Assessment and Instruction in Statistics
Education
– The main content of the K-12 Framework is divided
into three levels, A, B, and C that parallel the PreK-5,
6-8, and 9-12 grade bands of the NCTM Standards,
but these levels are based on experience not age.
GAISE (Franklin)
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.
3 levels of learning in the GAISE report
• 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. Handson, active learning is a predominant
feature throughout.
Distinction of Levels
• All four steps of the PCAI process are
applied at all three levels, but the depth of
understanding and sophistication of
methods used increases across the levels.
• One example of these is Graph
Comprehension
– reading the data
– reading between the data
– reading beyond the data
Distinction of Levels
• Level A: Reading the data: a literal reading of
the graph - "lift" the facts that are explicitly seen
on the graph - no interpretation
• Level B: Reading between the data: includes
interpretation, requires ability to compare and
identify mathematical relationships in the graph
• Level C: Reading beyond the data: make
inferences or predictions from the graph that are
not explicitly stated in the data; requires
integration of many areas of conceptual
understandings
Distinction of Levels
Another 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.
To summarize…
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… and this
leads us to Tinkerplots!
• Open TinkerPlots & note the empty window…
• PCAI: Questions? Collect Data… Analyze… Interpret.
In classes, collect your own data:
– drag down either the Cards or Table icon, add a New attribute
(or more) and then type in your own data…
• … or use built-in TinkerPlots datasets (File… Open…)
• … Copy and Paste (from a file - go to my website, STT
215 Honors, open the Lean Body Mass file (note .csv),
copy, paste into an open Cards icon). Let's work with
this TinkerPlots dataset for a few minutes to recall some
of the basics of the program…
• Import from File (this works for text files only)
• Import from URL (go to my website, copy link location
of the CO2 data, paste…)
• Once the data is in a dataset, notice that it is in the form
of cases (rows, observations) and attributes (columns,
variables) -
• PCAI: Questions? Collect Data… Analyze… Interpret. Graphics can
be created by organizing the icons in the plot window; so work with the
Lean Body Mass dataset…colors, categorical plots, icon types, fuse into
bar graph; then quantitative variable, line plot (stack), dividers,
averages, histogram, order vertically, drawing tool for boxplot,…
• Open the TinkerPlots file: Heaviest Backpacks.tp
– look at the lesson plan for this dataset, backpack_lesson.pdf and notice
the questions that are asked throughout (PCAI)
– do kids in the higher grades carry heavier backpacks?
– what about boys and girls? a difference in their backpack weights?
– what about the 15% of body weight cutoff recommended by doctors?
• Look at the next slide to see various parts of a plot… then try various
plots to help lead you to answers of the questions posed above…some
additional questions are given below…
– can you make a value bar graph showing the pack weights labeled by the
students names, ordered by the backpack weights? colored by the
variable grade? now a regular line plot of backpack weights, colored by
grade? put these one above the other and compare … note how to get the
line plot from the value bar graph.
– can you make a bar graph showing the frequency distribution of the
categorical variable grade? color the bars with the backpack weights?
QuickTime™ and a
decompressor
are needed to see this picture.
Can you make a plot similar to this one to answer the
question about backpack weights in the different
grades? Notice the labels for the icons with the
childrens' names and the colors correspond to the
grade level, and the bars are ordered by backpack
weights… this is a value bar graph. A line plot?
Here's what your formula
window should look like
when you're creating the
new attribute pctwt…
• Now let's try out the PCAI method on our signatures…
look at the lesson (part #1) on measuring the lengths of
our signatures and complete the first two pages…
– what are the questions that occur to you about dominant and
non-dominant signatures after doing this data collection activity?
– can you use the TinkerPlots skills you learned this morning to
answer those questions?
– write up your results in a TinkerPlots document using the Text
boxes, justifying your conclusions with graphics and statistics!
• Now look at part #2 of the Signatures lesson - I
anticipate these questions will keep us busy with
TinkerPlots for the remainder of the time!