Mathematics and Statistics
A look at progressions in Statistics
Jumbo Day Hauraki Plains College
15th June 201
Sandra Cathcart
Introduction
• Background to the workshop
• Important ideas
• What will you get out of this?
Objectives
• To enhance teacher knowledge of statistics
progressions to senior levels
• To experience a selection of statistics tasks for
use in the classroom to enhance the pedagogy
of NZC
• To help teachers develop a more responsive
scheme design
What we can’t do without!
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Statistics Achievement Objectives.
Census at School - all levels
PPDAC cycle – “How kids learn”
nzmaths to level 5
Senior secondary subject guides (L6 to L8)
nzamt
Figure it Out – revised for juniors
Level 1 and level 2
Level three
• What are variables?
• How do we introduce this?
Data Cards
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With or without variables
What are these cards telling us?
I notice……..statements
I wonder……..statements
Using the cards to answer the questions.
Making our own cards
Mode of transport
to school:
bus,bike,car,walk
No of
people who
slept in
your house
last night
Wrist
measurement
Estimate of
the time
takren to get
to school
Comparison
• At level 3 students should be able to talk about the features
differ for the two graphs they are comparing. Maybe draw a
circle around the middle group and talk about how circles sit
in relation to one another, maybe one is more to the right
than the other. Maybe compare boys to girls, or year 5 to
year 7
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Level 4
• Plan and conduct investigations using the statistical enquiry
cycle:
• determining appropriate variables and data collection
methods
• gathering, sorting, and displaying multivariate category,
measurement, and time-series data to detect patterns,
variations, relationships, and trends
• comparing distributions visually
• communicating findings, using appropriate displays.
Analysis: summary
At level 3/4/5 students should be talking about
•- the shape of the data (hills, bumps, skew, symmetrical, bimodal)
•- middle “group” (modal clump)
•- high/low range – describe the range rather than give the value
•- density (crowded, empty, piled up, clumped, busy)
•- spread (spread out, close together)
•- unusual/values of special interest (outliers, gaps, clumps)
Hungry Planet
Comparison at level 4
• At level 4 students can start to identify the middle group by
circling this group. They might also extend a line from the
middle group to the extreme values (highest/lowest) creating
a “hat plot” (Mexican on a bike)
• Comment on shape, spread, middle groups
Level 5
• Plan and conduct surveys and experiments using the
statistical enquiry cycle:
• determining appropriate variables and measures
• considering sources of variation
• gathering and cleaning data
• using multiple displays, and re-categorising data to find
patterns, variations, relationships, and trends in multivariate
data sets
• comparing sample distributions visually, using measures of
centre, spread, and proportion
• presenting a report of findings.
What makes a good investigative
question?
Comparison at level 5
• At level 5 the hat plot can be updated by adding the middle
value and then extending into formally finding the median and
quartiles, always keep the dot plot with the box plot.
• - comment on summary statistics
• - shape
• - spread
• - middle 50%
Clean it up
Growing Scatter
Shape activity
Using “brush strokes”
Level 6
• Plan and conduct investigations using the
statistical enquiry cycle:
• justifying the variables and measures used
• managing sources of variation, including through
the use of random sampling
• identifying and communicating features in context
(trends, relationships between variables, and
differences within and between distributions),
using multiple displays
• making informal inferences about populations from
sample data
• justifying findings, using displays and measures.
Descriptive or inferential?
Summary
Box plots: Making the call
• Lesson plan handout
• http://www.censusatschool.org.nz/2009/infor
mal-inference/workshops/
Level 7
• Carry out investigations of phenomena, using the
statistical enquiry cycle:
– conducting surveys that require random sampling techniques,
conducting experiments, and using existing data sets
– evaluating the choice of measures for variables and the
sampling and data collection methods used
• using relevant contextual knowledge, exploratory data
analysis, and statistical inference. Make inferences from
surveys and experiments:
– making informal predictions, interpolations, and extrapolations
– using sample statistics to make point estimates of population
parameters
– recognising the effect of sample size on the variability of an
estimate.
Level 8
• Carry out investigations of phenomena, using the
statistical enquiry cycle:
– conducting experiments using experimental design principles,
conducting surveys, and using existing data sets
– finding, using, and assessing appropriate models (including linear
regression for bivariate data and additive models for time-series
data), seeking explanations, and making predictions
– using informed contextual knowledge, exploratory data analysis,
and statistical inference
– communicating findings and evaluating all stages of the cycle.
• Make inferences from surveys and experiments:
– determining estimates and confidence intervals for means,
proportions, and differences, recognising the relevance of the
central limit theorem
– using methods such as resampling or randomisation to assess the
strength of evidence.