1. Writing statistical reports – for ESOL and low literacy level students
Malia Puloka
University of Auckland

2. Today’s focus: Discussing FEATURES of statistical graphs

3. Background of student ESOL class English is their second language
Recently migrated to NZ
English is the first language but not the language spoken at home
Never spoke English prior to starting at school
No prior formal education
Placed in a maths course made up of mostly statistics standards
Entrance level of literacy/numeracy is 3B or lower

4. Common Literacy issues
evident in students’ statistical reports:
Language barrier leads to poor sentence structure
Unfamiliar with statistical terms and concepts
Not knowing the specific features to talk about
Not knowing how to tell stories about features
Inadequate/incomplete descriptions of features
Misuse of statistical language
Unfamiliar context

5. Actual student work

6. Actual student work

7. Actual student work

8. Actual student work

9. Actual student work

10. Actual student work

11. Actual student work

12. Common mistakes – misuse of statistical language
“…the median height of male and the median height of female overlap…”
“…the seasonal trend is definitely increasing throughout the data…”
I noticed that the relationship between the weight of food and amount of fat in it is positive.

13. Actual student work

14. Actual student work

15. Starter / Brainstorming ACTIVITY: smartphone shopping
Help me decide the kind of smartphone to buy. What features of the smartphone would you consider before buying? Write words that describe each feature.
Memory
-GBs
-storage
Navigation
GPS
tracker
Bluetooth/ Wifi
Colour
Platinum
Shimmery
Sensor
Scan
Rotation
Camera quality HD
pixels
Media
Songs
Videos

16. Contextual interpretation
LANGUAGE
LANGUAGE
Telling a feature…
LANGUAGE
Identify and describe
Contextual interpretation
Numerical evidence

17. FEATURES OF GRAPHS

20. Teach students how to comfortably interact with statistical graphs
A graph comes with specific features that are relevant to the type of investigation and the analysis of the data in order to solve the problem at hand. Not all features are relevant. Relevant features must be described with proper associated language.

21. Activity: group work Get into groups of 3 or 4.
Your group will be given a graph on A3 sheet.
Choose one feature to discuss.
Discuss the feature:
Identify and describe (Achieved).
Re-tell (i) in the context. (Achieved/Merit)
Give numerical evidence (Merit)
Stick your chart and work on the wall. Don’t forget to write your names.

22. LANGUAGE OF SCATTER PLOTS– TARSOGRP
FEATURES
Language
Trend
Linear/non-linear
Association
Positive/negative, describe the association, e.g., “…the higher the carat the more expensive is the diamond…”
Relationship
Strong/moderate/weak, No relationship
Scatter
High/moderate/low, Consistent/inconsistent
Two-line test
Outliers
Mention if there’s any. Use two line test to decide.
Group
Mention if there’s any.
Regression line
Interpret the equation: ‘The ___ is increasing/decreasing at a rate of ___.’
Prediction
Use the equation of the regression line to predict
Confidence in Prediction
Use the two-line test and scatter to determine
Adapted from: Priscilla Allan; Jake Wills

23. LANGUAGE OF DOT & BOX PLOTS - CSSII
FEATURES
Language
Comparative words
Centre
Median, majority
E.g., Higher/lower than, heavier/lighter than, more/less, close/far, same, similar,
Shift
Shape
Unimodal/bimodal, peak, normal, symmetrical, evenly spread, clustered, skew L/R
What and where?
At about
Spread
Upper/lower quartiles
Interquartile range
Middle 50%
Overall range
More/less spread, wider/narrower
Overlap
Interesting feature
Extremely high/low
Unusual data, extremely high/low
Confidence Interval
Population median lies between ___ and ___ whereas…
Wider interval than…
Useful words: whereas, however, although, etc.
Adapted from: Pfannkuch & Wild; CensusAtSchool

24. LANGUAGE OF TIME SERIES - LSOMPC
FEATURES
Language
Long term trend
Increase, decrease, constant, etc.
Seasonal trend
Highest season – how much ‘above average’
Lowest season – how much ‘below average’
On average
higher/lower than trend line
Consistent/inconsistent
Outliers
Residual
Times when data was ‘higher/lower than expected’
Model
Appropriateness of the model – e.g., ‘…the model (NZGrapher) can fit in the predicted data well…’
Prediction
Use the equation
Confidence in prediction
Do you trust the model to give appropriate predictions?
Adapted from Jake Wills

25. Example: Comparison investigation STANDARD PROGRESSION
Simple steps
Example: Time Series
Example: Comparison investigation
STANDARD PROGRESSION
Tell me what you see (Identify and describe)
Seasonal trend: December has the highest number of penguins.
The median of group A is higher than the median of group B.
Contextual interpretation (What does it mean)
The number of penguins at the colony at Phillip Island (Aust) is at its highest in December.
The average house price in Auckland is higher than that in Tauranga.
Numerical support/evidence
The number of penguins at the colony at Phillip Island (Aust) is at its highest in December about 400 penguins above the trend line.
The average house price in Auckland ($970,000) is higher than that in Tauranga ($672,000).
What could have caused this?
It’s summer time and penguins are coming back as the weather is warmer.
There seems to be more people in NZ and migrating from overseas wanting to live in Auckland.
What impact does it have?
(Good for Conclusion)
This would make a better tourist attraction bringing more money to the Phillip Island.
With house prices too high in Auckland, this might push Maths teachers to move to Tauranga.
Achieved
Merit
Excellence

26. Resources http://new.censusatschool.org.nz/resources/