LITERACY AND THINKING
IN MATHEMATICS AND STATISTICS
Anna Martin
Avondale College
mar@avcol.school.nz
LITERACY AND THINKING
Statistics
• Thinking about data
• Thinking about relationships
• Thinking about comparisons
• Thinking about sources of variation
• Communicating understanding
Mathematics
• Deciphering word problems
• Teaching literacy
LITERACY AND THINKING STRATEGIES
SOLO for levels of thinking
• Identify, carry out steps, superficial thinking
• Explain, justify, link, deep thinking
Structuring paragraphs using TEXT
•
•
•
•
T (topic sentence) – Simple answer to question
E (evidence) – Linking to the displays/stats
X (explanation) – Interpreting analysis
T (tie up) – Generalising findings to……
CONFIDENCE INTERVAL EXAMPLE OF TEXT
THE CONTEXT
Scientists fear that more
and more teenagers are
becoming addicted to
technology.
Planning the
questionnaire
On the next few slides you
will be shown information
from an article. Write
down 3 key points from
each page.
NEWSPAPER ARTICLE
Have you ever interrupted childbirth,
a wedding, funeral or graduation
It talks about how sometimes we text during
ceremony to send a text? Does the
important stuff and how get interrupted or
thought of going cold turkey from
distracted. It also talks about how we can’t
technology make you want to daub
go without technology and how proud we
your social networking status in your
would be if the time we play video games
own blood across the nearest brick
got extended.
wall? Is your ideal six-month
sabbatical from work an extended
period playing World of Warcraft in a
windowless bedroom?
NEWSPAPER ARTICLE
People are contracting the computer bug
early: according to research published last
It by
talks
aboutUniversity
how people
are contracting
September
Cranfield
School
of Management
in Northampton,
of 260
the computer
bug early.
It also talks about
secondaryhow
school
pupils
26 the
per internet and
much
wesurveyed,
spend on
cent spenthow
more
than six hours
a day on
technology
is taking
over the world.
the internet. This bevy of high-tech tykes
yielded 63 per cent who felt they were
addicted to the web, 53 per cent who had a
compulsive attachment to their mobile
phones and 62 per cent who were bought
their first computer before the age of 8.
But is technophilia really such a plague?
NEWSPAPER ARTICLE
"If teenagers become more withdrawn they
run the risk of being developmentally out
This
article
talks
of step with
their
peers,"
saysabout
Capio how teenagers get
Nightingale's
consultant
psychiatrist Dr
sucked
into technology
and how they can
Richard Graham.
"It's asplit
very young
fieldour
of parents. It also
sometimes
us from
research, talks
but there
is some
to can have a big
about
howevidence
technology
suggest that girls who spend too much
impact
on
our
future.
time on Facebook miss out on key
developmental steps and could feel
immature. Extreme cases can put people's
education and employment at risk.
NEWSPAPER ARTICLE
Then there are the physical aspects. You
can have a poor diet, lose weight, not eat
This
talks about
howalltechnology is bad and
properly. If
teenagers
are pulling
nighters they
stimulants,
likeand that. It also
howmight
it canturn
gettous
into drugs
caffeine or
taurine,
and we
there
is evidence
tells
us how
can
get so addicted it can
that can increase
in the long-term."
stop us anxiety
from eating.
Teenagers, necessarily, are a high-risk
group, as are those who've had a
bereavement, separation or redundancy.
But no one is free from its impact.
NEWSPAPER ARTICLE
"At the moment people are trying to study
the effects of high exposure to technology
about
how technology
during theThis
earlyarticle
parts oftalks
people's
lives,"
continueswrecks
Graham.our
"There
are and it effects our
studies
developmental
windows
in which
'wiring' our
of brain.
learning
and how
it affects
the brain takes place. For example, if you
have a squint and it is not dealt with in the
first five years of your life, part of your
visual cortex switches off. It's a 'use it or
lose it' principle in neurology and it might
have relevance here."
UNPACKING LEARNING OUTCOMES
• LO: Use the statistical enquiry cycle to
investigate multivariate data
• Get students to try to explain what the
words enquiry, cycle and multivariate
mean
• Share understandings and
acknowledge contributions
• Model more than one way to explain
something
FROM ONE VARIABLE TO TWO
• Focus on rental prices (one variable)
• Explore what might be
affecting/linked/related to rental prices
e.g. rugby world cup, suburb, number of
bedrooms
• Lots of structure early on to help with
writing
FROM ONE VARIABLE TO TWO
• “How much is the typical weekly rent
for a house in Kingsland?”
Analysis: Mark on your dot plot the lowest rental price and the highest
rental price
Conclusion: Complete the sentence “In Kingsland, the rents range from
$____ to $_____”
Analysis: Mark on your dot plot the middle 50% of house prices (remind
them that half of 20 is 10, so where do the middle 10 house sit between).
Conclusion: Complete the sentence “The rents are typically between $____
and $____”
Analysis: Mark on your dot plot any common rent prices (modes)
Conclusion: Complete the sentence “Common rent prices in Kingsland are
$___ and $____”
WHY BIVARIATE?
Get the students into the habit of reflecting on their
investigation, in particular the data
Why do the rental prices in Kingsland vary so much?
(answers could be: because the condition of houses
are different, where they are located is different, how
many bedrooms they have etc.)
Why are there two common rental prices? (one
would be the typical price for 1-bedroom houses, and
one would be the typical price for 2-bedroom houses)
COMPLETE ANOTHER CYCLE…..
What happens when you compare the rent by
number of bedrooms?
Greater shift in rent prices (but still variation)
What appears makes more difference to rent –
where the house is, or how many bedrooms it has?
THE PAINT BRUSH
Houses with fewer
bedrooms tend to
rent for less than
houses with many
bedrooms
Still variation in
rental prices for
houses with the
same number of
bedrooms
THE PAINT BRUSH
THINKING ABOUT RELATIONSHIPS
Get the students to paint pictures e.g. use a paint brush
to show the relationship between your age and your
height
Very scaffolded at first – put age along the bottom (in
years) and put height along the side (in units of 10 cm)
Students verbally describe what would happen as you get
older
Then try to paint the relationship (direction, type and
strength by width of paint brush)
Build up ideas of suitable units, scales, ranges for
variables, explanatory/response, no relationships
THE ELLIPSE
Using for
relationships we
think are linear
Not easy at first
but students get
there
Helps position
line of best fit
Can use for
informal
predictions
LINKING FEATURES AND STATEMENTS
Use the names of the
Describe the
variables
relationship:
It’s a positive relationship
• in context
because….
• positive/negative
It’s a strong linear
• strength/type
relationship because….
• does it make sense?
Points are close to the line
Overall the points look like they make a line
The line slopes up
As one gets bigger the other gets bigger
Low goes with low, high goes with high
FORMATIVE ASSESSMENT
Is there a
relationship
between the size
of a family and
the number of
bedrooms for
their house?
BIVARIATE
INVESTIGATION
LO: Write a
plan for a
bivariate
investigation
LIST THE STEPS FOR A METHOD




Identify variables for the investigation
Describe how the variables will be measured
Explain how the data will be collected
Decide how much data to collect
PROBLEM
What is the relationship between the size of the harddrive memory and the selling price for laptops?
What is the relationship between the
size of the hard-drive memory and the
selling price for laptops?
WHAT VARIABLES WILL YOU
INVESTIGATE?
WRITE: The variables I will investigate are……
The size of the hard-drive memory and the selling
price for different laptops
WRITE: The explanatory variable will be ……
Hard-drive memory (because I think this will
explain the selling price of the laptop)
WRITE: The response variable will be ……
Selling price (because I think this will
change/respond to different sizes of hard-drives)
What is the relationship between the
size of the hard-drive memory and the
selling price for laptops?
HOW WILL YOU COLLECT DATA FOR THE
INVESTIGATION?
THINK: Are the variables things I can measure
myself or can I find measures for the variables from
somewhere? These variables have already been measured by
stores or people selling laptops
WRITE: I can collect data for this investigation by
……
Getting ads for laptops being sold that say how big
the hard-drive memory is and what price the laptop
is being sold for from advertising pamphlets.
What is the relationship between the
size of the hard-drive memory and the
selling price for laptops?
HOW WILL YOU MEASURE THESE
VARIABLES?
THINK: What units should I use? How accurate do I
need to be? What equipment do I need?
WRITE: I will measure the variables by using…..
GB for the hard-drive memory and rounding the
selling price to the nearest $100.
What is the relationship between the
size of the hard-drive memory and the
selling price for laptops?
WHAT THINGS MIGHT AFFECT THE
MEASURES YOU TAKE?
THINK: Does it matter where I get my data from? Do
I need to be careful about getting a range of data?
Should I focus my
the investigation
screen size, themore?
processing speed, how the
laptop looks, different shops selling for different
WRITE: I wonder
if things like…………. might also
prices…
affect the selling price for laptops. To try to stop this
affecting the relationship I will……..
Make sure I only collect data from laptops from one store and
include only laptops with similar specs apart from hard-drive
memory
What is the relationship between the
size of the hard-drive memory and the
selling price for laptops?
HOW MANY MEASURES WILL YOU
COLLECT?
THINK: How much data do I need? If I am working
in a group, how much should each of us collect?
30
WRITE: I will collect data about ______
different
laptops. We will make sure __________________
we each collect around 10
values each
What is the relationship between the
size of the hard-drive memory and the
selling price for laptops?
HOW WILL YOU RECORD YOUR
RESULTS?
THINK: What things should I write down for each
laptop? How will I organise this data?
table
WRITE: I will use a ________
to record my results. I
2
will use ______
columns for each of the two
variables.
What is the relationship between the
size of the hard-drive memory and the
selling price for laptops?
GROUP WORK!
In your group, discuss how you will each contribute
to the development of a plan for the assessment.
Make a commitment to each person that you will
attend each day of the assessment and that you will
not let them down. Write down how you will
demonstrate to your teacher that each person has
contributed to the writing of the plan.
L O : D E S C R I B E A N D C O M PA R E T H E D I S T R I B U T I O N O F VA L U E S
REPRESENTED ON A BACK -TO-BACK STEM - AND-LEAF PLOT
Key: 0 | 9 means 0.9 kg
The stem and leaf plot for the records the
weight (in kilograms) of babies born in the
Somerset Maternity ward last month. The
nurse says “We certainly have lots of big
healthy babies born in our ward”. Does the
data support this?
Identify the longest leaf. Count then number of values. If it is not at least half,
take the next adjacent longest leaf.
Sketch the outline of the shape of the
distribution.
Write a sentence about where
MOST of the values are (most
Write a sentence about the shape of
has to be over half)
the distributions (symmetric,
skewed, bi-modal, unusual values)
L O : D E S C R I B E A N D C O M PA R E T H E D I S T R I B U T I O N O F VA L U E S
REPRESENTED ON A BACK -TO-BACK STEM - AND-LEAF PLOT
Most of the tomatoes from Plant 1 weighed between 30 – 59 g, but
for Plant 2 most of the tomatoes weighed between 50 – 69 g
Plant 1 was grown without
fertiliser. Plant 2 was grown
with fertiliser. The values are
the weights of the tomatoes for
each plant grown (in grams).
Identify the longest leaf for
each variable.
The distribution of weights of tomatoes from both plants appear to be
Sketch the outline of the shape
symmetric, but Plant 1 weights are more inconsistent/spread out
of the distribution for each
than
Plant
2
Compare MOST of the values
variable.
are (most has to be over half).
Compare the shape of the
distributions (symmetric, skewed, bimodal, unusual values)
Draw stem and leaf.
Outline shape.
Identify longest leaf or
leaves.
Identify anything
unusual.
Most of the values….
Calculate statistics
(min,
LQ,
median,
UQ,
max,
range,
IQR,
mean,
standard deviation).
Typically higher…..
Draw box and whisker
plot.
Middle 50% similar ……(A lot of overlap
of boxes)
Shape of distribution (skewed,
symmetric, bi-modal….)
Weird….
More spread out…..
Average difference…..
More consistent….
Overall higher….(box shifted higher)
Middle 50% more varied …… (IQR
bigger, box wider)
Shape of distribution (skewed,
symmetric…)
Summar y for
US12332
WRITING COMPARISON STATEMENTS
The variable
The explanation
The number of minutes spent
doing homework
The median was higher
The link
The comparison
Year 9 vs Year 11
The feature
Typically higher
Because
The evidence
The median was 92 minutes
for Year 9 and 75 minutes for
Year 11
LEARNING REFLECTIONS
SNEAKY LITERACY
LO: SOLVE WORD
PROBLEMS USING TIMES
TABLES OR DOUBLES OR
HALVES
Copy the date and learning
outcome into your DO NOW
books.
Multiplication
and division
strategies
WRITING PROBLEMS
READ: Miss Martin has made up a problem
which involves doubling.
PROBLEM: Bob has $10 in his account, but
needs twice as much to buy a new video
game. How much does he need for the new
video game?
LINK: What words in the sentence tell you to
double?
WRITING PROBLEMS
DOUBLE  T WICE AS MUCH
THINK: Make up your own problem that
involves doubling.
WRITE: Write down what your made up
problem is.
SHARE: Give your problem to the person
beside you and try to answer theirs!
WRITING PROBLEMS
READ: Miss Martin has made up a problem
which involves the three times table.
PROBLEM: Ben has three friends. Each friend
has 4 video games. How many video games
do his friends have all together?
LINK: What words in the sentence tell you to
use the three times tables?
WRITING PROBLEMS
TIMES TABLES  EACH, ALL TOGETHER
THINK: Make up your own problem that
involves the four times table.
WRITE: Write down what your made up
problem is.
SHARE: Give your problem to the person
beside you and try to answer theirs!
WRITING PROBLEMS
READ: Miss Martin has made up a problem
which involves halving.
PROBLEM: Bob has 24 lollies. He wants to
share them equally between him and his
friend. How many lollies will each of them
get?
LINK: What words in the sentence tell you to
halve?
WRITING PROBLEMS
HALVE  SHARE EQUALLY BET WEEN T WO
THINK: Make up your own problem that
involves halving.
WRITE: Write down what your made up
problem is.
SHARE: Give your problem to the person
beside you and try to answer theirs!
TEACH FOR UNDERSTANDING SO STUDENTS CAN
COMMUNICATE UNDERSTANDING
Three key concepts
• Selecting and using
• Evaluating and comparing
• Considering other factors and explanations
MY ADVICE
The best way to improve the quality of what they
write/analyse is to get them to submit their work to
you on a regular basis, and for your to provide
specific feedback.
Get the students writing as much as possible, get
them discussing what they see and make them selfevaluate their work against the criteria
http://www.youtube.com/user/UCMSCI
http://www.youtube.com/user/CreativeHeuristics