Thinking and Literacy in Mathematics and Statistics 2

7/28/2019 Thinking and Literacy in Mathematics and Statistics 2

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LITERACY AND THINKINGIN MATHEMATICS AND STATISTICS

Anna Martin

Avondale College

[email protected]


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LITERACY AND THINKING

Statistics

Thinking about data

Thinking about relationships Thinking about comparisons

Thinking about sources of variation

Communicating understandingMathematics

Deciphering word problems

Teaching literacy


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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


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CONFIDENCE INTERVAL EXAMPLE OF TEXT


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THE CONTEXT

Scientists fear that more

and more teenagers are

becoming addicted totechnology.


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Planning the

questionnaire

On the next few slides you

will be shown informationfrom an article. Write

down 3 key points from

each page.


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NEWSPAPER ARTICLE

Have you ever interrupted childbirth,a wedding, funeral or graduation

ceremony to send a text? Does the

thought of going cold turkey from

technology make you want to daub

your social networking status in your

own blood across the nearest brick

wall? Is your ideal six-monthsabbatical from work an extended

period playing World of Warcraft in a

windowless bedroom?

It talks about how sometimes we text during

important stuff and how get interrupted or

distracted. It also talks about how we cantgo without technology and how proud we

would be if the time we play video games

got extended.


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NEWSPAPER ARTICLE

People are contracting the computer bugearly: according to research published last

September by Cranfield University School

of Management in Northampton, of 260

secondary school pupils surveyed, 26 percent spent more than six hours a day on

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?

It talks about how people are contracting

the computer bug early. It also talks about

how much we spend on the internet andhow technology is taking over the world.


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NEWSPAPER ARTICLE

"If teenagers become more withdrawn theyrun the risk of being developmentally out

of step with their peers," says Capio

Nightingale's consultant psychiatrist Dr

Richard Graham. "It's a very young field ofresearch, but there is some evidence to

suggest that girls who spend too much

time on Facebook miss out on key

developmental steps and could feel

immature. Extreme cases can put people's

education and employment at risk.

This article talks about how teenagers get

sucked into technology and how they can

sometimes split us from our parents. It alsotalks about how technology can have a big

impact on our future.


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NEWSPAPER ARTICLE

Then there are the physical aspects. Youcan have a poor diet, lose weight, not eat

properly. If teenagers are pulling all-

nighters they might turn to stimulants, like

caffeine or taurine, and there is evidencethat can increase anxiety in the long-term."

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.

This talks about how technology is bad and

how it can get us into drugs and that. It also

tells us how we can get so addicted it canstop us from eating.


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NEWSPAPER ARTICLE

"At the moment people are trying to studythe effects of high exposure to technology

during the early parts of people's lives,"

continues Graham. "There are

developmental windows in which 'wiring' ofthe 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."

This article talks about how technology

wrecks our studies and it effects our

learning and how it affects our brain.


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UNPACKING LEARNING OUTCOMES

LO: Use the statistical enquiry cycle to

investigate multivariate data

Get students to try to explain what thewords enquiry, cycle and multivariate

mean

Share understandings andacknowledge contributions

Model more than one way to explain

something


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FROM ONE VARIABLE TO TWO

Focus on rental prices (one variable)

Explore what might be

affecting/linked/related to rental pricese.g. rugby world cup, suburb, number of

bedrooms

Lots of structure early on to help withwriting


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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 highestrental 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 $____


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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? (onewould be the typical price for 1-bedroom houses, and

one would be the typical price for 2-bedroom houses)


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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?


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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


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THE PAINT BRUSH


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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


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THE ELLIPSE

Using for

relationships we

think are linear

Not easy at firstbut students get

there

Helps position

line of best fit

Can use for

informal

predictions


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LINKING FEATURES AND STATEMENTS

Describe the

relationship:

in context

positive/negative strength/type

does it make sense?

Use the names of the

variables

Its a positive relationship

because.Its a strong linear

relationship because.

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


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FORMATIVE ASSESSMENT

Is there a

relationship

between the sizeof a family and

the number of

bedrooms for

their house?


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LO: Write a

plan for a

bivariateinvestigation

BIVARIATE

INVESTIGATION


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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


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PROBLEM

What is the relationship between the size of the hard-

drive memory and the selling price for laptops?


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WHAT VARIABLES WILL YOU

INVESTIGATE?

What is the relationship between the

size of the hard-drive memory and the

selling price for laptops?

WRITE: The variables I will investigate are

WRITE: The explanatory variable will be

WRITE: The response variable will be

The size of the hard-drive memory and the sellingprice for different laptops

Hard-drive memory (because I think this willexplain the selling price of the laptop)

Selling price (because I think this willchange/respond to different sizes of hard-drives)


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HOW WILL YOU COLLECT DATA FOR THE

INVESTIGATION?




THINK: Are the variables things I can measuremyself or can I find measures for the variables fromsomewhere?

WRITE: I can collect data for this investigation by

These variables have already been measured bystores or people selling laptops

Getting ads for laptops being sold that say how bigthe hard-drive memory is and what price the laptopis being sold for from advertising pamphlets.


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HOW WILL YOU MEASURE THESE

VARIABLES?




THINK: What units should I use? How accurate do Ineed to be? What equipment do I need?

WRITE: I will measure the variables by using..GB for the hard-drive memory and rounding theselling price to the nearest $100.


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WHAT THINGS MIGHT AFFECT THE

MEASURES YOU TAKE?




THINK: Does it matter where I get my data from? DoI need to be careful about getting a range of data?Should I focus my investigation more?

WRITE: I wonder if things like. might alsoaffect the selling price for laptops. To try to stop thisaffecting the relationship I will..

the screen size, the processing speed, how thelaptop looks, different shops selling for differentprices

Make sure I only collect data from laptops from one store andinclude only laptops with similar specs apart from hard-drivememory


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HOW MANY MEASURES WILL YOU

COLLECT?




THINK: How much data do I need? If I am workingin a group, how much should each of us collect?

WRITE: I will collect data about ______ differentlaptops. We will make sure __________________

30

we each collect around 10values each


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HOW WILL YOU RECORD YOUR

RESULTS?




THINK: What things should I write down for eachlaptop? How will I organise this data?

WRITE: I will use a ________ to record my results. Iwill use ______ columns for each of the twovariables.

table

2


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GROUP WORK!




In your group, discuss how you will each contributeto the development of a plan for the assessment.Make a commitment to each person that you willattend each day of the assessment and that you willnot let them down. Write down how you willdemonstrate to your teacher that each person hascontributed to the writing of the plan.


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LO: D ESCRIBE AND COMPARE THE D ISTRIBU TION OF VALUES

R E P R E S E N T ED O N A B A C K - T O - B A C K S T E M - A N D - L E A F P L O T

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 bighealthy babies born in our ward. Does the

data support this?

Sketch the outline of the shape of thedistribution.

Identify the longest leaf. Count then number of values. If it is not at least half,

take the next adjacent longest leaf.

Write a sentence about where

MOST of the values are (most

has to be over half) Write a sentence about the shape of

the distributions (symmetric,

skewed, bi-modal, unusual values)

Key: 0 | 9 means 0.9 kg


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LO: D ESCRIBE AND COMPARE THE D ISTRIBU TION OF VALUES

R E P R E S E N T ED O N A B A C K - T O - B A C K S T E M - A N D - L E A F P L O T

Plant 1 was grown without

fertiliser. Plant 2 was grown

with fertiliser. The values are

the weights of the tomatoes foreach plant grown (in grams).

Sketch the outline of the shapeof the distribution for each

variable.

Identify the longest leaf for

each variable.

Compare MOST of the values

are (most has to be over half).

Compare the shape of the

distributions (symmetric, skewed, bi-

modal, unusual values)

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

The distribution of weights of tomatoes from both plants appear to be

symmetric, but Plant 1 weights are more inconsistent/spread outthan Plant 2


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Summary for

US12332

Draw stem and leaf.

Outline shape.

Identify longest leaf or

leaves.

Identify anythingunusual.

Calculate statistics

(min,

LQ,

median,

UQ,

max,

range,

IQR,

mean,

standard deviation).

Draw box and whisker

plot.

Most of the values.

Shape of distribution (skewed,

symmetric, bi-modal.)

Weird.

Typically higher..

More spread out..

Average difference..

More consistent.

Overall higher.(box shifted higher)

Middle 50% more varied (IQR

bigger, box wider)

Middle 50% similar (A lot of overlap

of boxes)

Shape of distribution (skewed,symmetric)


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WRITING COMPARISON STATEMENTS

The variableThe number of minutes spent

doing homework

The comparisonYear 9 vs Year 11

The featureTypically higher

The linkBecause

The explanationThe median was higher

The evidenceThe median was 92 minutes

for Year 9 and 75 minutes for

Year 11


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LEARNING REFLECTIONS


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SNEAKY LITERACY


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Multiplication

and division

strategies

LO: SOLVE WORD

PROBLEMS USING TIMES

TABLES OR DOUBLES ORHALVES

Copy the date and learningoutcome into your DO NOW

books.


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WRITING PROBLEMS

READ: Miss Martin has made up a problem

which involves doubling.

PROBLEM: Bob has $10 in his account, butneeds 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?


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WRITING PROBLEMS

DOUBLE TWICE 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 personbeside you and try to answer theirs!


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WRITING PROBLEMS


which involves the three times table.

PROBLEM: Ben has three friends. Each friendhas 4 video games. How many video games

do his friends have all together?


use the three times tables?


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WRITING PROBLEMS

TIMES TABLES EACH, ALL TOGETHER


involves the four times table.


problem is.



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WRITING PROBLEMS


which involves halving.

PROBLEM: Bob has 24 lollies. He wants toshare them equally between him and his

friend. How many lollies will each of them

get?


halve?


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WRITING PROBLEMS

HALVE SHARE EQUALLY BETWEEN TWO


involves halving.


problem is.



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TEACH FOR UNDERSTANDING SO STUDENT S CAN

COMMUNICATE UNDERSTANDING

Three key concepts

Selecting and using Evaluating and comparing

Considering other factors and explanations


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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 self-

evaluate their work against the criteria


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http://www.youtube.com/user/UCMSCI

http://www.youtube.com/user/CreativeHeuristics
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Thinking and Literacy in Mathematics and Statistics 2