Literacy and thinking in mathematics and Statistics Anna Martin Avondale College mar@avcol.school.nz

Thinking about relationships Thinking about comparisons 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 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-month sabbatical 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 can’t go without technology and how proud we would be if the time we play video games got extended.

NEWSPAPER ARTICLE People are contracting the computer bug early: according to research published last September by Cranfield University School of Management in Northampton, of 260 secondary school pupils surveyed, 26 per cent 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 and how technology is taking over the world.

NEWSPAPER ARTICLE "If teenagers become more withdrawn they run the risk of being developmentally out of step with their peers," says Capio Nightingale's consultant psychiatrist Dr Richard Graham.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 of research, 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 also talks about how technology can have a big impact on our future.

NEWSPAPER ARTICLE Then there are the physical aspects. You can 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 evidence that 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 can stop us from eating.

NEWSPAPER ARTICLE "At the moment people are trying to study the effects of high exposure to technology during the early parts of people's lives," continues Graham. "There are developmental windows in which 'wiring' of 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." This article talks about how technology wrecks our studies and it effects our learning and how it affects our brain.

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 Describe the relationship: in context positive/negative strength/type does it make sense? Use the names of the variables It’s a positive relationship because…. It’s 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

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 List the steps for a method

Problem What is the relationship between the size of the hard-drive memory and the selling price for laptops?

What variables will you investigate? 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)

How will you collect data for the investigation? 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.

How will you measure these variables? 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 things might affect the measures you take? 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 investigation more? the screen size, the processing speed, how the laptop looks, different shops selling for different prices… WRITE: I wonder if things like…………. might also 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

How many measures will you collect? 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

How will you record your results? 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 will use ______ columns for each of the two variables. 2

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.

Sketch the outline of the shape of the distribution. LO: Describe and compare the distribution of values represented on a back-to-back stem-and-leaf ploT 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? Key: 0 | 9 means 0.9 kg 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 has to be over half) Write a sentence about the shape of the distributions (symmetric, skewed, bi-modal, unusual values)

Identify the longest leaf for each variable. LO: Describe and compare the distribution of values 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 symmetric, but Plant 1 weights are more inconsistent/spread out than Plant 2 Sketch the outline of the shape of the distribution 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)

Summary for US12332 Draw stem and leaf. Outline shape. Identify longest leaf or leaves. Identify anything unusual. Most of the values…. Shape of distribution (skewed, symmetric, bi-modal….) Weird…. Summary for US12332 Calculate statistics (min, LQ, median, UQ, max, range, IQR, mean, standard deviation). 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…) Draw box and whisker plot.

Writing comparison statements The variable The number of minutes spent doing homework The explanation The median was higher The link Because The evidence The median was 92 minutes for Year 9 and 75 minutes for Year 11 The comparison Year 9 vs Year 11 The feature Typically higher

Learning reflections

SNEAKY LITERACY

LO: Solve word problems using times tables or doubles or halves Multiplication and division strategies Copy the date and learning outcome into your DO NOW books.

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  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 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 between TWo 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 self-evaluate their work against the criteria

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