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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 NEWSPAPER ARTICLE "If teenagers become more withdrawn they run the risk of being developmentally out This article talks of step with their peers," saysabout Capio how teenagers get Nightingale's consultant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