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Challenge the statistics! 2012 Overview • Examine rationale for developing statistical and graphing skills in a workplace context • Explore statistical techniques • Explore a learning sequence for use with graphs There are three kinds of lies: lies, damned lies, and statistics Mark Twain Getting to know graphs Most familiar Place the graphs on a cline from least familiar to most familiar Least familiar A shift in thinking... Number Statistics Critical Numeracy Four aspects of critical numeracy: • The ability to critique or make critical interpretations of mathematical information • The ability to unpack, interpret and decode mathematical situations • The ability to use mathematics in a self-reflective way • The ability to use mathematics to operate more powerfully in the world Stoessiger, 2002 Understanding statistics • Statistics help us to explain things • They provide agreed methods of presenting information Therefore statistics sit well inside the literacy/numeracy framework What do we want? We want employees to engage autonomously in critical analysis of statistical information – particularly in the workplace. This means supporting employees to: • Initiate quality questions • Identify limitations/strengths • Reflect on the information Statistical awareness Question: Estimate how many people will there be in Auckland in 70 years time if the population grows by 5% per year? 70 / 5 = 14 Therefore the population will double every 14 years. Question: How many times will the population double in 70 years? 70 /14 = 5 1.5 million x 2 x 2 x 2 x 2 x 2 = 48 million!!! Measures of centre The mean Mean girls are AVERAGE The median The middle of the road Finding the ‘mean’ Darrel records the time it takes him to travel to work every day for six days. He records the following times in minutes: 17, 19, 21, 22, 22, 27 Add all numbers and divide by how many there are. (17 + 19 + 21 + 22 + 22 + 27) = 128 6 Mean: 21.3 minutes Finding the ‘median’ The ‘median’ is the middle number in the series. 17, 19, 21, 22, 22, 27, Total amount of data points, plus one, divided by 2. Median = 21.5 6+1 2 Activity In your groups – describe the difference between the two packing sheds using statistical methods Measures of spread • Range • Interquartile range • Standard deviation Finding the range The range is found by subtracting the minimum value from the maximum value. max – min = range So... For example, our data from pack shed one is: 4 4, 5, 5, 6, 6, 9 7, 9 Range = 9 – 4 = 5 Interquartile range Question: How many cuts does it take to divide one plank of timber into quarters? Three To find the Interquartile range – you identify where the three cuts are made to your data. Pack shed one: 1 2 4, 55, 5, 66, 6, 7 7, 9 1 2 3 4 Q 1: 5 Q 2: 6 Q 3: 7 7+1 =4 2 3+1 =2 2 Pack shed two 3, 33, 7, 7 7, 8, 88, 9 Quartile 1: 3 Quartile 2: 7 Quartile 3: 8 Interquartile range Pack shed one: 4, 5, 5, 6, 6, 7, 9 Pack shed two: 3, 3, 7, 7, 8, 8, 9 Q 1: 5 Q 2: 6 Q 3: 7 Q1: 3 Q2: 7 Q3: 8 1 2 3 4 5 6 7 8 9 10 Interquartile range Pack shed one: 4, 5, 5, 6, 6, 7, 9 Pack shed two: 3, 3, 7, 7, 8, 8, 9 Q 1: 5 Q 2: 6 Q 3: 7 Q1: 3 Q2: 7 Q3: 8 1 2 3 4 5 6 7 8 9 10 Interquartile range Pack shed one: 4, 5, 5, 6, 6, 7, 9 Pack shed two: 3, 3, 7, 7, 8, 8, 9 Q 1: 5 Q 2: 6 Q 3: 7 Q1: 3 Q2: 7 Q3: 8 1 2 3 4 5 6 7 8 9 10 Critical analysis Generating questions • I wonder why...? • What if ...? • Has the sample size differed between the graphs? • Is the sample large enough? Teaching sequence The Learning Progressions provide a learning sequence for instruction on graphs. Learners will: 1. Describe the features of a graph 2. Analyse the data (ask critical questions) 3. Draw reasonable conclusions based on the data 4. Generate (or manipulate) a graph based on workplace data Instructional strategies Modelling • The tutor selects a graph and models verbally how it can be critiqued. Questioning • Present learner with a range of questions that encourages them to explore the graph – – – – What type of graph is being used (and why?) What does this graph represent? What unit of measures are used? What does the graph not show? Discussion • Interactive conversation in which tutor and learner become joint constructors of learning Activity 1. Design a learning plan for a workplace graph 2. Discuss with others Summary • Examine rationale for developing statistical and graphing skills in a workplace context • Understand how graphs represent data • Explore statistical techniques • Explore a learning sequence for use with graphs