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Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College 15 th June 201 Sandra Cathcart

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Introduction Background to the workshop Important ideas What will you get out of this?

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Objectives To enhance teacher knowledge of statistics progressions to senior levels To experience a selection of statistics tasks for use in the classroom to enhance the pedagogy of NZC To help teachers develop a more responsive scheme design

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What we can’t do without! Statistics Achievement Objectives. Census at School - all levels PPDAC cycle – “How kids learn” nzmaths to level 5 Senior secondary subject guides (L6 to L8) nzamt Figure it Out – revised for juniors

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Level 1 and level 2

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Level three What are variables? How do we introduce this?

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Data Cards With or without variables What are these cards telling us? I notice……..statements I wonder……..statements Using the cards to answer the questions.

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Making our own cards Wrist measurement No of people who slept in your house last night Estimate of the time takren to get to school Mode of transport to school: bus,bike,car,walk

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Comparison At level 3 students should be able to talk about the features differ for the two graphs they are comparing. Maybe draw a circle around the middle group and talk about how circles sit in relation to one another, maybe one is more to the right than the other. Maybe compare boys to girls, or year 5 to year 7

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Level 4 Plan and conduct investigations using the statistical enquiry cycle: determining appropriate variables and data collection methods gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends comparing distributions visually communicating findings, using appropriate displays.

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Analysis: summary At level 3/4/5 students should be talking about - the shape of the data (hills, bumps, skew, symmetrical, bimodal) - middle “group” (modal clump) - high/low range – describe the range rather than give the value - density (crowded, empty, piled up, clumped, busy) - spread (spread out, close together) - unusual/values of special interest (outliers, gaps, clumps)

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Hungry Planet

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Comparison at level 4 At level 4 students can start to identify the middle group by circling this group. They might also extend a line from the middle group to the extreme values (highest/lowest) creating a “hat plot” (Mexican on a bike) Comment on shape, spread, middle groups

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Level 5 Plan and conduct surveys and experiments using the statistical enquiry cycle: determining appropriate variables and measures considering sources of variation gathering and cleaning data using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets comparing sample distributions visually, using measures of centre, spread, and proportion presenting a report of findings.

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What makes a good investigative question?

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Comparison at level 5 At level 5 the hat plot can be updated by adding the middle value and then extending into formally finding the median and quartiles, always keep the dot plot with the box plot. - comment on summary statistics - shape - spread - middle 50%

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Clean it up Growing Scatter Shape activity

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Using “brush strokes”

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Level 6 Plan and conduct investigations using the statistical enquiry cycle: justifying the variables and measures used managing sources of variation, including through the use of random sampling identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays making informal inferences about populations from sample data justifying findings, using displays and measures.

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Descriptive or inferential?

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Summary

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Box plots: Making the call Lesson plan handout http://www.censusatschool.org.nz/2009/infor mal-inference/workshops/

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Level 7 Carry out investigations of phenomena, using the statistical enquiry cycle: –conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets –evaluating the choice of measures for variables and the sampling and data collection methods used using relevant contextual knowledge, exploratory data analysis, and statistical inference. Make inferences from surveys and experiments: –making informal predictions, interpolations, and extrapolations –using sample statistics to make point estimates of population parameters –recognising the effect of sample size on the variability of an estimate.

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Level 8 Carry out investigations of phenomena, using the statistical enquiry cycle: –conducting experiments using experimental design principles, conducting surveys, and using existing data sets –finding, using, and assessing appropriate models (including linear regression for bivariate data and additive models for time-series data), seeking explanations, and making predictions –using informed contextual knowledge, exploratory data analysis, and statistical inference –communicating findings and evaluating all stages of the cycle. Make inferences from surveys and experiments: –determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem –using methods such as resampling or randomisation to assess the strength of evidence.

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