Secondary School Statistics The effect of NCEA and technology

NCEA in 1 easy lesson Each year’s course split into non overlapping Achievement Standards Internal or external Standard can be passed at Achieved, Merit or Excellence Pass rates vary for each standard Year 11 = Level 1Year 12 = Level 2 Year 13 = Level 3Schol = Level 4

Year 11: Level 1 SC Prescription 7.1 Describe how an investigation would be carried out write question devise ways of obtaining representative sample 7.2 Use graphs and statistics to analyse data include grouped data comparing sets of data 7.3 Make and justify statements about the results 7.4 Identify features in time series data including seasonal factors 7.5 Suggest improvements 7.6 Communicate findings effectively

Year 11: Level 1 Achievement Standard 1.5 (Internal) Achievement Use statistical methods to respond to a question or hypothesis Use statistical information to answer straightforward questions Merit Pose a question and use statistical methods to produce a justified response Interpret statistical information Excellence Evaluate the statistical process used to respond to the question

So What’s Different? Emphasis pose a question limitations Missinggrouped data collecting own data (often) Added Advantagescoherent whole process Disadvantagesset procedure

Year 12: Level 2 SFC Prescription 6.1 Plan a statistical investigation to make inferences 6.2 Design and justify sample collection methods 6.3 Collect data, graph and discuss prominent features 6.4 Calculate sample statistics including mean and standard deviation 6.5 Analyse and discuss inferences evaluate statistics in the media and reports 6.6 Highlight features of simple time series graphs using moving averages and seasonal adjustments to make predictions identifying possible causes of features Use of appropriate technology for 6.3 and 6.4

Year 12: Level 2 Achievement Standard 2.5 (Internal) Achievement Select a sample to answer a question Calculate appropriate sample statistics Make an inference about a population Merit Describe and justify a sampling method and use it to select a sample Justify inferences made about a population Excellence Critically evaluate the sampling process

So What’s Different? Emphasis representative sampling make inference Missinggrouped data graphing time series in depth investigation evaluate reports Addedevaluate process, reliability Advantagescoherent whole process Disadvantagesset procedure

Year 13 Level 3 Bursary Prescription 1.1 Plan investigation, analyse data, present and discuss findings 1.2 Analyse statistical reports 1.3 Calculate and interpret sample statistics Derive identity 1.4 Sampling distribution of the mean and proportion 1.5 Explain the difference between statistics and parameters Calculate the sample size required 1.6 Explain and use the Central Limit Theorem 1.7 Confidence intervals: mean, proportion, difference between two means 2.1 Investigate a process which produces time series data Planning Graphing, smoothing Identifying patterns Features and predictions

Year 13 Level 3 Achievement Standard 3.1 (Internal) Achievement Determine the trend for time series data Merit Use time series analysis to make forecasts Excellence Analysis time series data and prepare a report on the analysis

Year 13 Level 3 Achievement Standard 3.2 (External) Achievement Calculate confidence intervals for population parameters Merit Demonstrate an understanding of confidence intervals Excellence Analyse estimates of population parameters Achievement Standard 3.5 (Internal) Achievement Plan and carrry out an investigation involving bivariate continuous data, analyse the data and report the findings Merit Carry out an in depth analysis of bivariate data within an investigation Excellence Produce a comprehensive report on the investigation

So What’s Different? Emphasis use of technology regression & correlation Missinggrouped data derive formulae excellence only design sampling method Addedregression more complex time series model Advantageslots of real data analysed coherent whole process Disadvantagesaccess to technology essential CI divorced from real data

Technology Graphics Calculator Calculates all stats mean, median, mode, range, IQ range, quartiles, totals, st dev, regression coeff Draws graphs scatter, line, box & whisker, histogram Fits all types of lines/curves, finds eqn Calculates confidence intervals Easy to analyse affect of outliers

Technology Excel Calculates all stats mean, median, mode, range, IQ range, quartiles, totals, st dev, regression coeff Draws graphs scatter, line, (box & whisker, histogram) Fits all types of lines/curves, finds eqn Calculate confidence interval for mean Easy to analyse affect of outliers

Pros and Cons of NCEA Pros Less repetitive - different focus at each level Focus shifted from number crunching to whole task approach Focus on purpose ie making inference about popn Forced more uniformity in standard of teaching Forced use of Excel etc Look at reasons behind data Plenty of time year 13 – add more content? Easy 9 credits for owners of graphic calculator Cons Teaching to assessment Lack of experience with grouped data Accuracy of stats or graphs not important Set procedure More time assessing Other subjects use more statistical methods Verification of individual work Access to technology Loss underlying mathematics