Difficulties in learning about sampling and approaches to overcoming these (AS1.10 & 2.9)
Jared Hockly - Western Springs Collegehocklyj@wsc.school.nz
Overview of this session:
Discuss the standards 1.10 and 2.9 briefly (some clarifications)Focus on developing understanding of sampling variabilityLook at a few activities that develop this understandingDiscuss how to get the best out of the learning and assessment of this topic
Achievement Objectives -Explanatory note 3
Questions for you
Why do we teach this topic/standard?(What are our beliefs, What do/should students get out of it)Are we turning students off stats by doing these standards?3) What do you think it is about sampling variability that makes it tricky?
Question about population(problem)
Answer about population. “making the call”(conclusion)
Get/organise your sample data(plan, data)
Compare the two groups using graphs and summary stat(Analysis)
a few off topic points before we get into it
technology should be used (but not exclusively in the teaching)Beware, some data is tricky to ask worthwhile questions about (titanic, world at a glance)1.10: don’t need a random process for selecting the dataStudents should be given opportunities to understand the context they are investigating (they need this at higher grades)2.9 is a bit odd, sampling from a “population database”...
Kinda off topic still - How sampling really works
(If possible) generate a list of the population: a sampling frame. (e.g electoral roll, register of schools, list of students)then randomly choose units for your samplethen you gather the data for those in the sample
Some of my beliefs about teaching stats
Compartmentalising the skills makes it hard for students to understand what they are really doingMore effective learning of skills is teaching them when there is a need.Use interesting data, data they may be invested in.This is hard but: don’t always be critical or accuracy. Let the intuitive statements have some air
A suggested overview of teaching this topic
Do some investigations where you have the whole population to investigate.- e.g are boys better atrobot unicorn attackthan girls in our class. (Get to do the PPDAC cycle without too much complexity)Move onto situations where it is impractical to have/use/collect the whole population.- data cards (similar tokarekare college2009 stats day)- census at school samples/dataviewerThe idea of a sample will develop. Do we all get the same result when we sample?
A suggested overview of teaching this topic (cont)
Develop the idea of sampling variability before they learn rules.The effect of sample size, the effect of the spread of the dataset(s), iNZight could make an appearance herea 1 variable variation of sample median (how different can out answers be, looking around the class)2 variable comparisons of sample medians. Use intuition.They are probably wanting to know when there is a big enough difference for us to make a call1.10 the rules for making a call2.9 the formula for confidence interval and the idea of overlapAre they correct with their calls? A mixture of knowing the population results (to see if they got it right and provide closure) and not knowing (because thats the way it really is)
And back to assessment
1.10 Why not get the students to create the sample, this will ensure they are well informed about the context2.9 does say “from a given set of population data”. Can we still get them to sample the data in a more real way?
A desire to adjust the teaching of these topics to:be engaging in the use of datauses a range of activitieshave multiple investigations developing in complexitydevelops understanding of sampling variability (rather than an emphasis on rules and canned statements)- A desire to create better assessments that involve students in the context/data
Level 6• plan and conduct surveys and experiments using the statistical enquiry cycle- determining appropriate variables- cleaning data- using multiple displays, and re-categorising data to find patterns, variations, in multivariate data sets- comparing sample distributions visually, using measures of centre, spread, and proportion- presenting a report of findings;• plan and conduct investigations using the statistical enquiry cycle- justifying the variables used- identifying and communicating features in context (differences within andbetween distributions), using multiple displays- making informal inferences about populations from sample data- justifying findings, using displays and measures.
Level 7• carry out investigations of phenomena, using the statistical enquiry cycle:− using existing data sets− evaluating the choice of sampling and data collection methods used− using relevant contextual knowledge, exploratory data analysis, and statisticalinference• make inferences from surveys:− using sample statistics to make point estimates of population parameters− recognising the effect of sample size on the variability of an estimate