Mathematics and Statistics

A look at progressions in Statistics

Jumbo Day Hauraki Plains College

15th June 201 Sandra Cathcart

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

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

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

Level 1 and level 2

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

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.

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

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

•  

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.

Analysis: summaryAt 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)

Hungry Planet

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

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.

What makes a good investigative question?

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%

Clean it up

Growing Scatter

Shape activity

Using “brush strokes”

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.

Descriptive or inferential?

Summary

Box plots: Making the call• Lesson plan handout• http://www.censusatschool.org.nz/2009/

informal-inference/workshops/

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.

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.