Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College
description
Transcript of Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College
![Page 1: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/1.jpg)
Mathematics and Statistics
A look at progressions in Statistics
Jumbo Day Hauraki Plains College
15th June 201 Sandra Cathcart
![Page 2: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/2.jpg)
Introduction• Background to the workshop• Important ideas• What will you get out of this?
![Page 3: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/3.jpg)
![Page 4: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/4.jpg)
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
![Page 5: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/5.jpg)
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
![Page 6: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/6.jpg)
Level 1 and level 2
![Page 7: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/7.jpg)
Level three• What are variables? • How do we introduce this?
![Page 8: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/8.jpg)
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.
![Page 9: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/9.jpg)
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
![Page 10: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/10.jpg)
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
•
![Page 11: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/11.jpg)
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.
![Page 12: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/12.jpg)
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)
![Page 13: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/13.jpg)
Hungry Planet
![Page 14: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/14.jpg)
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
![Page 15: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/15.jpg)
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.
![Page 16: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/16.jpg)
What makes a good investigative question?
![Page 17: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/17.jpg)
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%
![Page 18: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/18.jpg)
Clean it up
Growing Scatter
Shape activity
![Page 19: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/19.jpg)
Using “brush strokes”
![Page 20: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/20.jpg)
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.
![Page 21: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/21.jpg)
Descriptive or inferential?
![Page 22: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/22.jpg)
Summary
![Page 23: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/23.jpg)
Box plots: Making the call• Lesson plan handout• http://www.censusatschool.org.nz/2009/
informal-inference/workshops/
![Page 24: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/24.jpg)
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.
![Page 25: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/25.jpg)
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.
![Page 26: Mathematics and Statistics A look at progressions in Statistics Jumbo Day Hauraki Plains College](https://reader036.fdocuments.us/reader036/viewer/2022070421/568160cc550346895dd0003f/html5/thumbnails/26.jpg)