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MAT081C Planning for unit 1 - statistical invesigation

See also: mat081c-2024, statistics - mathematical content

Where I'll start my more detailed planning for my version of the unit.

Lessons#

Content and pedagogy resources#

Images

Misconceptions

Quotes#

Aaron Levenstein:

“Statistics are like a bikini. What they reveal is suggestive, but what they conceal is vital”.

Specific resources#

Steam and leaf plots

Driving question#

Possibilities

  • How do we know if someone is lying with data?
  • How can we make better data-informed decisions?
  • How do we use data to make better decisions?
  • What decisions are important to me?

Search for examples

  • Which toothpaste should I buy?
  • illustrate types of decisions that might need making

Terminology#

Art of smart - list of cogntive verbs

Term Definition
Plan knowledge utilisation
Conduct To organise and carry out action
Investigate Carry out research or a formal inquiry to uncover facts and draw new conclusions about data and information
Analyse Examine/consider something for the purpose of finding meaning or identifying similiarties or differences
Report
Compare Recognise similarities and differences & identify their significance
Recognise Identify features of information from knowledge of appearance or character
Solve To work out the answer or solution to a problem
Use To apply knowledge or rules to put theory into effect

Planning#

  • Driving question - Can I use this data to make a meaningful comment on a more general situation?

  • Question [ ] Can the student survey from the first lesson be used as an exemplar?

    • What type of data source is it?
    • What types of variables are there?
    • Draw on Likert styles from other similar surveys and use them to explore bias?

  • task [ ] Explore use of Australian Census data in the region as practical example/data source

  • idea [ ] Ask each student in the class to generate a sample to collate results and use to compare variation across samples

    • important for illustrating variability
    • different samples could be designed to explore different types of variability

  • point [ ] Surveys encouraging people to register an opinion are considered very unreliable - use popular online/phone surveys

  • task [ ] In general identify contemporary examples of bad sampling for nefarious means

  • task [ ] What visualisation methods for reveal/web can I use for dotplots and steam-and-leaf plot

    • including ways to visualise variation and range

Lessons#

13 lessons

  • ~7 teaching
  • ~6 investigation

Lesson 2 - Samples & Populations#

Learning outcomes

  • Understand the difference between a sample & a population

  • Understand the various methods of collecting data (survey, census, questionnaire)

    Question The relationship between "collecting data" and "collecting primary" data seems arbitrary

  • Select an appropriate sample and know if it is biased or not

  • Explain where you've seen data used in life - food, sports, online
Terms Definitions Examples and activities
Population The group of things to make conclusions about Give concrete examples (PISA, hottest January - 2024 versus 1964, and Oz census ) to illustrate the size of populations, which are then illustrated below
Census Collection of information bout the whole of a population - hottest temperature
- australian census data
Survey ?? Process of gathering information from a sample
Sample A subset of a population
Random Sample A subset of the population chosen such that every element of the population has an equal chance of being selected.
Representative sample Includes only members of the population being studied
Data A set of observations and measurements collected during any type of systematic investigation
Questionnaire
Observation
Measurement
Bias
Primary data Data you collected
Secondary data Data collected by someone else.

Lesson activities#

Starter

  • perhaps a notice-and-wonder activity with data/conclusions from a couple of the chosen "statistical investigations" or perhaps just data

    Perhaps a bit too group for a starter, but perhaps a leader into one of these might be useful. Could be just a TPS type activity. Aim here being perhaps to get them asking questions about bias, sample size, how do people know?

ToC

  • Introduce the driving question - including the Goompi version
  • use some of the sample SIs to draw out more discussions link to the Goompi model
  • touch on what we'll do in this lesson and the rest of the unit

Tour of statistical investigation samples

  • Delve more deeply into the different samples to introduce and illustrate the different terminology
  • Can we get them recording/discussing/filling out some sort of worksheet with details on whether or not the different types of terminology helps/hinders drawing conclusions etc. -- better, structure it with questions that they can use for their own statistical investigation

  • For example - question about if these questions should focus on the statistical investigation or the reporting of it - highlight the PISA.

    • What's the population?
    • What's the sample?
    • What methods were used to gather the data?
    • What's the variation?
    • What's the range?

Quality of decision making/reporting - build on the previous step but focus more on the reporting that has arisen around it (including mine re: temperature)

**Important** This distinction between the reporting and the details could be very useful to make. Linked to the Goompi model

- What did they say?
- Can they say it?
- Sources of bias and reliability? This might need to be exploratory and have some explicit teaching
- **Need** identify how to visualise/demonstrate using randomly generated numbers to demonstrate random sampling

Lesson 3 - Primary & Secondary data#

Learning outcomes

  • Understand the difference between primary and secondary data
  • Understand various methods of collecting primary data (observation, measurement & surveys)

  • Understand the source and reliability of secondary data

    • me Evaluate the quality of data
    • me Considering the constraints on them gathering data (small to medium)
    • me Have students start sharing the questions/topics they're interested in exploring

Lesson Activities#

Starter

  • Some connection with prior lesson and segue into this week

  • notice-and-wonder with using some secondary data - though all off the data I'm using is secondary

    • perhaps showing some of the conditions for the gathering of the data I used
    • the Colgate example would be useful
    • Something health related (e.g. this video) could be useful, esp. if recent and real
    • Aim being to get students to start identifying the components and start thinking about the source and reliability
    • The PISA example is particularly good

ToC (unordered)

  • Methods of collecting data

  • Sources of data (combine the two?)

    • newspaper story about a school answering the question "which times tables do students get wrong the most?" (or some such) - data generated by an app - and there's a spreadsheet with the data

    • Reliability of secondary data

    • purpose of the original gathering

    • available details on the data they gathered and analysed (types of questions they need to ask for their investigation)

Lesson 4 & 5 - Organising & displaying data#

  • Guardian article on road deaths includes a graph that might be useful as a starter - getting students to tell the story - but then showing wikipedia page on motor vehicle deaths in Australia by year

    Graphs on wikipedia are currently down. Maybe get students to generate their own graphs from the data

    Australian Automobile Association has a press release linking failure in government policy to reduce road deaths. A way to evaluate reality

Lesson 6 - Measures of centre & spread#

Lesson 7-8 Assignment lessons#

  • Hand out
  • Decide their topic
  • Design survey Q
  • Collect data
  • Organise data into frequency table

Questions

  • What scaffolds/activities/starters do we need for this

Lesson 9 - Measures of centre & spread#

Lesson 10-11 Assignment lessons#

  • Collect data from other class
  • Construct graph from frequency table

Lesson 12 - Analysing data#

Sources

Lesson 13-14 Assignment lessons#

  • Analyse data
  • Write report