Asking Better Questions

Overview

In this first lesson of the statistical investigations unit, students are introduced to the statistical enquiry cycle: posing a question, planning data collection, analysing data and communicating findings. They critique weak and strong questions, then collaboratively design an ethical survey about a relevant school or community issue.

Learning intentions

• WALT pose a worthwhile statistical investigative question that anticipates variability.
• WALT identify the population, sample and variables in an investigation.
• WALT plan an ethical and suitable method for collecting data.
• WALT recognise how privacy, consent and sampling bias affect data quality.

Success criteria

• I can write a question whose answers are expected to vary.
• I can identify a suitable population, sample and variable or variables.
• I can justify how data should be collected fairly and ethically.
• I can identify at least one possible source of bias or unreliability.

Curriculum links

• Mathematics and Statistics — statistical investigations and the statistical enquiry cycle.
• Mathsteasers — higher-order thinking and challenge through worthwhile investigative questions.
• Mathematics and Statistics — communicating mathematical thinking, reasoning and making judgements from data.
• Key competencies: thinking; managing self; participating and contributing; relating to others.

Lesson structure (60 minutes)

1. 0–5 min · Hook and prior knowledge. Open with the provocative survey hook and ask, “What could we find out about our school that would help make it better?” Students silently suggest one possible question, then share with a partner; the teacher records questions without evaluating them.

2. 5–15 min · Introduce the enquiry cycle. Use the statistical enquiry cycle slides to model the stages: pose a question, plan, collect, analyse and conclude. Explain that statistical questions anticipate different answers and require data from a population or sample; students identify the stage being described in three brief examples.

3. 15–25 min · Critique questions. Display the question-quality examples in the question critique slides: “What is the best sport?”; “How many minutes do Year 9 students spend travelling to school?”; and “Do students who walk to school arrive less stressed?” Students use the question-quality checklist on the investigation planning worksheet to decide whether each question is measurable, unbiased, specific and likely to produce variable data, then improve one weak question.

4. 25–42 min · Design a survey. In groups of three or four, students choose a relevant school or community issue, such as travel, recreation, wellbeing or use of school spaces, and complete the planning sections on the investigation planning worksheet. They record the investigative question, target population, proposed sample, variables and data types, sample size, collection method and how they will gain consent while protecting privacy. Circulate for conferences, asking: “Who do you want to learn about?”, “Will your sample represent them?” and “Could the wording influence responses?”

5. 42–52 min · Test fairness and reliability. Use the ethics and sampling discussion slides to introduce anonymous responses, voluntary participation, avoiding sensitive personal information, convenience sampling, random or systematic sampling, non-response and sampling bias. Groups exchange plans and give one warm comment and one question about ethical practice, representativeness and reliability; groups revise one part of their plan.

6. 52–60 min · Share and exit check. Invite two groups to explain their question and collection method, highlighting different populations, samples and variables. Students complete the final prompts on the investigation planning worksheet: state the population, sample and main variable for their investigation, name one possible bias and describe one ethical safeguard; collect the sheets as the formative exit ticket.

Resources

• the statistical investigation slide deck
• the investigation planning worksheet
• Whiteboard and markers
• Student devices or access to a spreadsheet/statistical software
• NZ Curriculum statistical investigation examples prepared by the teacher
• Timer
• Group discussion protocols

Assessment

• Use the question-quality checklist to check whether students recognise measurable questions, expected variability, specificity and possible bias.
• During group conferences, listen for accurate use of population, sample, variable, data type, consent and privacy; record students needing further support.
• Review the exit ticket for correct identification of population, sample and variable, plus a realistic ethical safeguard. No formal checkpoint is required this week.

Differentiation

• Provide question stems such as “How many…?”, “How often…?” and “Is there a difference between…?”; offer a variable bank including categorical, numerical and ordinal examples.
• Give students who need support a partially completed planning template, a choice of familiar topics and a partner role such as reader, recorder or checker.
• Allow EAL learners to discuss ideas before writing and provide word/picture prompts for population, sample, variable, privacy, consent and bias.
• Extend confident students by requiring comparison of two sampling methods, an explanation of likely sampling reliability, and identification of a specific source of bias or confounding.