How much bullying?


This unit requires students to look at the reported state of bullying in New Zealand schools and to develop and administer their own surveys about bullying. They analyse their data and create a report outlining the results of their investigation.

Specific Learning Outcomes
  • Critically explore the validity of claims based on data.
  • Evaluate the quality of survey items that are developed by others.
  • Create survey items that align to a research question.
  • Administer a survey, collate and display the data, and report findings.
Description of Mathematics

This unit addresses both Statistical Inquiry and Statistical Literacy. Statistical Literacy is about critically examining claims made by others, that are based on data that has been gathered or accessed. Critique includes verifying the identification of important variables, sampling, the method of analysing the data, unbiased display of results, and most importantly, whether the data answers the question, given uncertainty.

Statistical Inquiry involves investigating a question of interest, that involves an aspect of “I wonder” rather than a Yes or No answer. The PPDAC cycle is an established part of the New Zealand Curriculum and is applied in this unit.

  • Problem – the statement of the research questions
  • Plan – planning the procedures used to carry out the study
  • Data – the data collection process
  • Analysis – the summaries and analyses of the data to answer the questions posed
  • Conclusion – the conclusions about what has been learned.
Required Resource Materials
  • Copymasters One, Two, and Three
  • PowerPoints One, Two, and Three
  • Access to digital technology is recommended but not essential

Lesson One

In this unit students explore the statistics about bullying in New Zealand schools. There are several online articles about bullying available if you want students to search for information. However, a very brief summary is provided in PowerPoint One.

After Slide Three discuss these questions with your students:

  • Do the findings surprise you?
  • Do the findings match your experience at school?

Some students might perceive bullying to be only physical violence. Broaden the idea of bullying by asking:

What kinds of behaviours (things people do) might be bullying?

Make a list of bullying behaviours then look at Slide 4. Ask students to look at the graph and record some things that can be learned from it. A copy of the graph is available as Copymaster One. After an appropriate time discuss the findings. Look for the following capabilities in your students:

  • Do they recognise that the triple bars refer to data from different age groups?
  • Do they notice that the percentages of students reporting bullying are higher for younger students than older students? [Why might that be?]
  • Do they notice that the length of specific bars provides a percentage?
  • Can they read off specific percentages?
  • Do they know what percentage means? (A rate of x in every hundred students)
  • Can they classify the bullying behaviours? [e.g. physical, verbal, emotional, etc.]

Ask your students to discuss, in small groups, how the data about bullying may have been gathered.

How did the people who created this graph gather their data?

Rove around to see what students are thinking. Encourage them to be specific. In particular:

  • Do they discuss asking a group (sample) of people?
  • Who do they select? (School aged children at ages 9, 13 and 15 years)
  • How many people do they select? (Sample size)
  • What do they ask the people they select? (Specific response examples)

Gather the class and discuss the points above. The samples size in TIMSS and PISA are very large, e.g. over 8,000 students in TIMSS 2014/15. You might ask what a practical sample size might be for a small study. Students might highlight that asking a small number of people may not give reliable results. Why not? (variability)

Why couldn’t we ask a very large number of people? [Only so many students in our school, too much time, hard to process all the data]

Move on to the types of questions that might be asked. Show the students Slides Five to Seven of PowerPoint One. The questions are taken from publicly available surveys about bullying.

For each question, ask students about what is found out from the question.

Why might the investigators want that information?

The main purpose is to extend students’ ideas about what might be asked about bullying, from establishing its occurrence (what, when and where), to finding out actions that students take, and ideas about how the situation might be improved, if it needs to be.

Copymaster Two has the three slides on one page for students to answer. Discuss how it feels to answer each question and whether there are any issues with the wording of some questions. For example, the ethnicity question requires a student to opt for one ethnicity when some may identify themselves with two or more ethnicities, e.g. The child of a Thai mother and Samoan father. The open response question, about why no action was taken, might imply blame. That can lead to students not answering honestly.

Collate the data on all the questions using tallies. Student can come up to a set-up whiteboard or paper sheets to record their response. If you are concerned about responses being kept confidential then create the tally sheets yourself in a different time.

Discuss how the data might be represented graphically. Bar charts give a good picture of relative frequency while pie charts give a picture of proportions.


Ask your students to create their own data display for the responses to one of the questions. Look for:

  • Do your students create an appropriate display for category data?
  • Do they label the title, axes, and legends properly?
  • Are they aware of the vertical axis representing frequency?
  • Are they able to state approximate fractions or percentages for the sectors in the pie chart?

Lesson Two

In the next lesson students develop survey questions about bullying. Before writing questions discuss the areas about bullying that should be targeted.

What personal information should be find out about the students?

Students should suggest the usual demographic variables such as age, class level, gender, and ethnicity. They may suggest other variables of interest, such as position in the family, e.g. first born, middle child, youngest child.

Share with the students that bullying surveys usually include sections of questions. The sections are based on what the investigators want to find out. Common themes are:

  1. Types of bullying and frequency (What and how often?)
  2. Location and timing (Where and when?)
  3. Responses to bullying by students (How do they react?)
  4. Knowledge of help to counter bullying (Who/Where to go to? What do to yourself?)
  5. Effects of bullying on the well-being of victims (What are the effects?)
  6. Rationale for bullying (Why do students think bullies bully?)
  7. Improvements (How can the school improve?)

Ask your students to choose four themes and write one or two questions for each one. Suggest limited response questions rather than open questions to keep data handling manageable. Handling of open response data is dealt with later. You may want to discuss PowerPoint Two which shows the three most common types of closed questions. Focus on the advantages and disadvantages of closed questions.

  • Advantages: Short time for respondents to complete, data is easy to code and interpret, allows use of numbers (quantitative methods).
  • Disadvantages: Respondents are forced to select an answer they do not totally agree with, reasons why they answer as they do are not available.

Let your students work in teams of three to develop questions. Preferably they should do so digitally so the questions can edited, and combined with others, to form the final survey. Provide feedback as you go around.

Will the questions provide important data?
Are the questions simply, and briefly written?
Are the words and phrases unambiguous?
Does each question include only one idea, not multiple ideas?
Are the questions neutral, avoid leading statements, and offer a full range of options for students to choose?

Before sharing questions with the class, ask the students to trial each question with at least two other students who are not in their team. The questions should be rewritten if needed.

Share a few of the questions with the whole class. Focus on the above criteria for good survey questions. Begin to organise the questions under the seven themes above.

Lesson Three

Display all the questions that were developed under the theme headings. Challenge your students to develop a bullying survey in teams of three. Set the restriction that the survey must:

  • Ask three demographic questions (Name is not included – Why?)
  • Address four themes
  • Ask two or three questions per theme

Have the questions stored digitally on an accessible drive so that students can cut and paste to form their surveys. It is a good idea to introduce checking once the surveys are drafted. Each group can check to see that the survey of another group is sound. Alternatively, you might use online survey software, such as Google Forms, though other platforms often incur a charge. Two advantages of digital platforms are that the data is entered by respondents, and the data is downloadable as a spreadsheet. 

Next get each group to gather data from another class in the school using their survey. You might also survey a class from another location if you have a reciprocal arrangement. The advantage of reciprocal arrangements is that your students will experience first-hand being a respondent to a survey. That will make them sensitive to the importance of clear question construction, and the time taken to respond.

It is a good idea for students to number each survey form before administration. Numbering helps to identify particular forms, to account for all participants, and for easy retrieval of particular forms later, if needed.

Students will need to process their data. While processing can be done manually there are advantages to using digital technology in terms of display and calculating measures. 

The COUNTIF function in Excel can be used to count the frequency of each response. Creating a summary sheet would allow for students to create graphs to represent their data using Excel. 

Lesson Four

In the final reflection part of the unit students are required to report their findings about bullying. They are also encouraged to think about their process of investigation and what they have learned from it.

Provide time for your students to construct a report that shows the results of the investigation. Copymaster Three might be provided in docx form so that students can write into it, and import data displays they have created.

Invite different groups to share their findings. Accept the fact that a non-finding, such as little bullying is reported, is a legitimate result. Where bullying is reported, look for students to connect the variables as well as reporting on the results of individual questions. For example, there might be a connection between type of bullying and location or time that the bullying occurs, e.g. social bullying occurs most in the playground at play and lunch times. Also encourage the students to make recommendations about how the school can apply use anti-bullying strategies, such as educating students about how to respond to bullying, being aware of the most vulnerable students.

The class might compile a report for the Principal detailing the findings and recommendations. Any report should respect the confidentiality of the students who responded so that details about individuals, and classes, remain confidential.

If time permits you might like to investigate how to deal with data from open response questions. PowerPoint Three has an example of an open response question, and a fictitious set of examples of students’ answers. Coding of open responses generally proceeds in two ways:

  1. A set of categories is established beforehand based on expectations, preferably informed from reading.
  2. Builds categories as they become needed.

Ask your students to read the comments on Slide Two.

Are there things in common about the comments? How could we group them?

Students might suggest sensible ways to classify the comments. Alternatively, click the mouse so that the comments appear in different colours.

How have the comments been grouped?

Challenge students to describe the categories. They might suggest:

  • Yellow: Student’s behaviour encourages bullying
  • Green: Racial discrimination
  • Blue: Physical disability
  • Pink: Family circumstances
  • Purple: Learning disability

If any groups have collected open response data that might be used as an example where students can practise coding data.

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