Statistical investigations give us a process for learning about the world. Children are naturally curious. Statistical investigations, beginning informally, can encourage children to notice and wonder about the world, then guide students to understand that they can follow their observations and curiosity with a way to find out.
A common process for statistical investigations, used both by students and professional statisticians, is the PPDAC cycle. PPDAC stands for: Problem, Plan, Data, Analysis and Conclusion. It emphasises that an investigation is initiated by trying to solve a problem.
- Problem: Define the question to be answered through the investigation.
- Plan: Decide what data is needed to answer the question and how the data will be collected.
- Data: Collect, organise, and clean the data.
- Analysis: Represent the data, look for patterns, and make hypotheses.
Conclusion: Interpret the results, draw conclusions, and communicate findings.
Let’s use a context to think through the PPDAC process.
Imagine your class is having an end-of-year pizza party and want to find out what pizzas they should order. They could take that problem and pose a question, such as “How many of each kind of pizza should we order?”. A clear question helps to focus the investigation. Sometimes investigations can go off on a tangent, for example, “Which store do I like to get pizza from?”. The teacher can use the investigation question to refocus the class: “Do I need to consider the store in order to answer our question?”. Perhaps they do need the store if they want to consider different sizes of pizza, then that can be a quick conversation; usually, it helps to shift students back to the intended investigation.
Then the class can consider what information, or data, they will need to find out the kinds of pizza that people like. A survey may assist with this data collection, or students could place themselves into categories that represent different flavours. As a teacher, you may choose to provide students with a survey form, or co-construct one with the class. You could let students initially attempt and pilot their own survey then use the challenges they encounter to improve the survey. This experience optimises their learning about the decisions that are made in data collection and why some approaches to surveys work better than others.
Analysing their data may lead to the need to improve the process. For example, “We can’t order a full mushroom pizza because only one person likes that flavour. We may need to ask some classmates to make a second choice. Who do we need to ask?”
Finally, students communicating their findings can lead them to propose to the teacher which pizzas to order.
By engaging in statistical investigations, students will learn to recognise the purpose of each stage. They will value the use of data to find out something, and also experience the many decisions that are made throughout the process. This is important to help students to realise the importance of good methods for investigation, and to ask good questions about methods of data collection when they read a statistic in a news article or advertisement or social media post. Building “healthy scepticism” comes through multiple experiences with statistical investigations. Students come to learn the value, limitations and questions to ask about how a statistical investigation was conducted (e.g. “Who and how many people were asked? What question was asked to get this finding?”).
Not every statistical investigation needs to spend extended time on all five elements of the investigation. The teacher may choose to focus on helping students learn how to ask a question that can be investigated, then move more quickly through the other phases. It may be that the teacher provides the problem and poses the question to allow for more time to explore different types of representations or to improve ways to report on a statistical investigation. An investigation can take one lesson or last a couple of weeks. Longer investigations can integrate multiple skills and even multiple subject areas. For example, “How long does it take to read a chapter book?” could incorporate practice reading, measuring time for a page (or a few pages), or multiplicative reasoning in scaling up from one chapter to a full book. Science investigations can become statistical investigations if data is collected and analysed for a science experiment. The opportunities are endless!