Our viewpoints

Our viewpoints

After reading articles about statistical thinking, we have summarised what we think about statistical thinking in a diagram as attached below.

This is a simple diagram that summarizes what we think about statistical thinking and the examples of what these thinking would look like.

A simple definition of statistical thinking that we both agreed upon is : the ability to generate possible questions, collect useful data, organize and representing data, analyse and make sound and logical decision by taking factors (such as availability of resources, ethical concerns) into consideration.

How do teachers move students up to the next level?

Generate questions:

Lead students to some questions to think about the problem and help them to  generate a statistical question. Then make sure their question can answer the problem they want to know. For example,

• how do we go about answering this question?
• what do we need to know?
• how will we find the information that we need?
• what will we do with the information that we collect?
• who will find this information useful?
• is this information relevant to the problem

Collecting data:

After identifying what they need to know, teachers can facilitate students to collect relevant data with the most appropriate method. For instance, whether the data collected can be done through an

• online survey
• Interviews
• Questionnaires
• registry (for a related event) etc.

Teachers facilitate students in choosing the most appropriate and effective way of collecting relevant data by having discussions and consultation during a project.

Organising and representing data:

To organise data collected and summarise them is not as easy as it seems especially when the collected data is massive. Teacher can help students to master this process by giving some examples of organising data. For instance, making a

• Table with different aspects
• List

In addition, teachers can also teach the way to find average, mean and mode as an effort to organise data.

Then, students will need to choose the best way to represent these organised data using any visual display. This is where students need to choose among

• A bar chart
• Line graph
• Pie chart
• Histogram

To effectively represent their data. Teachers can show students the characteristics of each type of graph in order to aid students in selecting the best representation.

Analyse data:

Based on the data represented, students should be prompt to analyse the data with the aim of finding a solution to the generated question. For instance, if the problem was about how to solve food waste in the school canteen, based on the data represented students should be prompted to make conclusions such as “most students have their lunch in the school canteen on Fridays”. In the effort of prompting, teachers can ask questions such as:

• What can you conclude from the graph?
• What does the number of students having lunch at school canteen on Mondays tell you?
• What is the pattern of the data?
• What does the pattern tells you? (e.g. most students will only buy food from canteen on Fridays.)
• What do you think can be the reason behind this pattern?

Making decision:

This is critical in statistical thinking because the decision made by the students would determine whether the problem will be solved and would affect the outcome greatly. Teachers can help students in making a sound decision by having them:

• Search information from the internet or clarify with teachers or parents when having doubts
• Apply their knowledge, for instance, if students were to solve the food waste issue, they can then apply what they have learnt from moral or science such as how to tackle the food waste.
• Think of the limitations and consequences of the decision.
• Consider different aspects such as if the canteen staff can accept the decision made by the students and if this is applicable for all the students because there will be students who eat more than the others. 
• Always have a backup plan. 

All in all, we both agreed that although the frameworks suggested by statisticians may be useful guidelines for teachers in teaching statistics such as carrying out learning activities to encourage students to think statistically, in a real classroom however, teachers will need to consider other factors that will affect the effectiveness of teaching and learning to decide on how they will deliver a statistics lesson so that students will all benefit from the lesson. For instance, teachers need to consider students' prior knowledge, interest, and readiness before deciding what should be done to facilitate students in learning statistics in a meaningful way.