1. Inquiry learning What do inquiry tasks look like in mathematics?
Tool IE-1: Exploring inquiry activity and tasks
© 2016 mascil project (G.A. no ). Lead partner University of Nottingham; CC-NC-SA 4.0 license granted. The project mascil has received funding from the European Union’s Seventh Framework Programme (FP7/ ).

2. Overview
Aim:
To explore how tasks can be used to promote inquiry learning.
We will:
Discuss inquiry learning;
Examine and discuss two tasks.
Consider how these task could be used to promote inquiry learning.
The aim of this tool is to explore how tasks can be used to promote inquiry learning. The tool begins with a short discussion about the characteristics of inquiry learning in mathematics. The group then examine some specific tasks and consider how these might be used in a mathematics classroom to promote inquiry learning.

3. About inquiry What does inquiry look like?
What do students do in inquiry learning?
Exploring situations;
Planning investigations;
Experimenting systematically;
Interpreting and evaluating;
Communicating results.
First discuss with the teachers what inquiry looks like. Ask them to think about what sorts of things students would be doing if they were doing inquiry learning in mathematics. They should be able to get started, but if not, you might refer to the Mascil ‘Inquiry Learning Dimensions’. These are listed below:
Exploring situations;
Planning investigations;
Experimenting systematically;
Interpreting and evaluating;
Communicating results.
If you do use this list, ask them to what extent they agree with these dimensions, what they would add, what is less important to them and so on. You want them to consider the dimensions critically and not just to accept them.

4. Two tasks
Now show the teachers the two tasks you want them to look at.

5. A detailed look at the tasks
Examine each task and discuss:
What likely student activity would result from the task?
Where does the activity fit within the dimensions of inquiry learning?
How does the task connect to the world of work?
Ask the group to work in pairs, one on each task, to analyse the task in terms of the likely student activity it would provoke and to suggest where this activity might fit within the dimensions of ‘inquiry learning’. Also ask them to think about the extent to which the task fits with the world of work. They should then share with each other, first by outlining the task (what the student should do) and then by explaining what they have concluded about inquiry activity.

6. Sharing thinking
Present and discuss your findings to each other. Discuss the following questions:
What would you do or not do in your classroom to encourage inquiry activity?
How might you change the task so that it fits better with the world of work?
Bring the group together. Ask each pair to select one of the two tasks and to present their findings to the group.
Ask the group about:
What they as teachers would and would not do to encourage inquiry activity within their classrooms;
How they might change the task so that it fits better with the world of work.
(Note that all pairs will be looking at the same tasks. If you prefer, give out some other tasks as well, but be aware that the group sharing time would take much longer as all teachers will need to become familiar with the tasks presented before they could engage with the findings.)

7. Finishing off
Devise a research question together that concerns the use of tasks to promote inquiry learning. Choose a task and teach this to one of your classes, making observations related to your research question. Be ready to share your observations and reflections at the next meeting.
Ask the teachers to devise a research question related to the use of tasks to promote inquiry. They should select a task of their choice, but one that they consider to be effective in terms of promoting inquiry approaches.
Each teacher should then teach the task and make some observations that will allow them to answer the research question. They should be prepared to report about their experiences in the next professional development session. When they report back, you should encourage them to reflect on the lesson, the responses of the students and what they themselves have learned.