Nurturing students' curiosity
This guidance is part of our Primary and Secondary 'Developing mathematical mindsets' collections.
To complement this guidance, we hosted two teacher webinars. You may wish to watch the recording/s before or after taking a look at the guidance below.
Show Primary webinar recording
During this webinar we had a go at the following tasks:
Charlie's delightful machine (see also Light the lights, and Light the lights again)
Show Secondary webinar recording
During this webinar we had a go at the following tasks:
Charlie's delightful machine and A little light thinking
Students who are curious are much more likely to be engaged and motivated. We hope that "Hmmm... that's funny..." or "Wow!", will lead to "Why?", and encourage students to use mathematics to explain what has intrigued them... And then perhaps they will be curious enough to ask new questions of their own and explore further.
These are some of the ways in which NRICH suggests you can nurture students' curiosity in a mathematics classroom, with links to problems:
Creating a culture which encourages experimentation and welcomes diverse approaches
Eightness of eight (age 5-7)Lots of lollies (age 5-7)
Statement snap (age 7-14)
Fruity totals (age 7-16)
Cuboid challenge (age 11-16)
- Introducing contexts which prompt students to ask their own questions
Street sequences (age 5-11)
Consecutive numbers (age 7-14)
Polygon rings (age 11-14)
Offering contexts in which students can notice patterns and investigate whether/how/why the patterns might continue
School fair necklaces (age 5-11)Wipeout (age 11-16)
Attractive tablecloths (age 14-16)What's possible? (age 14-16)
Offering students intriguing and puzzling contexts
Five steps to 50 (age 5-7)Light the lights (age 5-7) and Light the lights again (age 7-11)
Make 37 (age 5-11)
Tumbling down (age 7-11)
Charlie's delightful machine (age 11-16) and A little light thinking (age 14-16)
- Presenting unusual situations and contexts
Little man (age 5-7)
Towers of Hanoi (age 11-14)
Twisting and turning (age 11-14)
Challenging students to explain surprising results
Digit addition (age 5-11)
Subtraction surprise (age 7-14)
The number jumbler (age 7-14)Pair products (age 14-16)
Same number! (age 14-16)
Offering situations which challenge students to find powerful strategies that apply to the initial context, but are also generalisable
Got it (age 7-14)Dicey operations (age 7-14) and More Dicey operations (age 7-14)
Consecutive seven (age 11-14)
Tilted squares (age 11-14)
Odds and evens made fair (age 14-16)
These Primary and Secondary collections of problems, organised by year group, are ideal for tapping into students' natural curiosity.
Questions to consider with your colleagues:
How do you create a culture in your classroom where students are confident to ask their own questions?
How do you adjust your lesson plan to accommodate students' own mathematical questions?
This collection of follow-up resources may help you answer the above questions:
Models for Teaching Mathematics - article by Alan Wigley
Peter Liljedahl's 14 Practices for Building Thinking Classrooms, in particular Practice 1 (What types of tasks we use in a thinking classroom) and Practice 6 (When, where, and how tasks are given in a thinking classroom)
Here is one possible example of how to start a lesson
Tasks Promoting Inquiry talk given by Dan Meyer in Cambridge
Inquiry Maths offers resources and support for teachers who want to 'establish a culture of curiosity, collaboration and openness in the classroom'
If you'd like to know more about the beliefs that inform the work of NRICH, take a look at What We Think and Why We Think It