Engaging Students, Developing Confidence, Promoting Independence

Age 5 to 18
Article by Charlie Gilderdale and Alison Kiddle

Published 2009 Revised 2020

The NRICH Team have organised a series of three Teacher Inspiration Days in Cambridge for several years. The aim has been to support secondary mathematics teachers who are committed to nurturing confident, resourceful and enthusiastic learners.

During the first day teachers were asked to list the issues that most concerned them. The workshops on the next day focussed on these issues.

Broadly speaking, teachers were interested in ways to engage students, promote independence and challenge learners.

We would like to share with you the seven issues that the delegates identified, together with the ideas that came out of the second meeting:

How do we develop positive attitudes towards mathematics and learning mathematics?

- Use a wide range of tasks and resources
- Enthusiastic teachers, with a 'can do' positive attitude
- Plenty of opportunities for students to experience success
- Hands-on approaches to learning
- Use real life examples and explore links with other subjects
- Offer positive role models of mathematicians
- Maths Clubs - e.g. older students mentoring younger students
- Posters publicising maths
- Share learning with parents (e.g. maths evenings to encourage positive attitudes amongst parents)
- 'Make it enjoyable': Maths challenges, competitions, puzzles of the month, celebrate achievements

How do we develop confident learners who are able to work independently and willing to take risks?

- Acknowledge all contributions positively, encourage learning from mistakes, welcome wrong answers as the springboard to new understanding
- Use positive language
- Encourage independent and small group research
- Value different approaches to solving problems

How do we develop good communicators - good at listening, speaking and working purposefully in groups?

- Plan lessons which focus on group work
- Set 'group-worthy' tasks that offer plenty to talk about
- Set a rule that groups are not 'allowed' to move on until all the students understand
- Allow time for presentation of findings
- Set the rule: "Don't ask the teacher - ask at least three other students first"
- Teachers take a step back and ask students to explain to the class their methods and reasoning
- Teachers question the answers, rather than answer the questions
- Mix up groups - expect students to take on a variety of roles and work with a variety of people
- Ask students to prepare tests and answers for younger age group
- Ask students to make a podcast or film on a given topic

How do we develop students who have appropriate strategies when they get stuck?

- Offer higher-order, open ended tasks to get students used to being 'stuck'
- Encourage students to explain their difficulty to the rest of the class - vocalise the problem, "say it out loud". Follow-up with an open discussion of the options available
- Offer easy access to a variety of resources
- Offer tasks in which students have to identify and correct errors and encourage similar reflection on their own work
- Create a culture in which 'thinking outside the box' is valued

How do we develop lessons that maintain the complexity whilst making the mathematics accessible?

- Gradually increase the complexity of tasks
- Give plenty of time to engage in and 'solve' problems - the process is more important than the answer
- Use investigational tasks which can be accessed by everyone but can have different levels of outcome - low threshold high ceiling tasks
- Be positive about any steps students take towards solving the problem, however small
- Present tasks in different formats
- Encourage a supportive environment in which students work together, discuss ideas and turn to each other for help

How do we develop students' ability to make connections (e.g. see/utilise different aspects of mathematics in one context, see applications in other areas)?

- "Where have we seen this before?"
- Present problems that can use many areas of maths
- Present open problems which allow students to ask their own questions and develop the need to learn something new
- Present problems based on real life and cross curricular contexts
- Invite outside speakers and professionals to discuss the use of maths in their jobs

How do we develop critical learners who value and utilise differences (e.g. different approaches/ routes to solution)?

- Encourage group work, peer assessment, rotation feedback, discussion
- Change the composition of groups regularly
- Ask key questions:

What are the strengths and weaknesses of this method?
When might you use this method?
- Encourage contributions from all the students
- Require students to explain their solution
- Emphasise method rather than outcome
- Bring students together for mini-plenaries to share and compare approaches
- Set problems which can be solved in a variety of ways