Saturday, 29 September 2012

Engaging Students, Developing Confidence, Promoting Independence

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

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