You may like to work with this as a whole school and investigate one key aspect at a time, for example ‘who does most of the talking? This will give you the opportunity to share good practice across the school as well as support each other in developing high-quality mathematics classrooms. Putting the words inside ready-cut out laminated, speech bubbles can be very effective and create an appealing and interactive display. You can stimulate some talk by joining in with a pair/group of students and ‘playing dumb’.

Generally, in a strong problem-solving environment the teacher needs to be doing around 30% of the talking and the students 70%. For example, make a deliberate mistake and see how the students respond.

To explore this aspect further take a look at Number 7 in this article. Try these out and see if that helps you to talk less! • Resist the urge to finish their sentence for them with what you think they want to say or what you hope they will say!

Idea to try • Look for problems that require little explanation to start yet are rich in thinking. • Give the students 5 minutes to explore the problem and see how they might get started. • Use our games that have a video clip to show the students the game being played: Dotty Six or Strike It Out. See what happens if you just repeat back to the student what they have said, using the same words they have used, and see if that helps them to finish the sentence.

It also offers suggestions to help you develop the culture further so that students are encouraged to develop as independent mathematicians with strong problem-solving skills.

This is important as we know that independent problem-solving skills are essential for students for 21st century life and work.Do I ask the student a ‘clarification’ question, such as ‘can I just check what I think you said was ...’? Do I simply evaluate their answers with comments such as ‘Good’, ‘Well done’, ‘Right’, ‘OK’, ‘No’, ‘Think again’? Generalising, Conjecturing Of what is this an example? We may not hear clearly what they say as we may be expecting them to give us a fixed answer that we have pre-determined – this can be called, ‘guess what is in the teacher’s head!Do I carry on with the next thing I was going to say? ’ We need to be ready to be open to their answers and be curious to understand what they are trying to say.In this article, the author describes how "Scratch" can be used to design games to develop mathematical concepts.He examines the ways mathematical thinking emerges when children work with "Scratch," an interactive, programming language.To read more about this, have a look at the ACME report Mathematical Needs: Mathematics in the workplace and in Higher Education.How to use this resource You can use this article and its activities as an individual, with a colleague, in a focus group or as a whole school staff together, as you seek to offer students the highest-quality learning opportunities in mathematics. (1998) Questions and Prompts for Mathematical Thinking.It needs to be one where questioning and deep thinking are valued, mistakes are seen as useful, all students contribute and their suggestions are valued, being stuck is seen as honourable and students learn from shared discussion with the teacher, Teaching Assistant (if present) and peers. How does the cameo above compare with your classroom? What can change and what has to stay the same so that … Explaining, Justifying, Verifying, Convincing, Refuting Explain why … This means that some modelling of talk is useful – between you and your Teaching Assistant, you and a puppet or you and one of the more articulate students in the class.We invite you to investigate this by videoing your next ‘problem-solving’ lesson to watch by yourself, or with a trusted colleague, and see what you notice about the key aspects detailed below. Give a reason (using or not using…) How can we be sure that …? • Capture key words and phrases that you hear students using as they talk and put them up on your mathematics 'talk wall' or other display to support the students to use those words.When students are confident to behave in these ways they are then able to step into problems independently rather than immediately turning to us as teachers to ask what to do! • Encourage the students to become fluent with the mathematical vocabulary.As teachers we can support our students to develop the skills they need to tackle problems by the classroom culture we create. Students learn to join in conversations by hearing what others are saying, listening to how words are being used and ‘playing around’ with those words themselves.

## Comments A Problem Solving Approach To Mathematics

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