Do I ask other students to comment on what was said? Do I explain how it needs to be done and make sure they understand it as fully as possible before working on their own? Changing, Varying, Reversing, Altering What happens if we change …? If this is the answer to a similar question, what was the question? Ideas to try • Be curious about what the student was saying and ask a clarifying question such as, ‘so what you are saying is ...?

Do I ask another follow-up question such as ‘are you sure? Do I give them key pointers/hints/clues to help them? ’ You could alternatively invite the students to tell a partner what they think their peer said.

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.

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.

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.

You can develop this idea further by playing any new game under the visualiser with a Teaching Assistant or student so that the students can then try working out the rules. Then use large equipment and gather the students round. Are there one or two new questions that you could include in your lesson? Here’s an excerpt from Bernard’s article What’s All the Talking About?

• Discipline yourself to only make a comment on a student’s answer to your question after another student has responded to clarify what was said, ask a question or take the thinking further. Exemplifying, Specialising Describe/demonstrate/show/choose/draw one of … that illustrates how easy it is to make an assumption: When subsequently sharing this experience with teachers they were quick to identify the mistakes that the boy had made and which indicated his lack of understanding of place value.

## Comments A Problem Solving Approach To Mathematics

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