PEDAGOGY

Reflecting using reflection questions

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Posted by , August 24, 2017 | 0 comments

Why use the Reflection Questions? The reflection questions at A Learning Place A Teaching Place have been designed to allow children to demonstrate and develop their understanding of mathematical concepts. The reflection questions have also been developed to allow you to collect formative assessment data in every lesson. How could we Engage Children in Reflection? Quality Maths lessons involve 3 aspects: Explicit Learning Guided and Independent Investigation Reflection Reflection allows children to identify and explain their current understanding of mathematical concepts. To reflect, children think about a specific reflection question. A reflection question is an open-ended broad question, allowing all children to access regardless of their current level of understanding. A child’s response to the question will provide formative assessment data about their current understanding, including any misunderstandings (misconceptions). To reflect, children share their understandings when reflecting with other children. The children are within one another’s zones of proximal development. Vygotsky defines a zone of proximal development(i) as closely related levels of understanding. Reflecting within their zone of proximal development, and with others within their zone of primal development, serves to develop both children’s understanding and meta-language as the depth of their explanation will be greater than when explaining to an adult who’s zone of development is considered by the child to be much higher. To reflect, children record their current understanding of mathematical concepts. Recording requires and develops logical thought and language. Vygotsky’s research on Thought and Language(ii) demonstrates that to learn, we need to think, then talk, then record. All three are vital to learning. After children have thought about, then discussed their current understanding, giving them to opportunity to record allows them to reconcile and synthesise their previous understanding with new understanding developed in the lesson. Recorded responses to reflection questions allow teachers to see growth in each child’s understanding over lessons, weeks and terms.  When to ask the Reflection Question The reflection question may be asked at any time during lessons, for example: at the start of the lesson to identify the specific explicit learning you will include in the lesson. at an opportune time during the lesson, to allow children to reflect on their current understanding before continuing to investigate. at the end of the lesson to provide formative assessment data of each child’s current level of understanding at the end of their investigation. Children think about the reflection question, then discuss the reflection question with a friend. Children then record their response to the reflection question. Recording Reflection Question Response There are many ways that students can record their response to a reflection question. Collecting Books: At the end of the lesson, collect each child’s book open at the page they recorded their investigations and reflection today. You can then place the books in piles according to the level of understanding demonstrated. The piles provide you with formative (iii) (and summative) assessment of the children’s understanding, and also give you the levels for the Explicit Learning and Guided and Independent Investigations for the next lesson! Record response...

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Problem solving

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Posted by , May 20, 2017 | 0 comments

Problems allow children to investigate concepts in new and varied situations. Any problem worth solving takes time and effort – that’s why they’re called problems! Problems are designed to develop and use higher order thinking. Allowing children to grapple with problems, providing minimal support by asking strategic questions, is key. Differentiating problems allows children to solve simpler problems, before solving more complex problems on a concept. Problems may not always be solved the first time they are presented – or at all. The focus of problem solving is the development of problem solving understanding and capacity – not mastery! Returning to a problem after further learning, develops both resilience and increased confidence as children take the necessary time and input the necessary effort. After solving problems, children also create their own problems. For videos and professional learning and development on Teaching Problem Solving, select ‘Problem Solving’ in the banner on the Home Page. Create 3 levels of a problem. GUIDE children through the first level using the problem solving steps (described below) included with all problem solving in all levels of all concepts: Allow children to investigate the second level with friends, with minimal guidance. Allow children to investigate the third level INDEPENDENTly. Children create their own problem. The problem solving resources, included with EVERY level of EVERY concept at A Learning Place A Teaching Place, are designed to allow you to engage children in differentiated problem solving. As Dan Meyer perceived, children are often pre-loaded with viruses when it comes to problem solving! They lack initiative, perseverance and retention, have an aversion to word problems and are often eager for formula. (Dan Meyer – TED talk) Paul Lockhart proposed ‘A good problem is something you don’t know how to solve. That’s what makes it a good puzzle and a good opportunity’. (Paul Lockhart A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form) Problems are designed to develop and use higher order thinking. John Wesley Young explained, ‘It is clear that the chief end of mathematical study must be to make the students think’ and John Dewey added ‘We only think when confronted with a problem’. Allowing children to grapple with problems, providing minimal support by asking strategic questions, is key. Problems may not always be solved the first time they are presented. Returning to a problem after further learning, develops both resilience and increased confidence as children take the necessary time and input the necessary effort. Albert Einstein felt that, ‘It’s not that I’m so smart – I just stay with problems longer’. Differentiating problems allows children to solve simpler problems, before solving more complex problems on a concept. George Polya found that ‘If there is a problem you can’t solve, then there is an easier problem you can’t solve: find it’. As the expert in your classroom, you may differentiate the problems, and the problem solving process using the levels of understanding demonstrated by the children in your class. These are...

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