SCITT Day 7

Session objectives Understand how pattern provides the key to early work with algebra and generality (Understand how work with pattern in key stage 1 and lower key stage 2 provides the foundation for algebraic thinking) Use of practical equipment Access good problem solving activities Consider methods of whole class assessment and record keeping

Day 7 Session 1 Session 2 Session 3 Session 4 Assessing children Problem Solving Session 3 Genres of problems (incl Pattern  exploring generality) Session 4 Intro tasks

Starter Probability: ‘Number Spinners’ ITP What will the total be after 10 spins?

What sort of assessment are we talking about? Day-to-day Close up Standing back Periodic Transitional Public view

NCETM

Supporting judgements

Feedback and Marking Be based on clear learning intentions/ success criteria Take account of pupil self-evaluation Highlight where success occurred and where improvement could take place Be in a form which is accessible to the learner Give strategies for improvement (often oral if this is beyond the means of the learner) Have allocated time in which to take place or be read.

3 types of closing the gap prompts A reminder prompt – suitable for brighter children, this simply reminds the child of what could be improved. A scaffolded prompt – most suitable for children who need more structure than a simple reminder, this prompt provides some support. This can take the form of a question, a directive or an unfinished sentence. An example prompt – very successful with all children, but especially with average or below average children, this prompt gives the child a choice of actual words [calculations] or phrases. ( Shirley Clarke, 2001)

“Children need to solve problems to become problem solvers.” Oxford: University Press (2013)

NC 2014 Where is ‘Using and Applying’? Look in one two-year section… Is it mentioned? What examples are given?

Purpose of Study Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary in most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, and a sense of enjoyment and curiosity about the subject.

Aims become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

How can I make children think in maths lessons? Good Problem Solving… How can I make children think in maths lessons?

NCETM “Problem solving means engaging in a task for which the solution/ method is not known in advance. In order to find a solution, students must draw on their knowledge and through this process, they will often develop new mathematical understandings. Solving problems is not only a goal of learning mathematics, but also a major means of doing so.”

Information Processing NC2000 Thinking Skills Information Processing Reasoning Enquiry Creative thinking Evaluating

Nrich Skills 31 – 12 = ? Discuss these answers: 11, 43, 19, 20

Questions for Thinking Reasoning Progressions - for Assessment Cold/ Hot Tasks?? Progress?

Using and Applying – AT1 Different Types of Problem Finding All Possibilities Logic Puzzles Finding Rules and describing patterns Visual Problems

A word problem There are 7 shelves with 25 books on each shelf. If I remove 47 books, how many books are left? How many ‘full’ shelves would there be? What did you do to solve this problem?

Word Problems Read Underline Choose Solve Answer? Check Read Underline Decide Estimate Calculate Answer? Test it

TASKS Maths Task 4 Deliver a Problem Solving lesson to a group, or class, of children. Focus on one set of skills that you wish to make explicit to learners. Evaluate the lesson – how & when did you make the skills explicit? How successful were the learners in acquiring them, what do they need to do next? Maths Task 5 Identify a learning objective that requires consolidation. Create a game (or other practical activity) for your learners to use in-class and/or at home. WITH SECOND PLACEMENT LEARNERS SHARE ON DAY 10