Inspire Maths Text books Inspiring children to succeed

Aim of this presentation: To introduce the Inspire Maths program for sustained improvement in schools To provide the background to its development To familiarise ourselves with the resources and the teaching sequence To transform the teaching and learning of mathematics for all children in our school, teaching to mastery.

The case for reform

Although our top performing students perform equally with Singapore students there is a definite skew in the data. Source PISA 2012 dataset

Jerome Bruner. American. 1915 – Concrete – Pictorial – Abstract. Jerome Bruner. American. 1915 – Variation Theory. Zoltan Dienes. Hungarian. (1916 – 2014) Conceptual and procedural understanding. Richard Skemp. British. (1919 – 1995) Only briefly mention these theories as we will work on each in more depth illustrating with hands on activities. Growth mind set – ‘I can’t do this yet!’ Carol Dweck. American. (1946)

Concrete-Pictorial-Abstract Concrete – internalised action Pictorial – iconic with sensory imagery Abstract – symbolic with symbols e.g. numerals, which bear only an arbitrary relation to what they stand for.

Variation Theory One of the theories underpinning Inspire Maths text books Two underlying principles: Perceptual variation – presenting one concept in a variety of contexts (e.g. using a variety of manipulatives and models to represent one addition number sentence) Systematic variation – mathematical variation which provides a variety of examples of one mathematical concept (e.g. providing a variety of addition number sentences for practice and consolidation )

The approach to teaching maths in Singapore is based on a few fundamentals: Problem solving curriculum Emphasis on the development of intellectual competence such as ability to visualise Emphasis on conceptual understanding Systematic development of skills and concepts Emphasis on the C-P-A approach

True or false? 2 + 3 = 3 + 2 6 X 7 = 7 X 6 20 ÷ 5 = 5 ÷ 20 30 X 9 = 9 X 30 5 – 4 = 4 – 5 23 + 25 = 22 + 26 4 X 12 = 8 X 6 68 – 27 =59 – 18 Discuss with your neighbour the structures, relationships and connections you can see.

Inspire Maths Provides opportunities for problem solving Emphasis on the development of the intellectual competence, such as the ability to visualise Conceptual understanding Systematic development of skills and concepts; the spiral approach Emphasis on the C-P-A approach Guides children into making connections between different areas of mathematics Textbooks give structure and a systematic approach

Fluency and Mastery Become fluent in the fundamentals of mathematics including through varied and frequent practice with increasingly complex problems over time so that pupils develop conceptual understanding and are able to recall and apply their knowledge rapidly and accurately

A Mastery Curriculum The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on. (NC p3) The slower pace is a cornerstone of this approach to teaching math, which is based on the national maths system of Singapore and aims to emulate that country’s success by promoting a deeper understanding of numbers and maths concepts. Students in Singapore have repeatedly ranked at or near the top on international math exams since the mid-1990s. Singapore approach devotes more time to fewer topics, to ensure that children master the material through detailed instruction, questions, problem solving, and visual and hands-on aids like blocks, cards and bar charts. Ideally, they do not move on until they have thoroughly learned a topic. Principals and teachers in the USA say that slowing down the learning process gives students a solid maths foundation upon which to build increasingly complex skills, and makes it less likely that they will forget and have to be retaught the same thing in later years. “And with the Singapore approach, the pace can accelerate by fourth and fifth grades, putting children as much as a year ahead of students in other maths programs as they grasp complex problems more quickly.”

National curriculum for England: mathematics programmes of study https://www.gov.uk/government/publications/national-curriculum-in-England-mathematics-programmes-of-study

Inspire Maths Programme Lesson planning and using the text books: Teacher’s Guide 1a and 1b Pupil Text book 1a and 1b Practice book 1a, 1b, 1c, 1d Assessment book Oxford Owl and digital offering*

Teaching Sequence The suggested sequence is: Let’s learn – direct teaching/instruction Guided practice – all working on the same concepts and skill at the same time by using pupil textbooks on the carpet Independent practice – using practice book to consolidate * Homework opportunities provided within pupil textbooks and practice books Deep conceptual understanding is developed through the spiral curriculum of core topics teaching to mastery

Proactive or reactive teaching of maths? Preventing the gap rather than closing the gap! Depth and breadth not acceleration TLLM: Teach less – learn more Inclusive of everyone – mastery for all