1 (The Role of) Mental Imagery in the Teaching and Learning of Mathematics John Mason Tower Hamlets June 08.

Slides:

Advertisements

Similar presentations

Literacy Strategies in Maths Adapted from the work of John Munro

Advertisements

Empowering Learners through the Common Core State Standards

1 The Micro-Features of Mathematical Tasks The Micro-Features of Mathematical Tasks Anne Watson & John Mason Nottingham Feb The Open University.

1 The Role of Attention in Teaching & Learning Mathematics John Mason Stockholm Biennalen 2008.

Thinking Mathematically

1 When and How is Mathematics Actually Learned? John Mason Trondheim Oct 2007.

1 Learning to Think and to Reason Algebraically and the Structure of Attention 2007 John Mason SMC.

1 Generalisation: Fostering & Supporting Algebraic Thinking John Mason Trondheim Oct 2007.

Example spaces: how to get one and what to do with it! Anne Watson Matematikbiennalen 2008.

1 Getting Students to Take Initiative when Learning & Doing Mathematics John Mason Oslo Jan 2009 The Open University Maths Dept University of Oxford Dept.

1 Learning Mathematics as a domain for Creativity John Mason Tower Hamlets June 2008.

1 Learner Generated Examples in the Teaching of Mathematics John Mason Grahamstown May 2009 The Open University Maths Dept University of Oxford Dept of.

1 Phenomenal Mathematics Phenomenal Mathematics John Mason AAMT-MERGA Alice Springs July The Open University Maths Dept University of Oxford Dept.

1 Progress in Mathematical Thinking John Mason SMC Stirling Mar

Generalisation in Mathematics: who generalises what, when, how and why? John Mason Trondheim April 2009.

1 Making Use of Mental Imagery John Mason East London June 2010 The Open University Maths Dept University of Oxford Dept of Education Promoting Mathematical.

1 The Open University Maths Dept University of Oxford Dept of Education Thinking Algebraically as Developing Students’ Powers John Mason OAME Toronto Feb.

1 Making the Most of Mathematical Tasks John Mason Overton Jan 2011 The Open University Maths Dept University of Oxford Dept of Education Promoting Mathematical.

1 Attention to Attention in the Teaching and Learning of Mathematics John Mason Open University & University of Oxford Flötur Selfoss Sept 2008.

1 Construction Tasks John Mason Open University & University of Oxford Flötur Selfoss Sept 2008.

1 Necessary Movements of Attention John Mason ATM March 2009.

1 Mathematics: with good reason John Mason Exeter April 2010 The Open University Maths Dept University of Oxford Dept of Education.

1 John Mason IMEC9 Sept 2007 Using Theoretical Constructs to Inform Teaching.

1 Wherein lies the Richness of Mathematical Tasks? John Mason Windsor & Datchett Feb 2008.

1 With and Across the Grain: making use of learners’ powers to detect and express generality London Mathematics Centre June 2006.

THE TRANSITION FROM ARITHMETIC TO ALGEBRA: WHAT WE KNOW AND WHAT WE DO NOT KNOW (Some ways of asking questions about this transition)‏

1 Exploiting Exercises in order to develop Conceptual Appreciation John Mason CENEZ High School Maseru 2013 The Open University Maths Dept University of.

The Use of Student Work as a Context for Promoting Student Understanding and Reasoning Yvonne Grant Portland MI Public Schools Michigan State University.

Why do I, as a middle grades math teacher, need to know about calculus and analytic geometry?

1 Working with the Whole Psyche: what can a teacher do for students? Nurturing Reflective Learners Mathematically in Secondary School Working with the.

1 A Lesson Without the Opportunity for Learners to Generalise …is NOT a Mathematics lesson! John Mason ‘Powers’ Norfolk Mathematics Conference Norwich.

1 Generalisation as the Core and Key to Learning Mathematics John Mason PGCE Oxford Feb The Open University Maths Dept University of Oxford Dept.

+ Socially Inclusive Teaching in Higher Education.

1 On the Structure of Attention & its Role in Engagement & the Assessment of Progress John Mason Oxford PGCE April 2012 The Open University Maths Dept.

1 While you are waiting: Warm Up 1: in a certain club there are 47 people altogether, of whom 31 are poets and 29 are painters. How many are both? Warm.

1 Transformations of the Number-Line an exploration of the use of the power of mental imagery and shifts of attention John Mason MEI Keele June 2012 The.

Northern Metropolitan Region Achievement Improvement Zones Session 3: BUILDING MATHEMATICAL UNDERSTANDING Peter SullivanSue Gunningham.

1 Responsive, Reflective & Responsible teaching John Mason AIMSSEC ACE Yr 2 Jan 2013 The Open University Maths Dept University of Oxford Dept of Education.

Supporting Rigorous Mathematics Teaching and Learning Tennessee Department of Education High School Mathematics Algebra 2 Illuminating Student Thinking:

+ Revisiting Collaboration and RtI October 11, 2011 Math Alliance Teaching All Learners Judy Winn Beth Schefelker Mary Ann Fitzgerald.

1 Drawing on Learners’ Perspectives Anne Watson & John Mason STEM Education NW July The Open University Maths Dept University of Oxford Dept of.

Children’s ideas of mathematics. Maths can sometimes be challenging so can also make some people feel uncomfortable! We will be discussing what is needed.

Introduction: definition of a lesson plan It can be simple as a mental checklist or as a complex as a detailed two-page typed lesson plan.

Calculation strategies used at Barley Close. Parental involvement in education is so important. However, the way maths is taught in schools is very different.

1 Pedagogical Mathematics for Student Exploration of Threshold Concepts John Mason KHDM Hannover Dec 2015 The Open University Maths Dept University of.

Welcome Day 2. Overview Reflection The Art of Questioning Best Size Task Selecting and Sequencing Lesson Planning.

Questioning in Mathematics Anne Watson Cayman Islands Webinar, 2013.

1 Designing and Using Tasks Effectively for Conceptual Development Anne Watson John Mason Agder College Kristiansand Norway September 2006.

Key Stage 3 National Strategy Planning and teaching mathematics 2 Geometry, ratio and proportion, and problem solving.

1 Reasoning Reasonably in Mathematics John Mason Schools Network Warwick June 2012 The Open University Maths Dept University of Oxford Dept of Education.

1 Teaching for Mastery: Variation Theory Anne Watson and John Mason NCETM Standard Holders’ Conference March The Open University Maths Dept University.

1 Digging at the Foundations of Mathematics Education (Part 1) John Mason PTAN Karachi August 2008.

Doing, Learning & Teaching Mathematics: developing the inner explorer

Woodlands Information Evening

Winwick CE Primary School

Curriculum Evening Maths at St Nic’s

© Copyright Showeet.com ORAL PRESENTATION Nº1 Subject: Curriculum Evaluation Date: May 11 th, 2018 Cycle: VI Topic: Unit 1: Evaluation and Innovation and.

Chapter Summary The chapter makes the link between mental calculation strategies and more formal written methods It suggests that mental methods should.

Entry work/ “Do Now!” This connects the learning from the previous session or introduces a new topic. It is a short activity that the students commence.

Example spaces: how to get one and what to do with it!

Mathematical Task 2.3A.

Overview of the reSolve: Mathematics by Inquiry Project

Reasoning and Problem Solving Maths Café

John Mason Lampton School Hounslow Mar

Teaching for Mastery: variation theory

MATH UNIT #2 Multiplication and Division

John Mason ATM Reading Oct 2018

Scaling New Heights in order to Master Multiplication

Variation/Invariance: pupils’ experience

Algebra (Solving Equations)

Presentation transcript:

1 (The Role of) Mental Imagery in the Teaching and Learning of Mathematics John Mason Tower Hamlets June 08

2 Conjectures  Mental imagery is perhaps THE fundamental power possessed by humans –It is the basis for planning and for carrying out plans; –It is the root of expectation and the mechanism for motivation –It is the basis for algebra and geometry

3 Outline  Some tasks (paration)  Some reflection (post-paration)  Some pre-paration

4 Imagine …  A straight line …

5 Backwards Arithmetic  When I call out a number, you must write it down from right to left, with the units digit on the left Useful Strategy: impose an unusual constraint so as to force yourself to bring internalised procedures to the surface

6 Tulips

7 Kites

8 CopperPlate Calculations

9 What’s Being Done?  Does ‘it’ always work?  What is the it? The calculation comes from an Arabic manuscript Hindu Reckoning written by Kushyar ibn-Lebban about 1000 C.E. (quoted in NCTM 1969 p133)

10 Layout Treviso and Pacioli Multiplications Historical Topics for the Mathematics Classroom, NCTM p

11 Construction

12 Construction

13 Raise your hand when you can see  Something which is 2/5 of something  Something which is 3/5 of something  Something which is 2/3 of something –What others can you see?  Something which is 1/3 of 3/5 of something  Something which is 3/5 of 1/3 of something  Something which is 2/5 of 5/2 of something  Something which is 1 ÷ 2/5 of something

14 What fractions can you ‘see’?  What relationships between fractions can you see?

15 Using Mental Imagery  When planning a lesson  When reflecting on a lesson  When introducing a lesson or a task  Getting learners to use their imagery –Anticipating –Predicting –Going beyond the physically possible