Planning for Success

1. Planning for Success Mathematics and Numeracy Programs

2. Mathematics & Numeracy • What’s the difference? • Which do we teach?

3. Mathematics • A powerful learning tool • A way of thinking • A language • A body of knowledge • A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement

4. Mathematics • Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.

5. Numeracy • The capacity to bridge the gap between mathematics and the real world ... and people are considered more or less numerate based on how well they choose and use the mathematical skills they have in the service of other things. (Willis, as cited in National Numeracy Review Report 2008, p3)

6. Numeracy • To be numerate is to use mathematics effectively to meet the general demands of life at home, in paid work and for participation in the community and civic life. (AAMT. 1997: 10)

7. Numeracy Using mathematics effectively Maths Learning Tool

8. Why teach Mathematics & Numeracy?

9. Principles of Planning for Success • Learning is built on existing knowledge • Learning requires that existing ideas be challenged • Learning occurs when the learner makes sense of the new ideas • Learning involves taking risks and making errors • Learners get better with practice • Learning is enhanced by clarity of purpose

10. Planning

11. Key Documents of Planning for Success • Yearly & Term Overview – content and procedures • Weekly Program • Key Lesson Plans

12. Key Features of a Balanced Program • Conceptual and procedural understanding (the what and the how) • Skill development and problem solving • A variety of lesson types • Guided, shared and independent instructional approaches • Variety of groupings • Variety of assessment strategies

13. Quantity Operational Sense Relationships Representation Proportional Reasoning (Ontario Education) Big Ideas in Number

14. Focusing on Students Coaching for Student Success in Mathematics

15. Guided Mathematics instruction • Brief and dynamic • Teacher introduces the learning experience, demonstrates effective strategies and makes the mathematics explicit • “Think aloud” technique • Students observe, ask questions and model the strategies themselves under teacher direction

16. Quantity as “howmuchness” Angie has 5 new toy cars. She is deciding how many cars to leave at home and how many to take to her babysitter’s house to play with there. What are the different choices that Angie could make? Early Quantity using Manipulatives

17. Shared Mathematics instruction • Teacher guides whole class or small group as they think, talk and work their way through a mathematical experience • Students should be given the opportunity to choose strategies and materials • Students communicate their understandings as they share, discuss and explore

18. Independent • Follows a guided maths session • Students work individually • Teacher prompts at appropriate points

19. Key resources • Manipulatives – all classes • Children’s Literature • ICT (including calculators) • Teacher resource books • Textbook (optional) • Mathematics games and puzzles

20. Characteristics of Effective Mathematics Instruction • Focused on having students make sense of mathematics • Based on problem solving and the investigation of important mathematical concepts • Begins with the students’ understanding and knowledge of the topic • Includes students as active rather than passive participants in their learning

21. Characteristics of Effective Mathematics Instruction (continued) • Has students communicate and investigate their thinking through ongoing discussion • Includes all students, whether in the choice of problems or in the communicating of mathematical ideas • Incorporates ongoing assessment of student understanding to guide future instruction

22. Lining Up Your class is lining up in one line. You are fifteenth (15th) from each end. How many people are in your class? What if you were seventh (7th) from each end? What if you were third (3rd) from each end? Can you find a rule for working out the answer if you are Nth from each end? Middle Algebra

23. Weekly Program • Major Focus – core concept or procedure - approx two thirds of time • Minor Focus – regular revision of strands and concepts - two or three 15 minute sessions per week • Routine activities – often lesson starters - mental maths, algorithms, hundreds board, number facts, counting

25. A Suggested Lesson Schedule • Routine activities (warm-ups) – 5 min • Whole Class Teaching – 15 min • Paired or small group work – 30-40 min Questioning, clarification and discussion Communication of new ideas Examination of errors and misconceptions • Independent work – 10 min • Summary and plans for the future – 5 min

26. Routine Activities – 5 minutes • Counting • Skip counting • Number rhymes or songs • Hundreds board • Number facts • Flash cards • Algorithms • Mental maths • Guess my number games

27. Whole Class Teaching – 15 min • Guided instruction • Introduce or revisit a new concept • Guided instruction includes teacher prompts and support for the students to reinforce, modify or extend their skills and understandings

28. Shared instruction –Paired or small group work – 30 – 40 min • Extension of the same concept • Teacher chooses a problem that offers a range of entry points for students at different levels • The problem is posed without giving the students the steps for solution • Students work in pairs or small groups to solve the problem – sense-making, connections, careful questioning

29. Paired or small group work (cont’d) • Students communicate their mathematical thinking to one another, explain their ideas, listen to their peers and talk with the teacher • Students learn to persevere • Teacher remains focussed on the key topic • Students and teacher examine errors and misconceptions (learning opportunities) • Students share their solutions and understandings

30. Independent work – 10 min • Students formally record their learnings • Students may independently solve a similar problem

31. Summary and planning – 5 min • Teacher and students summarise the key learnings of the lesson • Teacher anticipates the next lesson and/or new connections for the future

32. Using Maths Pads for Student Communication • Need to cater for thinking space (potentially messy) and a good copy space • If 1 pad – left side could be for thinking, right side page could be good copy, or use back and front of pad • If 2 pads – one is their thinking book, one is for good copies and outside audiences

33. Jigsaw Clues Each group member has 1 or 2 clue cards Members must not give their cards to others Share your clues Use available materials Record your working and solution/s Are there more possible solutions? Middle-Upper Problem-Solving Meg’s Number Alexander’s Number

34. Assessment - purposes • Determine the students’ prior knowledge • Know what students have learned on a given topic • Make decisions about future lessons • Identify individual difficulties • Obtain information for communication with student, parents and administration

35. Assessment methods • Informative and non-intrusive • Students are able to show what they know and can do • Mostly informal – observation of oral and written work and discussion with the students • Some short formal written tests, a portfolio of work, mathematical projects, short interviews

36. Fraction Walk • Place your cards as accurately as possible on the number line • Discuss which fractions/decimals that might trick up students (or yourself!)

37. Questions, Challenges, Issues….