Planning for SuccessMathematics and Numeracy

Programs

Mathematics & Numeracy

•What’s the difference?•Which do we teach?

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

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.

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)

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)

Learning Tool

Using mathematics effectively

Why teach Mathematics & Numeracy?

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

Planning

Key Documents of Planning for Success•Yearly & Term Overview – content and

procedures•Weekly Program•Key Lesson Plans

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

Big Ideas in Number

•Quantity•Operational Sense•Relationships•Representation•Proportional Reasoning

(Ontario Education)

Coaching for Student Success in Mathematics

•Focusing on Students

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

Early Quantity using Manipulatives•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?

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

Independent

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

Key resources

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

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

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

Middle Algebra 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?

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

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

Routine Activities – 5 minutes

•Counting•Skip counting•Number rhymes or songs•Hundreds board•Number facts•Flash cards•Algorithms•Mental maths•Guess my number games

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

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

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

Independent work – 10 min

•Students formally record their learnings•Students may independently solve a

similar problem

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

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

Middle-Upper Problem-Solving

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?

Meg’s Number

Alexander’s Number

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

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

Fraction Walk

•Place your cards as accurately as possible on the number line

•Discuss which fractions/decimals that might trick up students (or yourself!)

Questions, Challenges, Issues….