SCHOOL IMPROVEMENT DIVISION

OFFICE FOR GOVERNMENT SCHOOL EDUCATION © Copyright

BASTOW INSTITUTE OF EDUCATIONAL LEADERSHIP

Leading Numeracy Topic 1: Reviewing current numeracy

achievement and teaching practice

Workshop 1A

2

+ Introduction

+ Overview of details and expectations of Module 1

+ Framing objectives

+ Numeracy

+ Annual Implementation Plans

+ Teaching and learning numeracy/mathematics

+ Gathering information about numeracy/mathematics

teaching and learning

+ Connect & Challenge

Workshop 1

3

Welcome and Introduction

� Introduction of staff

� Overview of course - aims and objectives

� Course expectations:

� Attendance,

� Assessment strategies

� Online community

� Numeracy improvement

� What is involved?

� What does it look like?

Introduction

4

� Cath Pearn – Lead Facilitator

� Jim Spithill – Assistant Facilitator

� Roger Wander - Assistant Facilitator

Introduction of Staff

5

+ Aim:

� The aim of this module is to develop school leaders strategic knowledge and capacity to achieve and sustain high levels of student learning and engagement in numeracy through an evidence-based culture that supports improvement in instructional practice.

+ Objectives: Topics

� Reviewing current numeracy achievement and teaching practice

� Building teacher capacity in teaching numeracy � Building teacher capacity to link assessment with instruction � Enhancing teacher knowledge in numeracy and building

capacity to provide for individual differences in numeracy.

+

Overview of Course

6

+ Attendance at the 8 face-to-face workshops.

+ Participation in workshop activities and discussions.

+ Participation in the online community: Bastow 307.

+ Completion of all Performance of Understandings

� Including:

• Written reports

• Presentations

• Journal

Course Expectations

7

For each Performance of Understanding artefact there will be

a number of different assessment strategies employed.

+ Each participant will have the opportunity to participate in

each of the Assessment and Feedback strategies.

+ This approach gives each participant the opportunity to

experience and participate in a number of different

assessment strategies: assessment of, as and for learning,

and build their confidence in being able to improve their

knowledge of assessment strategies and improve their

leadership of numeracy teaching and learning.

Assessment and Feedback

8

+ Each participant will be required to submit one

Performance of Understanding artefact for formal assessment.

+ The Performance of Understanding artefact will be formally

reviewed against specifically set criteria by the Lead Topic

Facilitator.

+ Criteria will be specifically set and the participant will

receive a full written assessment of the Performance of

Understanding artefact.

+ Participants will be allocated a particular topic and given the

date by which the assessment must be received by the Lead

Topic facilitator.

Formal Assessment

9

+ Each participant will be required to present a Performance

of Understanding artefact to about half the group.

+ Each participant will receive feedback about the

effectiveness of their presentation from the facilitators, peers

and you will need to complete a self evaluation.

+ Facilitator, peer and self evaluation will be carried out within

set guidelines and protocols.

+ Criteria will be specifically set in the form of a rubric.

Informal Assessment (Presentations)

10

+ Each participant will contribute to the online discussions.

+ The online discussions will be monitored by one of the

Facilitators.

+ Participants will be asked to make comment on their own

reflections and respond to the questions and comments of

others.

+ Participants will be asked to contribute resources and

materials and share their learning.

+ Online communications and discussions will be carried out

within set guidelines and protocols.

Online Reflections

11

+ Each participant will document their Performances of

Understanding, ideas, and self reflections in a Journal.

+ The Journal will assist participants develop the confidence

to seek new ways of improving their leadership of numeracy

and a means by which they can build a base for discussions

and action/s required with their Workplace Mentors.

+ Facilitators, as well as the Workplace Mentors, will review

these Journals at intervals throughout the Module.

+ The Workplace Mentor will specifically use the Journal as a

starting point for discussions about the way forward in leading

numeracy in the specific school context.

Journal Entries

12

13

Handout 1.1

+ Why are you attending the course?

+ What do you expect to achieve by attending this course?

+ What is your goal?

+ How will you know you have achieved your goal?

+ What does the Principal expect you to gain from this

course?

+ How will the Principal and your colleagues know whether

you have achieved your goal?

Participant Goals

14

Numeracy

15

• To be numerate is to use mathematics effectively to meet

the general demands of life at home, in paid work, and

for participation in community and civic life.

• See: AAMT, 1998, p.2, http://www.aamt.edu.au/Publications-and-

statements/Position-statements.

Numeracy

16

In school education, numeracy involves the disposition to

use, in context, a combination of:

• underpinning mathematical concepts and skills from

across the discipline (numerical, spatial, graphical,

statistical and algebraic)

• mathematical thinking and strategies

• general thinking skills &

• grounded appreciation of context

(AAMT, 1998, p.2).

Numeracy

17

http://www.australiancurriculum.edu.au/GeneralCapabilities/Numeracy/Introduction/Introduction

Students become numerate as they:

• develop the knowledge and skills to use mathematics

confidently across all learning areas at school and in their

lives more broadly.

• recognise and understanding the role of mathematics in the

world &

• have the dispositions and capacities to use mathematical

knowledge and skills purposefully.

A highly numerate population is critical in ensuring the nation’s

ongoing prosperity, productivity and workforce participation

(MCEETYA, 2008)

Australian Curriculum: Numeracy

18

The Numeracy learning continuum is organised into six

interrelated elements:

Numeracy: Organising elements

http://www.australiancurr

iculum.edu.au/GeneralC

apabilities/Numeracy/Or

ganising-

elements/Organising-

elements

19

Using spatial reasoning

20

• Students use numeracy skills when interpreting, analysing and creating texts involving quantitative and spatial information such as percentages and statistics, numbers, measurements and directions.

• Visual texts may present a range of numeracy demands.

• Interpreting and creating graphic organisers requires students to examine relationships between various components & characteristics that can be measured or counted.

Numeracy in English

21

• The Mathematics curriculum needs to provide the opportunity to apply mathematical understanding and skills in context, both in other learning areas and in real world contexts.

• A particularly important context for the application of Number and Algebra is financial mathematics.

• In Measurement and Geometry, there is an opportunity to apply understanding to design.

• Through Statistics and Probability students can interpret data and make informed judgments about events involving chance.

Numeracy in Mathematics

22

• Many elements of numeracy are evident in the Science Curriculum e.g. practical measurement and the collection, representation and interpretation of data from investigations.

• Students are introduced to measurement, initially informal units then formal units.

• Students collect qualitative and quantitative data, analyse and represent it in graphical forms.

• Numeracy demands include the statistical analysis of data (including accuracy) and linear mathematical relationships to calculate and predict values.

Numeracy in Science

23

• Students develop numeracy skills as they organise and

interpret historical events and developments.

•

• Students learn to analyse numerical data to make

meaning of the past.

• Students learn to use scaled timelines, including those

involving negative and positive numbers, as well as

calendars and dates to recall information on topics of

historical significance and to illustrate the passing of

time.

Numeracy in History

24

Solve mentally:

29 + 44 =

39 + ? = 56

• How did you work them out?

• How do you know you are right?

• Talk to other participants in your group - did they do it in the same way you did?

Explanations of strategies

25

What strategies is she using?

20 – 10 = 10 16 – 8 = 0

15 – 13 = 2 17 – 16 = 9

13 – 7 = 0 9 – 8 = 0

10 – 5 = 5 15 – 9 = 0

Megan

26

Megan (Year 3): reliance on rules

27

All teachers need to:

• identify the specific numeracy demands of their learning

area

• provide learning experiences and opportunities that

support the application of students’ general

mathematical knowledge and skills

• use the language of numeracy in their teaching as

appropriate

• be aware of the correct use of mathematical language in

their own learning areas.

• understand mathematical terminology and the specific

uses of language in mathematics that is essential for

numeracy.

28

The Australian Curriculum: Mathematics aims to ensure that students:

are confident, creative users and communicators of mathematics, able to investigate, represent and interpret situations in their personal and work lives and as active citizens

develop an increasingly sophisticated understanding of mathematical concepts and fluency with processes, and are able to pose and solve problems and reason in Number and Algebra, Measurement and Geometry, and Statistics and Probability

recognise connections between areas of mathematics and other disciplines and appreciate mathematics as an accessible and enjoyable discipline to study.

Australian Curriculum: Mathematics

29

Understanding, Fluency, Problem Solving, and Reasoning.

• describe how content is explored or developed, that is, the thinking and doing of mathematics.

• provide the language to build in the developmental aspects of the learning of mathematics

• describe the actions in which students can engage when learning and using the content.

Mathematics: Proficiency Strands

30

John has to take 20 ml of medicine three times a day.

How long will a 300ml bottle last?

• How would you solve this problem?

• How did each of the students solve the problem?

From N3.25: Choosing multiplication and division http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/continuum/Pages/multidiv325.aspx#r1

Choosing multiplication and division

31

Amy

From N3.25: Choosing multiplication and division

http://www.education.vic.gov.au/school/teachers/teachingreso

urces/discipline/maths/continuum/Pages/multidiv325.aspx#r1

32

Ellen

From N3.25: Choosing multiplication and division

http://www.education.vic.gov.au/school/teachers/teachingresources/disc

ipline/maths/continuum/Pages/multidiv325.aspx#r1

33

Daniel

From N3.25: Choosing

multiplication and division

http://www.education.vic.gov.au/sc

hool/teachers/teachingresources/d

iscipline/maths/continuum/Pages/

multidiv325.aspx#r1

34

Elisha

From N3.25: Choosing multiplication

and division

http://www.education.vic.gov.au/stude

ntlearning/teachingresources/maths/m

athscontinuum/number/N32507P.htm

35

Ben

From N3.25: Choosing

multiplication and division

http://www.education.vic.gov.au/

school/teachers/teachingresourc

es/discipline/maths/continuum/P

ages/multidiv325.aspx#r1

36

Bob

From N3.25: Choosing

multiplication and division

http://www.education.vic.g

ov.au/school/teachers/tea

chingresources/discipline/

maths/continuum/Pages/

multidiv325.aspx#r1

37

Con

http://www.educ

ation.vic.gov.au/

school/teachers

/teachingresour

ces/discipline/m

aths/continuum/

Pages/multidiv3

25.aspx#r1

38

• start from what student knows

• provide range of appropriate materials

• students should draw or represent materials

• expect students to explain strategies

• ask questions:

– “How did you do that?”

– How do you know you are right?

• use alternative solution strategies

• patient, praise, encourage risk taking, appreciate

differences

Improving numeracy outcomes

39

Standard 2: Know the content and how to teach it

2.5 Literacy and Numeracy Strategies

• Graduate: Know and understand literacy and

numeracy teaching strategies and their application in

teaching areas

• Proficient: Apply knowledge and understanding of

effective teaching strategies to support students’

literacy and numeracy achievement

National Professional Standards for Teaching

http://www.teacherstandards.aitsl.edu.au/Static/docs/aitsl_

national_professional_standards_for_teachers_240611.pdf

40

2.5 Literacy and numeracy Strategies

• Highly Accomplished: Support colleagues to implement effective teaching strategies to improve students’ literacy and numeracy achievement

• Lead: Monitor and evaluate the implementation of teaching strategies within the school to improve students’ achievement in literacy and numeracy using research based knowledge and student data

Standard 2: Know the content and how to teach it

http://www.teacherstandards.aitsl.edu.au/Static/docs/aitsl_n

ational_professional_standards_for_teachers_240611.pdf

41

Research shows that teachers’ skills, knowledge,

beliefs and understandings are key factors in

improving achievement of all students.

42

http://www.pz.harvard.edu/vt/visibleThinking_html_files/03_ThinkingRoutines/03d_

UnderstandingRoutines/Headlines/Headlines_Routine.html Handout 1.3

+ This routine draws on idea of newspaper-type headlines as

a vehicle for summing up and capturing the essence of an

event, idea, concept, topic, etc. The routine asks a core

question: � If you were to write a headline for this topic or issue right now

that captured the most important aspect that should be

remembered, what would that headline be?

+ A second question involves probing how students’ ideas of

what is most important have changed over time: � How has your headline changed based on today’s discussion?

How does it differ from what you would have said yesterday?

Headlines Routine

43

Handout 1.3

Task:

+ In small groups participants create a newspaper headline

that reflects their feelings and thoughts about their situation at

the moment e.g. Leadership languishes in learning

environment.

+ One participant from each group to present each group’s

headline and explains the feelings behind it.

Headlines Routine

44

+ describe how the key improvement strategies in the school

strategic plan and other significant projects will be put into

operation in each of the four years of the strategic plan.

The annual implementation plan outlines: � the one-year targets to identify progress towards the targets for

improved student outcomes identified in the school strategic

plan

� the actions that will be undertaken in order to implement the

key improvement strategies and significant projects

� how the actions are to be resourced, who is to be involved and

the associated timelines

� the achievement milestones that will be used to assess the

desired changes in practice or behaviour that should occur

through the implementation of strategies.

Annual Implementation Plans

45

Effective annual implementation plans comprise of two parts: 1. Strategic intent, including the goals, targets and key

improvement strategies from the school strategic plan, as well

as one-year targets.

2. Implementation details, including a breakdown of the key

improvement strategies and significant projects.

See Annual Implementation Planning Guidelines 2013 (Figure

2, p.4). � The shaded areas indicate those sections of the annual

implementation plan that a school completes each year;

� the non-shaded sections can be drawn from the school

strategic plan.

Developing the Annual Implementation Plan

46

Participants compare and discuss the strengths of the Strategic

Intent and Implementation sections of their Plans (Handout 1.4).

Consider: � Is numeracy included in this Plan? How?

� What are the strengths of the Plan particularly in terms of

numeracy?

� Does the Plan address current practice in teaching numeracy?

� What appears to be missing from your specific school Plan?

� What would you like to see included in your specific school Plan?

� What evidence do you need?

� What evidence do you have?

� How could you find out?

Annual Implementation Plans

47

What do you know about the teaching and learning of numeracy

in your school? (Handout 1.5)

� What do you know about the numeracy/mathematics knowledge of your students? What evidence do you have? That is, what assessment data do you already have about the students?

� Have you identified any particular school weaknesses and/or strengths in numeracy/mathematics?

� Have you decided on any clear or challenging targets your school needs to achieve in numeracy/mathematics?

Teaching and Learning Numeracy /Mathematics

48

What do you know about the way numeracy/mathematics is

taught in your school? (Handout 1.6)

� How do you know? What evidence do you have?

� Have you observed the way numeracy/mathematics is

taught in some or all your classes?

� How could you find out?

� Why might it be difficult to determine the way

numeracy/mathematics is taught?

� Is numeracy/mathematics taught in exactly the same way

for all topics? What changes? Why?

Teaching and learning Numeracy/Mathematics

49

+ Guided classroom observations are used to

address and solve a ‘problem of practice’ such as:

“Do we have a common approach to teaching …?”

+ Educators need to develop a shared practice of

observing, discussing, and analysing learning and

teaching.

Gathering information

50

http://www.danielsongroup.org/article.aspx?page=frameworkfo

rteaching

+ Charlotte Danielson’s framework for teaching identifies

aspects of a teacher’s responsibilities that have been

demonstrated as promoting improved student learning.

Danielson divides the complex activity of teaching into four

domains of teaching responsibility:

+ planning and preparation

+ the classroom environment

+ instruction, and

+ professional responsibilities.

Framework for Teaching

51

+ Demonstrating knowledge of content and pedagogy

+ Demonstrating knowledge of students

+ Setting instructional outcomes

+ Demonstrating knowledge of resources

+ Designing coherent instruction

+ Designing student assessments

Domain 1: Planning and Preparation

http://www.danielsongroup.org/article.

aspx?page=frameworkforteaching

52

+ Creating an environment of respect and rapport

+ Establishing a culture for learning

+ Managing classroom procedures

+ Managing student behaviour

+ Organizing physical space

Domain 2: Classroom Environment

http://www.danielsongroup.org/article.as

px?page=frameworkforteaching

53

+ Communicating with students

+ Using questioning and discussion techniques

+ Engaging students in learning

+ Using assessment in instruction

+ Demonstrating flexibility and responsiveness

Domain 3: Instruction

http://www.danielsongroup.org/article.asp

x?page=frameworkforteaching

54

+ Reflecting on teaching

+ Maintaining accurate records

+ Communicating with families

+ Participating in a professional community

+ Growing and developing professionally

+ Showing professionalism

Domain 4: Professional Responsibilities

http://www.danielsongroup.org/articl

e.aspx?page=frameworkforteaching

55

+ The Framework can be used as to start professional

conversations as teachers seek to enhance their skill in the

complex task of teaching.

+ The Framework may be used as the foundation of a school

or district's mentoring, coaching, professional development,

and teacher evaluation processes, thus linking all those

activities together and helping teachers become more

thoughtful practitioners.

+ See also Assessing teacher effectiveness (Charlotte

Danielson) http://www.youtube.com/watch?v=86WKG_M0fgQ

The Teaching Framework

56

+ Connect and Challenge

Evaluation: Learning Wall

CONNECT