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
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