The document discusses the importance of developing mathematical resilience in students. Mathematical resilience refers to a student's ability to adapt and persist when facing new or difficult mathematical concepts. The key aspects of mathematical resilience include students taking responsibility for their own learning, having confidence to try new strategies, and viewing challenges as opportunities to grow. Successful students demonstrate resilience through a growth mindset, self-reflection, adapting their approaches, collaborating with peers, and finding purpose and meaning in their learning. The classroom aims to cultivate resilience by emphasizing open-ended problem solving, strategy use, process over answers, and celebrating student discoveries and achievements.
Creating Mathematical Opportunities in the Early Years
Presenter, Dr Tracey Muir, for Connect with Maths Early Years Learning in Mathematics community
As teachers, we are constantly looking for ways in which we can provide students with mathematical opportunities to engage in purposeful and authentic learning experiences. On a daily basis we need to select teaching content and approaches that will stimulate our children through creating contexts that are meaningful and appropriate. This requires a level of knowledge that extends beyond content, to pedagogy and learning styles. As early childhood educators, we can also benefit from an understanding of how the foundational ideas in mathematics form the basis for key mathematical concepts that are developed throughout a child’s school.
In this webinar, Tracey will be discussing the incorporation of mathematical opportunities into our early childhood practices and considering the influence of different forms of teacher knowledge on enacting these opportunities.
Teaching Mathematics to English Language Learners admills
This session will present strategies to help teachers teach mathematics to English language learners including hands-on differentiation activities for teachers to do in the session.
This Connect with Maths Early Years Learning in Mathematics community webinar discusses the importance of talk as part of a quality mathematical learning environment for young children. Denise makes links to the Early Years Learning Framework and the Australian Curriculum and share some ideas for facilitating mathematical talk with young children.
Creating Mathematical Opportunities in the Early Years
Presenter, Dr Tracey Muir, for Connect with Maths Early Years Learning in Mathematics community
As teachers, we are constantly looking for ways in which we can provide students with mathematical opportunities to engage in purposeful and authentic learning experiences. On a daily basis we need to select teaching content and approaches that will stimulate our children through creating contexts that are meaningful and appropriate. This requires a level of knowledge that extends beyond content, to pedagogy and learning styles. As early childhood educators, we can also benefit from an understanding of how the foundational ideas in mathematics form the basis for key mathematical concepts that are developed throughout a child’s school.
In this webinar, Tracey will be discussing the incorporation of mathematical opportunities into our early childhood practices and considering the influence of different forms of teacher knowledge on enacting these opportunities.
Teaching Mathematics to English Language Learners admills
This session will present strategies to help teachers teach mathematics to English language learners including hands-on differentiation activities for teachers to do in the session.
This Connect with Maths Early Years Learning in Mathematics community webinar discusses the importance of talk as part of a quality mathematical learning environment for young children. Denise makes links to the Early Years Learning Framework and the Australian Curriculum and share some ideas for facilitating mathematical talk with young children.
Connect with Maths Early Years Learning in Mathematics Webinar series - Mathematical Thinking in the Early Years ( Part 2) Supporting children as mindful mathematicians presented by Louise Hodgson.
This presentation is focused on key mathematical processes - problem solving, reasoning and proof, communication and connections and habits of mind such as curiosity, imagination and persistence which together are as important as mathematical content in a high quality early childhood mathematics program. Practical strategies will be discussed to support young children to develop reasoning which is central to learning about mathematics.
Connect with Maths~ Teaching maths through problem solvingRenee Hoareau
Connect with Maths Early Years Learning in Mathematics community
Teaching Maths Through Problem Solving: Facilitating Student Reasoning
Presenter: Louise Hodgson
This session will focus on teacher actions, which promote problem solving and reasoning in early years classrooms. We will workshop some tasks and have opportunities for discussion.
Connect with Maths ~ supporting the teaching of maths ONLINE
Join a Connect with Maths community today http://www.aamt.edu.au/Communities
AAMT website: http://www.aamt.edu.au
Effective Walkthroughs in Math and ELA Classroomscatapultlearn
Participants will be introduced to a model for conducting effective and focused walkthroughs that are grounded in research-based teaching strategies, the necessary look-fors in rigorous ELA and Math classrooms, and how to engage teachers in reflective conversations on teaching and learning.
In this webinar you will learn:
how to conduct effective walkthroughs in your schools
how to identify the necessary look-fors in Math and ELA classrooms
how to engage in reflective and robust conversations with teachers
From novice to expert: A critical evaluation of direct instructionChristian Bokhove
Direct instruction is a hot topic in school, but discussions about it often end up with people talking past each other, as the term can mean several things. In this talk I will look at different ways of conceptualising 'direct instruction', for example as scripted Direct Instruction (in capitals) from the seminal Project Follow Through, lecturing and more interactive teaching like Rosenshine's 'explicit instruction' and 'active learning'. I will also highlight strengths and limitations of their respective evidence bases. I will frame these more generally as a 'guidance dilemma': what amount of guidance do we use in teaching and learning in learners' journey from novice towards more expert. I will finish with some concrete recommendations.
To those who would like to have a copy of this slide, just email me at martzmonette@yahoo.com and please tell me why would you want this presentation. Thank you very much and GOD BLESS YOU
Connect with Maths Early Years Learning in Mathematics Webinar series - Mathematical Thinking in the Early Years ( Part 2) Supporting children as mindful mathematicians presented by Louise Hodgson.
This presentation is focused on key mathematical processes - problem solving, reasoning and proof, communication and connections and habits of mind such as curiosity, imagination and persistence which together are as important as mathematical content in a high quality early childhood mathematics program. Practical strategies will be discussed to support young children to develop reasoning which is central to learning about mathematics.
Connect with Maths~ Teaching maths through problem solvingRenee Hoareau
Connect with Maths Early Years Learning in Mathematics community
Teaching Maths Through Problem Solving: Facilitating Student Reasoning
Presenter: Louise Hodgson
This session will focus on teacher actions, which promote problem solving and reasoning in early years classrooms. We will workshop some tasks and have opportunities for discussion.
Connect with Maths ~ supporting the teaching of maths ONLINE
Join a Connect with Maths community today http://www.aamt.edu.au/Communities
AAMT website: http://www.aamt.edu.au
Effective Walkthroughs in Math and ELA Classroomscatapultlearn
Participants will be introduced to a model for conducting effective and focused walkthroughs that are grounded in research-based teaching strategies, the necessary look-fors in rigorous ELA and Math classrooms, and how to engage teachers in reflective conversations on teaching and learning.
In this webinar you will learn:
how to conduct effective walkthroughs in your schools
how to identify the necessary look-fors in Math and ELA classrooms
how to engage in reflective and robust conversations with teachers
From novice to expert: A critical evaluation of direct instructionChristian Bokhove
Direct instruction is a hot topic in school, but discussions about it often end up with people talking past each other, as the term can mean several things. In this talk I will look at different ways of conceptualising 'direct instruction', for example as scripted Direct Instruction (in capitals) from the seminal Project Follow Through, lecturing and more interactive teaching like Rosenshine's 'explicit instruction' and 'active learning'. I will also highlight strengths and limitations of their respective evidence bases. I will frame these more generally as a 'guidance dilemma': what amount of guidance do we use in teaching and learning in learners' journey from novice towards more expert. I will finish with some concrete recommendations.
To those who would like to have a copy of this slide, just email me at martzmonette@yahoo.com and please tell me why would you want this presentation. Thank you very much and GOD BLESS YOU
Children are not things to be modeled but people to be unfolded (Jess Lair). Discuss the process of children learning and tips and strategies for teachers to facilitate children learning.
Ritchhart (2007) Education Quarterly Australia 1 The.docxWilheminaRossi174
Ritchhart (2007) Education Quarterly Australia
1
The Seven Rʼs of a Quality Curriculum
Ron Ritchhart
Project Zero, Harvard Graduate School of Education
To teach for understanding, teachers must be able to identify the big
ideas of their subject and know what it is they truly want students to
understand. They also must engage students in understanding
performances, that is, opportunities for actively building personal
understanding, and provide meaningful feedback on learning as it
unfolds. It is at this intersection of big ideas, understanding goals,
performances, and assessment feedback that curriculum lives, in what I
call the enacted curriculum.
Over the past fifteen years I have worked with teachers exploring the
enacted curriculum of understanding. During that time I’ve had the
opportunity to reflect on the qualities that make an activity, a unit, a
curriculum something that effectively engages students in developing a
deeper understanding. Seven common criteria emerge: rigorous,
rewarding, real, requires independence, rich in thinking, revealing, and
reflective. I present these here as guidelines for the planning, enacting,
and evaluating of a curriculum focused on understanding.
Ritchhart (2007) Education Quarterly Australia
2
Rigorous
What does it mean for a curriculum itself to be rigorous? For a task or a
lesson? Rather than think of difficulty, I think in terms of affordances. A
rigorous curriculum embodies and affords students opportunities to
develop a deeper understanding and not just show what they already
know. Too often curricula state carefully defined objectives that put an
unintentional cap on students’ understanding and obscure the big ideas of
the discipline, leading to superficial coverage. A rigorous curriculum
must point the direction for learning but be open enough to extend
students’ understanding beyond a minimal outcome.
When I look at an activity a class is to do, I ask myself, “How can
students further their learning of big disciplinary ideas through this task?
How does this task launch the learning but avoid truncating it?” I also
ask myself if students can do a particular task without understanding, by
merely walking through the steps or repeating back information. If so,
that performance doesn’t offer the rigor of understanding.
Real
Disciplinary learning can be thought of as a process by which individuals
gradually increase their participation in communities of practice. As
such, a curriculum that builds understanding must look to engage
students in authentic disciplinary activities so that students’ classroom
activities mirror the real work of adults in the field. Rather than learning
about math, science, writing, history, and so on, students must become
mathematicians, scientists, authors, and historians to build true
disciplinary understanding. When a topic is assigned to a curriculum, we
need to ask: When, where, and ho.
In this section, we will provide some basic formats for putting plans into action. The first challenge is to match your teaching methods to your objectives.
Sydney Opera House is a state, national and World Heritage-listed item described by UNESCO as ‘a masterpiece of human creative genius’. What is lesser known is that in designing the Opera House, Jorn Utzon was inspired by nature. Building on this legacy, the Opera House has an Environmental Sustainability Plan that aims improve resource efficiency, protect the environment and engage and inspire others about sustainability.
The purpose of the session is to give real life case studies of mathematics applied to sustainability and the design of the Opera House that teachers could use to help inspire the next generation of young people to learn mathematics and science.
Presented by Naomi Martin, Manager, Environmental Sustainability Sydney Opera House.
Pulsars in the Classroom: Presenter Stephen Broderick
"Let's do real world mathematics" The "Pulsar" project is designed to engage students in scientific projects that will give them a positive attitude towards science and mathematics, and appreciation of how maths is applied in the real world.
PULSE@Parkes allows students to directly control Parkes radio telescope over the Internet and use it to do real science. It is the only program of its kind in the world.
Make it Count: Maths and Indigenous Learners presented by Caty Morris
Make It Count is for educators working with Aboriginal and Torres Strait Islander learners in mathematics education. It is a teaching and learning resource, and a professional learning tool. Make It Count is about a way of thinking – and a way of doing. http://mic.aamt.edu.au
Connect with Maths supporting the teaching of mathematics online
Connect with Maths, Make it count with Indigenous Learners community event, YuMi Deadly Maths ~ what it is and how it works. Presenters: Dr Grace Sarra and Robyn Anderson
The webinar will be discussing YuMi Deadly Maths – what it is and how it works. Within these program we aim to:
•facilitate whole school change that builds pride and positive identity, emphasises high expectations, and strengthens relationships with community
•enhance student learning at all levels: early childhood, middle school, senior school and post-compulsory
•support school and TAFE staff to teach effectively
•develop decolonising research methodologies to empower the researched
The YuMi Deadly Centre's vision is Growing community through education. Through research and tailored programs, the YuMi Deadly Centre strives to enhance the learning of Indigenous and non-Indigenous children, young people and adults to improve their opportunities for further education, training and employment, and to equip them for lifelong learning.
Yumi Deadly Centre website: ydc@qut.edu.au
Using Real Life Contexts in Mathematics Teaching is a conference presentation by Peter Galbraith for the Queensland Association of Mathematics Teachers in June 2013. It has now been generously shared with the Connect with Maths ~ Maths in Action~Applications and Modelling community as a resource.
Presentation for Parents as Educators ~ Mathematics in the Home is presented by Jennifer Bowden (Maths Education Consultant) Megan Gibbs (K4 year Kinder Teacher) and Bree Collins (Prep/Foundation Classroom Teacher) discuss and share ideas about the way parents can become more effective “educators” as they engage in mathematics through play, conversation and creativity.
This presentation, YuMi Deadly Maths, by Dr Grace Sarra and Robyn Anderson for the Connect with Maths Make it count with Indigenous Learners community is part of a webinar series.
AAMT~ supporting and promoting the teaching of mathematics
Connect with Maths Early Years Learning in Mathematics: Pattern, Number and Geometry presentation helps students to build knowledge and make connections between number and pattern in the early years
Connect with Maths Webinar presented by Professor Peter Sullivan: Six Principles of Effective Mathematics Teaching
There are many recommendations on how to teach mathematics but fewer about the teaching of mathematics’ classes with Indigenous students. This webinar will examine how six principles for effective mathematics teaching were adapted to advice for teachers of schools with high numbers of Indigenous students.
Connect with Maths: Early Learning in Mathematics webinar March 2014
Nicola Yelland, Research Professor at Victoria University in Melbourne, looks at the ways in which young children use new technologies. Nicola explains how we can help young children make sense of their experiences in multimodal formats.
Presentation used for professional learning workshop for Education Assistants and Aboriginal and Islander Education Officer run by Tracey Armstrong and Sharon Lee from the Make It Count Swan Cluster.
Presentation used for professional learning workshop for Education Assistants and Aboriginal and Islander Education Officer run by Tracey Armstrong and Sharon Lee from the Make It Count Swan Cluster.
2. Why focus on Mathematical
Resilience?
Working on the assumption that...
mathematical resilience will improve mathematical
achievement.
• Students taking a greater responsibility for their own learning – students
are discovering mathematical concepts rather than just accepting information
that is passed on
• Resilience can be taught and learnt
• Resilience positively impacts learners, empowering them and creating
success for all students
• It can become a common classroom and school language about learning
• Maintains high expectations of all Aboriginal students to achieve
• Valuing mathematics and its connection to the world
• Learnt skills are transferrable to others areas of learning and also life for
future learning
3. Defining mathematical resilience
Resilience in general...
“Resilience refers to the ability to successfully manage your life and
adapt to change and stressful events in healthy and constructive ways”
(Dent, M).
“An individual’s ability to thrive and fulfil potential despite or perhaps
because of stressors or risk factors” (Neill, J).
How does this connect with mathematical learning and success?
“When mathematically resilient pupils are required to use mathematics
in a new situation they will expect to find it hard at first but will have
strategies or approaches to overcome the initial “can’t do it” response”
(Johnston-Wilder S & Lee C).
4.
5. Resilience Indicators
How can we identify resilience in students?
• Confidence in their own ability to try something new
• Sharing their knowledge willingly with others
• A range of useful strategies to apply in different situations
• Challenging themselves
• Solving different problems
• Formulating their own questions – identify what they don’t already know and
possible ways to explore this
• Identifying what comes next in their learning
• Reflecting on their learning and describe the processes that have taken – using
metalanguage and mathematical vocabulary
• Maintaining their attention and focus for longer periods of time in order to gain
a better understanding
• Noticing themselves achieving new understandings through “A-ha” or “Wow!”
moments and they are interested in sharing these with others
• Knowing their own strengths and weaknesses
• Persisting in their learning instead of giving up and declaring “I don’t know how
to”
6. Five Main Indicators for Resilience
Growth mindset – after building a complex robot first that wouldn’t stay together, Hope
decided to rethink her construction and designed a simpler model.
7. Meta-cognition – during reflections of the maths learning a student wrote on a post-it note
that they could figure out where to place numbers on a number line between 0 and 1 but couldn’t
go past one. They identified that they would have to explore this tomorrow, highlighting different
ways that they could do this.
Student responses during reflection to describe what they did or didn’t
understand and how they worked.
8. Adaptability – understanding that mathematics is interrelated and that knowledge in one area
is useful and required in another.
When sorting Hope first arranged her bears in
colour groups only. She reflected on this and
rearranged her bears in sub-groups according to
size as well as colour. This broke the bears into
smaller groups, which made is possible to estimate
at a glance the group that had more.
When sorting ,Cayleb first arranged his blocks in
random order and found it difficult to tell which was
the largest amount. He reflected on this and
rearranged his blocks in ascending order and found
it easier to determine the size of the groupings. We
often use the terminology “have I seen something
like this before? What worked and what didn’t
work?”
9. Interpersonal – Developing and valuing working relationships with their peers. When
problem solving students are encouraged to seek the help of their peers and work alongside
different people in group situations rather than independently. Majority of students thrive in these
groupings due to their conversations about learning and working problems out together.
“Uh oh” moment. Alexander realised
that Fadia wasn’t counting one to
one. He suggested that she ‘make a
line’ so that her amount of fences
could match his.
Resilience strategies: Trying another
idea, teaching someone else.
10. Sense of purpose – Before learning about fractions, decimals and percentages
students brainstormed and gathered information about where we use these in our lives and
continued to add to their ideas as they came across examples. Students had to create a plan
of a robot for their partner to construct. Their plans had to be informative and descriptive
enough for their friend to understand.
Fractions, decimals and
percents brainstorm
Picture of a house
11. How the classroom supports this
• Discovering new information for themselves that are connected to reality
• Problem solving situations
• Primary Years: Students are allowed the opportunity to decide which
processes they will take, what materials they will use, where they will work
and with who, how they will record and explain their discoveries.
• Junior Primary Years: Open ended process where students have a choice of
materials but the possible strategies are modelled and students are guided
through their problem solving. The language is explicitly used and taught
throughout the thinking process.
• Results are not the key focus, rather than the process taken. Reflections are
focused on not necessarily their ‘answers’ but the strategies they used,
obstacles they faced and overcame and what they could try next time.
• Mathematical discoveries are celebrated daily and students are experiencing
fun while learning. They are given the opportunity to be mathematical,
without worrying whether or not their answers are correct.
• Strategies are explicitly spoken about and other people’s ways of working out
are considered and shared and at times even copied.
12. Language for Resilience
Resilient strategies used when problem solving
Keep trying
Ask a question
Work with a friend
Try all ideas
Make a model
Use concrete materials
Break it into smaller parts
Draw a picture or a graph
Have I seen something like this before?
Guess and check answer
Make a list
WOW! or Ah-Ha! moment
13.
14.
15. Feeling pride in their discoveries and
learning...celebrating their
achievements
Hope experienced frustration when her first model wouldn’t stay together because of the more difficult design. She pulled all the pieces apart and decided to start over, making a simpler design that required less blocks and joins. Even though she was upset and frustrated she persisted and tried a new strategy. Students are able to... *WILL BE INCLUDING STUDENT WORK SAMPLES/PHOTOS/VIDEOS UNDER EACH OF THESE HEADINGS. HEADINGS WILL BE SEPARATED ONTO A PAGE EACH. Resilience strategies: Tried another idea (robot fell apart), Broke task into smaller parts (made it in two halves), Keep checking (measuring and counting continuously)
Student examples at the bottom pictures/videos/responses.
Having a sense of purpose means that students are explicit and clear about the reason as to why they are learning the concepts and participating in structured activities. They are aware that there is an outcome that is meaningful to them. So for example, when they needed to construct a house out of blocks, they first needed to plan and build their structure and take a photo of it in order to give it to a buddy to recreate. When beginning to explore fractions, decimals and percents, students brainstormed ideas about where they ‘see’ this type of maths in their everyday lives to begin to think about practical applications of the concepts.
Discovering new information for themselves that are connected to reality Explorations involve complex problem solving situations that are connected to the abstract mathematical concepts. Primary Years: Students are allowed the opportunity to decide which processes they will take, what materials they will use, where they will work and with who, how they will record and explain their discoveries. Junior Primary Years: Open ended process where students have a choice of materials but the possible strategies are modelled and students are guided through their problem solving. The language is explicitly used and taught throughout the thinking process. Results are not the key focus, rather than the process taken. Reflections are focused on not necessarily their ‘answers’ but the strategies they used, obstacles they faced and overcame and what they could try next time. Mathematical discoveries are celebrated daily and students are experiencing fun while learning. They are given the opportunity to be mathematical, without worrying whether or not their answers are correct. Strategies are explicitly spoken about and other people’s ways of working out are considered and shared and at times even copied.
This list of strategies was originally developed and presented to the students and reflected on which strategies they used the most and developed and modified new strategies that they were using that weren’t originally planned for. The language is clearly displayed on a resilience wall in the classroom for students to use and manipulate. Put each one in a separate box and then use two separate working out examples and talk about which ones each student used. One JP and one MP example explaining what they used.
Put student video of problem solving and get people to identify which strategies they can see them using. Whether or not they are showing resilience.