The Principles of Learning Mathematics
Beliefs
Teaching implications
At Fountain Gate Primary School we believe that
As a collective team of teachers we will therefore
children best learn mathematics when:
endeavour to provide a learning environment where:
Engagement/Motivation/Attitudes
The teacher reflects positivity and passion about the
subject taught.
Maths has purpose and meaning.
Maths is engaging and interesting.
Children learn when they interact with each other.
Children want to be challenged – no limitations put
upon them.
When children believe in themselves the potential
for success is heightened.
Language used, body language.
Whole demeanour.
Real-life activities relating to content.
Relating activities to prior knowledge.
Activities that allow students to question and find
meaning and content.
Resources used should vary (PowerPoint, hands-on
materials etc.). Much discussion involved. Games
included.
Exploration and understanding gained using varied
group work situations (e.g. group work, partner
work, mixed-ability groups).
Open-ended questioning and activities.
Taking what students learn/understand and apply to
their own interests and level of expertise.
Teachers provide skills for success by giving
students time to think for themselves–less rescuing;
and in doing so, celebrate their attempts and
successes.
The individual learner
Individual learning styles are considered and catered Lessons are open-ended with multiple entries and
for.
exits.
Tasks are differentiated so that all children
experience success.
Find out all students’ individual learning styles and
ensure tasks cater for individual differences.
The classroom provides a stimulating, positive and
Establish norms and protocols in the classroom.
supportive learning environment to individual
Allow risk taking. Celebrating ‘having a go’.
students.
Use open-ended activities.
All students’ opinions are valued. No put-downs.
Implementing the You Can Do It (YCDI) principles.
Establish routines.
Use ICT to support learning.
Students participate in tasks at their own level of
Teachers use a variety of resources and methods that
ability, needs and interest.
identify individual learning styles: MI, Blooms
taxonomy.
Students are able to work in a variety of grouping
Support students to use their own learning styles,
models.
however expose and encourage students to develop
using other styles.
All tasks/activities need to include differentiation.
Teachers need to ask ‘good’ open questions.
Create tasks based on real-life learning
opportunities.
Carpe Diem – seize and look for the opportunity
(e.g. iPhone photo of milk bar lolly display!)
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Students are able to make connections to prior
learning.
Students articulate or demonstrate their thinking.
They experience success at their developmental
level.
Tasks provide scaffolded learning.
Personal reflections.
Reflection is a regular component of maths sessions.
Students are explicitly taught the skills of reflection.
Sharing learning in a variety of ways (e.g. partner,
buddy grade).
Monitoring student reflections using a variety of
tools (e.g. journal, rubrics, continuums, personal
running records, and self-reflection).
Specific feedback.
Use specific feedback to achieve personal best.
Given continuum of learning to identify where the
student is at.
Experiences, hands-on materials & abstract understanding.
The activities relate to relevant real-life situations.
The task/problem has some connection with what
they already know.
Students understand why they are learning and can
see the application of it.
Abstract understanding is developed by transferring
specific learning experiences into mental images.
Students are given the opportunity to collaborate
and share their experiences so others can see
different ways of solving problems.
Where practicable, activities are set in real-life
contexts which are age and ability appropriate.
Expose students to the experiences underpinning
successful engagement in a task.
Learning intentions and success criteria relate to a
real-life purpose.
Expose students to a range of activities, resources
and discussion to enable them to understand the
abstract concept.
Students have concrete resources to help them
manipulate the task/problem.
Students work in a variety of grouping models.
Students consider and discuss the processes and
strategies throughout the lesson.
Problem Solving
Students are encouraged to use various higher-order
thinking processes.
Students are given the opportunity to verbalise and
demonstrate their thinking and understandings.
Students are able to share their understandings when
necessary, not only during ‘reflection time’.
When they are interested and want to find an
answer.
Students feel supported to investigate the process of
solving a problem.
Maths is seen as part of everyday life, and is
purposeful and meaningful.
Open ended tasks are incorporated.
Provide tasks that encourage students to apply what
they know.
Provide ‘good’ questions.
Teams work to design tasks.
Students feel safe to take risks, confident in their
own ability.
Discussion is encouraged and supported.
It is ok to talk about the task – student directed.
‘Turn & talk’ occurs regularly during lessons.
Students should be involved in creating their own
problems for other students to solve.
Visual references are available.
Acknowledge and celebrate different approaches to
tasks.
Hands-on materials are freely available (‘maths
basket’).
Use real-life anecdotes.
Use maths in other teaching areas.
Use photos and multimedia to support tasks.
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Risk Taking
The teacher models risk taking in their own learning
and teaching.
Teachers to acknowledge when they make mistakes.
Model common misunderstandings (showing
different answers).
Have students identify mistakes or check teacher
answers.
Teacher to model how to rectify and react to making
mistakes.
Students are persistent, despite the level of difficulty Allow students sufficient time for completing tasks.
of the task.
Make explicit the different strategies you can use to
solve problems.
Encourage students to see more than one way to
approach a task and solve a problem.
Teach resilience through social skills programs such
as YCDI.
Modify tasks so that all children can achieve
success.
Build confidence in order to promote persistence.
Students’ efforts (rather than the end results) are
Teacher to be aware of each child’s development
celebrated.
and ability.
Display students’ work.
Teacher to acknowledge even the smallest
successes.
Use positive reinforcement.
Reinforce to the whole class that it is the process of
getting to the answer that more important than the
answer itself.
Use share time to have students discuss the process
they followed or the strategy they used.
Verbalisation of thinking.
Students are supported in a safe learning
Clear and shared understanding of class rules and
environment.
values.
Mutual respect.
Not tolerating any criticism.
Acceptance of each child’s idiosyncrasies.
Allow students to be themselves.
Children helping and supporting each other’s
learning.
Students are prepared to step out of their comfort
Raise the bar for every child.
zone to extend their knowledge and skills.
Have high expectations.
Have students reflecting on their learning.
Build confidence.
Students feel confident to ‘have a go’.
Instil in students that you value their contribution.
Inform parents of the importance of students taking
risks.
Make students aware of the resources available to
them.
Students understand that making a mistake can be a Regularly discuss the fact that mistakes are part of
learning opportunity.
life’s learning.
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Language
Correct mathematical language is used.
There is a consistent use of mathematical language
throughout the school community.
They have a common understanding of
mathematical language.
Establish a glossary of mathematical language
throughout the school.
Modelling of mathematical language by teachers
and students.
Use of class, published and online maths
dictionaries.
Use of charts as a visual representation.
Use of big books for maths, discussion books and
online resources.
Include vocabulary as a component in maths
planners.
Use of learning intentions to make the focus
explicit.
Explicit teaching of this vocabulary.
They have the opportunity to use and apply the
Regular use of share time.
language.
Students are working and talking collaboratively.
Students are expected to explain the strategies they
used.
Worded problems are used including multi-steps.
Students write problems for others to solve.
Tasks are related to real-life experiences.
Use a variety of visual and concrete aids to support
their learning.
Home/Parent
There are authentic connections to the home and
work environment.
The families are actively involved in mathematics at
home.
The parents are aware of the language, techniques
and methods used by the teachers.
Invite parents into the school to explain how they
use maths in everyday situations e.g. gardening,
building, cooking, and shopping.
Homework where parents and students have to work
together for example:
 Shopping - students are given $10 to purchase
ingredients to bake a cake.
 Newsletter – family maths problem whereby an
answer to a maths problem is submitted to the
office for a weekly prize to be drawn.
 Reading – use stories to consolidate
understanding of mathematical language.
 Mathletics – use at home as well as school.
A handout (mathematical dictionary) given to
parents to explain the correct mathematical
terminology.
Level newsletters at the beginning of each term to
include anticipated outcomes for maths.
Taking photographs of the students working
mathematically.
Information night to model classroom strategies and
showcase materials.
Allocated time after school to meet with parents
who have questions or concerns.
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Parents, teachers and students accept that there are
different ways of working mathematically.
Teddy bear/party maths/games nights/open nights.
Have a proforma for prompting how to work out
maths problems.
Show how maths problems were worked out using
the home/school scrapbook.
Curriculum
When the curriculum is sequential.
All teachers are aware of and understand the
curriculum.
Program
When the program is flexible.
Flexible timeframe.
Cater to specific needs.
Repetition of concepts throughout the year.
When the teacher understands the program content, Thorough understanding of the curriculum.
including the year level above and below the one
they are teaching.
When the program is well planned and sequential.
Team planning.
When we adopt a whole school approach – Whole school planning.
Research.
pedagogy of school.
When students are given time to hypothesise, test Time and flexibility in program implementation.
and experience within the maths program.
Assessment
When assessment is an essential element of the Assessment informs and is informed by teaching,
teaching and learning cycle.
learning and planning.
A variety of assessment contexts are involved.
Use self-evaluation, games, clinical, annotated
checklist, anecdotal, test–oral/written, observation,
peer-assessment, moderation, on-demand tests,
student self-assessment, clinical interview, good
questions, games, student journal and rubrics.
Assessment is open to look beyond and below the Know and use the developmental stages of teaching
expected level.
mathematics (refer to Booker, developmental
continuums and VELS standards).
Assessment is ongoing and is used to inform Refer to Ymer’s assessment sample schedules.
planning and teaching.
Assessment is inherent in all tasks.
Teachers must look for assessment opportunities
continually when planning lessons.
Teachers provide effective, regular, timely and The most important person in the process is the
informative feedback.
student-let them know how they’re going, where
they are and where they’re going next.
Resources/Technology
The technology and a variety of resources are made
readily available to students and teachers.
They (students? teachers?) are shown how to use
resources effectively.
Catalogue of maths resources across the school.
‘Tool kit’.
Teacher knowledge and demonstration (fishbowling).
Modelling.
Teachers have a clear understanding of content and Teachers engage in ongoing professional learning.
available resources.
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