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MATHEMATICALLITERACY / NUMERACY

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NTIP Requirement

Mathematical Literacy

Mathematical literacy involves more than executing procedures. It implies a knowledge base

and the competence and confidence to apply this knowledge in the practical world. A

mathematically literate person can estimate; interpret data; solve day-to-day problems; reason in

numerical, graphical, and geometric situations; and communicate using mathematics. - Leading Math Success: The Report of the Expert Panel on Student Success in Ontario, 2004.

The Ontario Mathematics Curriculum is based on the belief that "all students can learn

mathematics and deserve the opportunity to do so" (Ontario Curriculum Grades 1 to 8, Mathematics, p.3).

Key Messages

T All students can learn and be confident in mathematics, given appropriate time and support..

T The teacher plays a critical role in student success in mathematics.

T The use of concrete materials is fundamental to learning and provides a means of

representing concepts and student understanding. (Education For All, 2005)

T Students need to develop conceptual understanding of mathematics.

T Students need to apply important facts, skills, and procedures to problem solving situations.

T Teachers need to teach the seven processes of math (problem solving, reasoning and

providing, reflecting, selecting tools and computational strategies, connecting, representing,

communicating) as the actions of mathematics - what it means to do mathematics (Ontario

Curriculum, Grades 1 to 8, Mathematics, p.11)

T Effective classroom instruction can have a strong, positive impact on student attitudes and

learning in mathematics.

Professional Applications

Teachers are encouraged and required to read Ontario College of Teachers Member's Handbook,

2010. We have isolated a few specific look fors that pertain directly to planning. This is not a

comprehensive list and does not preclude the understanding that teachers will read the entire

Member's booklet.

When applying the standards of practice to the planning process teachers are encouraged to

demonstrate many practices including the following:

A. Commitment to Students and Student Learning

T Models for students the curiosity, enthusiasm and joy of learning.

T Creates a classroom environment that engages students' interest in mathematics.

T Develops programs for students that incorporate a knowledge and understanding of human

development and learning theory.

T Encourages students to become active, inquisitive and discerning citizens.

T Encourages students to know about, reflect on and monitor their own learning.

T Understands and uses a range of teaching methods to address learning, cultural, spiritual,

and language differences, and family situations.

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8. Professional Knowledge

T Understands the subject matter.

T Knows how knowledge in their subject area is created, linked to other subjects and applied

to life experiences.

T Knows the curriculum relevant to their subject area.

T Shapes instruction so that it is helpful to students who learn in a variety of ways.

T Manages time for instruction.

T Assesses and evaluates student learning, student approaches to learning and the

achievement of curriculum expectations.

T Makes knowledge and skills accessible to others.

C. Teaching Practice

T Collaborates with professional colleagues to support student learning.

T Applies knowledge of how students develop and learn.

T Adapts teaching practice based on student achievement.

T Adapts the methods of inquiry, content knowledge, and skills required in the curriculum.

T Links content and skills to everyday life experiences.

T Integrates a variety of teaching and learning strategies, activities, and resources.

T Keeps a continuous and comprehensive record of group and individual achievement.

T Assists students to develop and use ways to access and critically assess information.

D. Leadership and Community

T Motivates and inspires through sharing their vision.

T Engages others through shared problem-solving and conflict resolution.

T Acknowledges and celebrates effort and success.

E. Ongoing Professional Learning

T Understands that teacher learning is directly related to student learning.

T Anticipates and plans the kinds of learning they will need to respond to a variety of

educational contexts.

T Demonstrates a commitment to continued professional growth.

Considerations

“An effective mathematics program should include a variety of problem-solving experiences and

a balanced array of pedagogical approaches. An essential aspect of an effective mathematics

program is balance." (Kilpatrick, Swafford & Findell, 2001, Education For All).

T daily 60 minute math block is recommended (Teaching and Learning Mathematics - The

Report of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario, p.52, Leading Math

Success, pp.53, 78)

T textbooks are only one of many resources needed to support a mathematics classroom

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Resources

T The Ontario Curriculum, Grades 1-8, Mathematics, Revised 2005

T Early Math Strategy, Report of the Expert Panel on Early Math in Ontario, 2003

T Teaching and Learning Mathematics - The Report of the Expert Panel on Mathematics in

Grades 4 to 6 in Ontario, 2004

T Leading Math Success, The Report of the Expert Panel on Student Success in Ontario, 2004

T The Guide to Effective Instruction in Mathematics, K-6, 2006

T TIPS - 4 RM - Ontario Ministry of Education

T Think Literacy -Math Approaches, Grades 7-12 - Ontario Ministry of Education

T Showcasing Mathematics for the Young Child 2 - NCTM, 2004

T Young Mathematicians at Work -Catherine Fosnot and Maarten Dolk

T Elementary and Middle School Mathematics - John Van de Walle

T Fostering Children’s Mathematical Power - Creative Publications

T Impact Math - Ontario Ministry of Education

T These York Region District School Board sites require username and password:

Curriculum Sharepoint- https://teamserver.yrdsb.net/department/cis

T New Teacher Sharepoint - https://teamserver.

Yrdsb.net/department/cis/newteach/default.aspx

T Mathematical Literacy Sharepoint -

https://teamserver.yrdsb.net/department/cis/mathlit/default.asp

T Websites - TWW (Long Range Plans) https://tww.yrdsb.net

• LMS (Leading Math Success - Support documents)

http://www.curriculum.org

• OAME (Ont. Assoc. For Math Educators)

http://www.oame.on.ca/main/index1.php

• E-workshop (Ministry On-line support)

http://www.eworkshop.on.ca Also available in French

Reflective Questions

T How do you know what your students know and understand in math?

T How do you move your students forward in their mathematical thinking and understanding?

T How can you ensure your students are engaged in their math learning?

T What kind of support network can you establish for yourself within your school? (ie: Is

there anyone in your school who attends the board math in-service workshops? Is there

anyone in your school that you can work with when planning and assessing mathematics?

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Mathematical LiteracyTemplates or Samples

Individual Learning Profile Templates

Mathematics

Please note:

The following resources are samples or models, not mandated templates. The BGCDSB recognizes

that each teacher will approach assessment and evaluation in a way that reflects his/her personal

organizational and instructional style, with guidance and input from the administration at each school.

We suggest that you work collaboratively whenever possible and feasible to develop insight into how

to approach assessment and communication in a timely and professional manner.

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Student's Name:

Knowledge and Understanding

Retrieves factsautomatically

Uses mathtermsappropriately

Uses mathtermsappropriately

Usesproceduresappropriately

Usesmanipulativesor concretematerials andother toolseffectively

Demonstratesunderstandingof mathconcepts

Thinking

Identifies theproblem tosolve

Selects anapproach forsolving aproblem

Carries out aplan

Evaluates thesolution

Makesconvincingarguments

Uses criticaland creativethinkingprocesses

Communication

Expressesunderstandingorally

Expressesunderstandingpictorially

Expressesunderstandingwithmanipulativesor concretematerials

Expressesunderstandingin writing

Communicatesfor differentaudiences andpurposeseffectively

Usesconventions,vocabulary,andterminologyeffectively

Application

Appliesknowledge andskills in familiarcontexts

Appliesknowledge andskills to newcontexts

Makesconnectionsbetweenconcepts withinmathematics

Makesconnectionsbetween priorand newknowledge

Makesconnectionsbetweenmathematicsand othersubject areas

Makesconnectionsbetweenmathematicsand the worldoutside school

Education For All, 2005

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The Three-Part Lesson in Mathematics

Beginning T The teacher chooses a problem that offers a range of entry

points for students at different levels.

T The teacher poses the problem or sets the investigation without

giving the steps for solution.

Middle

T Students work in pairs or in small groups to solve the problem.

T Students work to make sense of the problem in their own way.

They look for patterns and for connections with other problems.

T The teacher asks careful questions that will help students to

deepen and clarify their thinking.

T Students communicate their mathematical thinking to one

another ,explain their ideas, listen to their peers, and talk with

teacher.

EndT The teacher organizes the discussion by choosing particular

samples of students' strategies to build understanding of specific

mathematical concepts and to support students' movement

towards efficient methods.

T Students share, explain, and examine a range of solutions with

the whole class, discussing the common elements, looking for

patterns and making sense.

Expert Panel on Mathematics in Grades 4 to 6 in Ontario. (2004). Teaching and learning mathematics: The report of theexpert panel on mathematics in grades 4 to 6 in Ontario. Toronto: Ontario Ministry of Education. p.1O

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The Three-Part Lesson in Mathematics

Beginning

Middle

End

Expert Panel on Mathematics in Grades 4 to 6 in Ontario. (2004). Teaching and learning

mathematics: The report of the expert panel on mathematics in grades 4 to 6 in Ontario. Toronto:

Ontario Ministry of Education. p.1O

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Mathematical Process Expectations

Primary Junior Intermediate Senior

Problem

Solving

apply developing problem-

solving strategies as they

pose and solve problems

and conduct

investigations, to help

deepen their mathematical

understanding

develop, select, and apply

problem-solving strategies

as they pose and solve

problems and conduct

investigations, to help

deepen their mathematical

understanding

develop, select, apply, and

compare a variety of

problem-solving strategies as

they pose and solve problems

and conduct investigations,

to help deepen their

mathematical understanding

develop, select, apply, compare,

and adapt a problem-solving

strategies as they pose and

solve problems and conduct

investigations, to help deepen

their mathematical

understanding

Reasoning and

Proving

apply developing

reasoning skills (e.g.,

pattern recognition,

classification) to make and

investigate conjectures

(e.g., through discussions

with others)

develop and apply

reasoning skills (e.g.,

pattern recognition,

classification) to make and

investigate conjectures

(e.g., through discussions

with others)

demonstrate and apply

reasoning skills (e.g.,

recognition of relationships,

generalization through

inductive reasoning, use of

counter examples ) to make

mathematical conjectures,

assess conjectures and justify

conclusions, and plan and

construct organized

mathematical arguments.

develop and apply reasoning

skills (e.g., generalization

through inductive reasoning, use

of deductive reasoning,

construction of proofs) to make

mathematical conjectures,

assess conjectures and justify

conclusions, and plan and

construct organized

mathematical arguments.

Reflecting demonstrate that they are

reflecting on and

monitoring their thinking

to help clarify their

understanding as they

complete an investigation

or solve a problem (e.g.,

by explaining their

thinking to others)

demonstrate that they are

reflecting on and

monitoring their thinking to

help clarify their

understanding as they

complete an investigation

or solve a problem (e.g.,

by comparing and

adjusting strategies used

and recording results)

demonstrate that they are

reflecting on and monitoring

their thinking to help clarify

their understanding as they

complete an investigation or

solve a problem (e.g., by

assessing the effectiveness of

strategies and processes

used)

demonstrate that they are

reflecting on and monitoring

their thinking to help clarify

their understanding as they

complete an investigation or

solve a problem (e.g., by

proposing alternative

approaches)

Selecting Tools

and

Computational

Strategies

select and use a variety of

concrete, visual and

electronic learning tools

and appropriate

computational strategies

to investigate

mathematical ideas and

solve problems

select and use a variety of

concrete, visual and

electronic learning tools

and appropriate

computational strategies to

investigate mathematical

ideas and solve problems

select and use a variety of

concrete, visual and electronic

learning tools and appropriate

computational strategies to

investigate mathematical

ideas and solve problems

select and use a variety of

concrete, visual and electronic

learning tools and appropriate

computational strategies to

investigate mathematical ideas

and solve problems

Connecting make connections among

simple mathematical

concepts and procedures

and relate mathematical

ideas to situations drawn

from every contexts

make connections among

mathematical concepts and

procedures and relate

mathematical ideas to

situations or phenomena

drawn from other contexts

(e.g., other curriculum,

daily life, sports)

make connections among

mathematical concepts and

procedures and relate

mathematical ideas to

situations or phenomena

drawn from other contexts

(e.g., daily life, current events

and culture)

make connections among

mathematical concepts and

procedures and relate

mathematical ideas to situations

or phenomena drawn from other

contexts (e.g., daily life, current

events and culture, art, sports)

Representing create basic

representations of simple

mathematical ideas (e.g.,

using concrete materials,

physical actions,

diagrams, invented

symbols), make

connections among

representations and apply

them

create a variety of

representations of

mathematical ideas (e.g.,

by using physical models,

pictures, variables), make

connections among

representations and apply

selected ones

create a variety of

representations of

mathematical ideas (e.g.,

numeric, geometric, algebraic,

graphical, pictorial), connect

and compare representations

and apply the appropriate

representations

create a variety of

representations of mathematical

ideas (e.g., numeric, geometric,

algebraic, graphical, and

onscreen dynamic

representations) connect and

compare representations

Communicating communicate

mathematical thinking

orally, visually and in

writing, using everyday

language and math

vocabulary

communicate mathematical

thinking orally, visually and

in writing, using everyday

language and math

vocabulary

communicate mathematical

thinking orally, visually and in

writing, using math

vocabulary and observing

mathematical conventions

communicate mathematical

thinking orally, visually and in

writing, using math vocabulary

and observing conventions

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Weaving the Literacies

Productive Disposition: belief in one’s

ability and efficacy; view of mathematics

as sensible, useful and worthwhile

Strategic Reasoning: ability to

formulate, represent and solve problems

Conceptual Understanding:

comprehension of mathematical concepts,

procedures and relationships

Procedural Fluency: skill in carrying

out procedures flexibly, accurately,

efficiently and appropriately

Adaptive Reasoning: capacity for logical

thought, reflection, justification and

explanation

Mathematics

York Region District School Board, April 2004

Reading, Writing, Oral and Visual Communication

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Shared Mathematics

Reasons for shared mathematics:

T Shared mathematics provides students with opportunities to acquire and use content knowledge

and skills through problem solving, investigation and proof, communication, connection, and

reflection.

T Shared mathematics takes key concepts / big ideas from the curriculum that need to be

addressed and considers how to incorporate them in a developmentally appropriate manner

through problem solving or discussion.

T Students learn from one another. The teacher is not the only source of knowledge, and the

students need a variety of opportunities to construct their own mathematical understanding with

others.

What shared mathematics look like:

T Shared mathematics may occur between teacher and student, teacher and a group of students,

student with other students.

T Reflection, discussion, and sharing occur at the end of the session to bring closure and

clarification to the key mathematical ideas.

T Groupings could be pairs, small groups, or whole class.

Students could be: Teacher could be:

• working in partners exploring a problem

together;

• working at centres in small groups;

• teaching other students;

• using manipulatives;

• playing games;

• participating in a mathematics walk;

• working on a puzzle;

• working on computers;

• singing songs to reinforce mathematical

ideas;

• exploring concepts, finding

answers/solutions to problems, and

generating or asking questions;

• working together to learn a new

concept/idea or skill;

• talking, sharing -the classroom is

productively noisy

• facilitating, observing, and asking key

questions as students work;

• promoting individual, small group, or whole

group discussion;

• gathering assessment data

• participating in a mathematics to:

- make decisions about where to go next

with program planning;

- make modifications for individuals or

groups of students;

- provide extensions for individuals or new

groups of students.

Adapted from: The Report of the Expert Panel on Early Math in Ontario, 2003

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Guided Mathematics

Reasons for guided mathematics:

• Guided mathematics helps to clarify new knowledge or skill.

• Guided mathematics takes key concepts / big ideas in the curriculum and incorporates or

presents them in a developmentally appropriate manner.

What guided mathematics look like:

• Focus lessons are used.

• Instruction is sequential and planned by the teacher.

• Class instruction is well thought out yet flexible to capitalize on alternative ideas and strategies

provided by students.

• The teacher works with the whole group or small group, and at times with individual students.

• Reflection, discussion, and sharing are vital components to help bring closure and clarification of

key mathematical ideas but needs not occur at the end of class and may happen throughout.

• The teacher and students work with manipulatives, at a chart, standing in a group, at the

overhead/blackboard, or sitting on the floor.

Students could be: Teacher could be:

• responding to the teacher's questions and

offering next steps;

• guiding and Modeling mathematical thinking

or ideas for other students while the teacher

provides support and guidance.

• activating the concept and connecting it with

prior knowledge;

• Modeling mathematics language, problem

solving, and thinking (think aloud);

• leading the discussion and sharing;

• setting up a learning experience so that

students gain new knowledge or skills;

• pointing out and highlight students' different

strategies while addressing the key concept

/ big idea or focus of the lesson;

• acting as a guide or facilitator to ensure that

strategies are appropriate, effective, and

correct;

• including good questions that are thought

provoking and capture the essence of the

mathematics.

Adapted from: The Report of the Expert Panel on Early Math in Ontario, 2003

New Teacher Induction Program - 2011 Page 157

Independent Mathematics

Reasons for independent mathematics:

• Children demonstrate their understanding, practise a skill or consolidate learning in a

developmentally appropriate manner through independent work.

• Students have time to grapple with a problem on their own.

• Students need time to consolidate ideas for and by themselves.

What independent mathematics looks like:

• Independent mathematics may occur at various times and not just at the end of the activity or

lesson.

• Reflection, discussion, or sharing could occur to bring closure and clarification of the key

mathematical concepts.

• Independent mathematics may include practising a mathematical skill, journal writing,

explaining an idea to the teacher, playing an independent game, working alone on the computer,

or using manipulatives to gain a better grasp of a key concept.

Students could be: Teacher could be:

• working in partners exploring a problem

together;

• working at centres in small groups;

• teaching other students;

• using manipulatives;

• playing games;

• participating in a mathematics walk;

• working on a puzzle;

• working on computers;

• singing songs to reinforce mathematical

ideas;

• exploring concepts, finding

answers/solutions to problems, and

generating or asking questions;

• working together to learn a new

concept/idea or skill;

• talking, sharing - the classroom is

productively noisy

• facilitating, observing, and asking key

questions as students work;

• promoting individual, small group, or whole

group discussion;

• gathering assessment data to:

- make decisions about where to go next

with program planning;

- make modifications for individuals or

groups of students;

- provide extensions for individuals or

groups of students

Adapted from: The Report of the Expert Panel on Early Math in Ontario, 2003