MATHEMATICAL LITERACY / NUMERACY - Home - … Teacher Induction Program - 2011 Page 148 Resources T...
Transcript of MATHEMATICAL LITERACY / NUMERACY - Home - … Teacher Induction Program - 2011 Page 148 Resources T...
New Teacher Induction Program - 2011 Page 146
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.
New Teacher Induction Program - 2011 Page 147
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
New Teacher Induction Program - 2011 Page 148
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?
New Teacher Induction Program - 2011 Page 149
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
New Teacher Induction Program - 2011 Page 152
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
New Teacher Induction Program - 2011 Page 153
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
New Teacher Induction Program - 2011 Page 154
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
New Teacher Induction Program - 2011 Page 156
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