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System Implementation and Monitoring
Regional Session
Winter, 2015
Welcome and Agenda
Morning
Tasks in Mathematics Classrooms
Afternoon
Sharing of Implementation Steps
and
Monitoring Actions in Like-Role Groups
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#WINTERSIM
#SIMK12
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Determine where you might be in Ontario
given the information in the chart below.
Think on your own for 5 minutes.
City
Distance as bird flies
(km)
Driving Distance
(km)
Windsor
Toronto
Ottawa
Thunder Bay
Niagara Falls
North Bay
454
398
549
544
463
245
763
540
647
902
653
289
City
Windsor
Toronto
Ottawa
Thunder Bay
Niagara Falls
North Bay
Distance as bird
flies (km)
454
398
549
544
463
245
Driving Distance
(km)
763
540
647
902
653
289
Determine where you might be in Ontario given the
information in the chart below.
Think on your own for 5 minutes.
This is an example of a contextual mathematics task.
Best Evidence Synthesis on Effective
Pedagogy in Mathematics
Effective mathematical pedagogy is a coherent
system rather than a set of discrete,
interchangeable strategies. This pedagogical
system encompasses:
• A non-threatening classroom environment
• Instructional tasks
• Tools and representations
• Classroom discourse
Effective Pedagogy in Mathematics/Pangarau by Glenda Anthony
& Margaret Walshaw, New Zealand (2007)
Quality Instruction in a Math Class
You have a representative sample of your thinking
about quality instruction in mathematics grouped
according to the four components of an effective
pedagogical system in mathematics.
Review and discuss any observations that you
have.
The Learner
Discuss at your tables what the student
should be able to do if there is quality
instruction.
What is the image of the mathematics
learner that emerges if the four
components of the pedagogical system
are evident?
Effective Teaching and Learning
The learning of mathematics has been defined to
include the development of five interrelated
proficiencies that, together, constitute
mathematical proficiency (NRC 2001):
• Conceptual understanding
• Procedural fluency
• Strategic competence
• Adaptive reasoning
• Productive disposition
Posing Worthwhile Mathematical Tasks
“It is through tasks that the curriculum and the
discipline of mathematics comes alive.
Starting with students’ prior knowledge and
then creating rich, mathematical tasks,
teachers help students to proceed gradually
from their informal knowledge of the ideas in
the domain to more formal notions.”
(Romberg and Kaput, 1999)
Posing Worthwhile Mathematical Tasks
“Tasks should be created or selected that
have the potential to encourage students
to wonder why things are, to inquire, to
search for solutions and to resolve
incongruities”.
(Hiebert et al. 1996)
Rich Tasks
What is also apparent to me is that much of what it
takes to make a rich task “rich” is the environment in
which it is presented, which includes the support and
questioning that is used by the teacher and the roles
the learners are encouraged to adopt. That is, an
environment in which learners are not passive
recipients of knowledge, accepting what is given, but
independent assertive constructors of their own
understanding, who challenge and reflect. On its
own a rich task is not rich – it is only what is
made of it that allows it to fulfil its potential.
Jennifer Piggot
http://nrich.maths.org/5662
“On its own a rich task is not rich –
it is only what is made of it that
allows it to fulfil its potential”.
Jennifer Piggott
http://nrich.maths.org/5662
Time for Chocolate!
Chocolate Bar Task
• This is an example of a purposeful representative task
• These tasks are usually not “contextualized”, however
there was sometimes a hook to engage students
• While the mathematics may be explicit, extensive
exposition by the teacher is not necessary as the
provision of the model or representation enables the
students to generate the mathematical ideas and
justification.
• The model, representation, or tool is ideally closely
linked to the mathematical concept being developed,
in order to be effective.
Types of Mathematics Tasks
In studies of mathematics tasks, four general types
have been identified:
Purposeful
representative
tasks
Contextual
tasks
Contentspecific tasks
Practice and
consolidation
tasks
Purposeful
representative
tasks
Contextual
tasks
Contentspecific tasks
Practice and
consolidation
tasks
Content-Specific Task
If the perimeter of a rectangle is 64 m
what might be the area?
Purposeful
representative
tasks
Contextual
tasks
Contentspecific tasks
Practice and
consolidation
tasks
Content-Specific Task
• Often an open task
• Although, the student needs specific content
knowledge to solve
• Involves investigating, creating, communicating,
generalizing and coming to know procedures
Purposeful
representative
tasks
Contextual
tasks
Contentspecific tasks
Practice and
consolidation
tasks
Practice and
Consolidation Tasks
Factor the expression
x 2+ 5x + 6 = 0
Find the value of
½+¾
• Are an important part of a balanced mathematics
program
• Provide students with opportunities to solidify
mathematical concepts and procedures
• Provide independent practice
DOG PEN
How Tasks Contribute To Students’
Mathematical Proficiency
Type of Task
Purposeful Representative
Mathematical Proficiency
Conceptual Understanding
Mathematical Fluency
Contextual
Content-specific
Strategic competence
Adaptive reasoning
Strategic competence
Adaptive reasoning
It is understood that there can .be overlap of proficiencies across
various tasks. These are the main ones that are developed.
P. Sullivan et al. Teaching with Tasks for Effective Mathematics Learning.
• This is one way to monitor the effectiveness of the
mathematics teaching and learning in your system
• It is one component of the pedagogical system;
however as many researchers have argued it is a
critical element
• Even though looking at tasks without student
thinking and/or work has limitations, it does give us a
window into the mathematics that students
experience in our classrooms
Conversation Tool for Reflection on
Mathematical Tasks
Conversation Tool for Reflection on
Mathematical Tasks
Grade Groups
Each grade group will collaboratively
discuss a selection of mathematical tasks.
The Conversation tool has been designed
as a starting point for your discussion.
Think about the collection of tasks to see if
there is a sampling of the four types:
contextual, purposeful representative,
content-specific and practice/consolidation.
K-2
3-5
6-8
9-12
Grade Groups and Rooms
TASK
6-8
K-2
3-5
9-12
ROOM
Venetian
Castelli AB
Castelli C
Dolce
12:00 – 12:45
Board Teams
Analyze the tasks that you brought using the
conversation tool.
Cross-Board Like-Role Sharing
ROLE
Principal/ Vice-Principal
Consultant/Co-ordinator/
Teacher
Superintendent
ROOM
Venetian
Castelli AB
Castelli C
Feedback Survey
Complete your feedback survey
Your feedback is important to us!
See you at the Spring 2015 SIM K-12!
DOG PEN

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