The Curriculum

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The Curriculum Powered By Docstoc
					Sustaining Quality
   Curriculum

   Supporting students and teachers by
   keeping Ontario’s K - 12 curriculum
           current and relevant
         Are You…?
• A Classroom Teacher

• A consultant, co-ordinator,
  resource teacher

• An Administrator

• A Parent of a child in grade 7 - 10
  Introduce your MATH-self to the
        others at your table


My name is….
As a result of this training I hope….
Teaching is my chosen profession because….
Home for me is….
      GOALS OF THE TRAINING
• become familiar with important changes
  in the 2005 revised mathematics
  curriculum document
• clarify the purpose of the Achievement
  Chart and establish common assessment
  and evaluation terms, definitions and
  messages
• share resources, and presentation ideas to
  conduct your school board training
  sessions
Throughout the training…..


                - E + NING
PARKING LOT
WHAT IS SUSTAINING QUALITY
       CURRICULUM?

 A staged process to review Kindergarten to
 Grade 12 curriculum documents by
 discipline area that:
       • builds on the quality curriculum
         foundation already in place, and
       • ensures that the curriculum remains
         current and relevant
RATIONALE FOR SUSTAINING
  QUALITY CURRICULUM

 • ensures ongoing high quality education
 and continuous improvement in student
 achievement
• assures curriculum coherence and age-
   appropriateness from Kindergarten through
   Grade 12 in all disciplines
• sustains the effectiveness of Ontario’s
   curriculum for students in a knowledge-based
   society
  RATIONALE FOR SUSTAINING
    QUALITY CURRICULUM
• supports students, teachers, schools and
  boards by identifying targeted areas in
  need of support

• allows lead time for development or updating
  of related support materials as required
  (e.g., textbooks, exemplars)

• supports continual improvement to the
  curriculum
 WHAT REMAINS THE SAME                    ?

• high standards for all students

• the framework of grade-by-grade and
  course-by-course overall and specific
  curriculum expectations
• destination-related secondary school
   course types
 WHAT REMAINS THE SAME ?

• criterion-referenced assessment based on
  four levels of achievement as described
  in the achievement charts

• standardized provincial report cards

• diploma requirements under Ontario
  Secondary Schools (OSS) Grades 9 to 12
              Review Process
Analysis included:
• Technical analysis of the English- and French-
  language curriculum policy documents completed
  by educators

• Content Analysis of information from over 500
  educators through province-wide Focus Group
  sessions

• Consultations held with the Minister’s Advisory
  Council on Special Education, Faculties of
  Education, parents, students, colleges, and
  workplace organizations
               Review Process
Analysis included:
• A joint report by English- and French-language
  teams of educators recommended a draft common
  framework for achievement charts to promote
  consistency in assessment

• Focused benchmarking of the Ontario curriculum
  against other provinces

• A literature search of recent curriculum reviews
  was done
      Focus Groups: Strengths
    Prominent Role of

          1
Mathematical Processes
like Problem Solving and
     Communication
                                    4
                                Elements of a
                           Developmental Continuum




          2
    Broad Range of
  Mathematical Topics                5
                             Overall and Specific
                                Expectations




           3
 Use of Technology and
     Manipulatives                    6
                             Emphasis on Real Life
                                Applications
   Focus Groups: Suggestions

         1
 Eliminate Gaps and
    Redundancies                    4
                             Reduce Number of
                               Expectations




         2                          5
   Improve Concept        Cluster Expectations More
Development and Grade      Appropriately Using Big
   Appropriateness                  Ideas


                          Improve Balance Between

         3                           6
Strengthen Link Between    Expectations Related To
    Expectations and        Facts/Procedures and
   Achievement Chart          Those Related To
                          Conceptual Understanding
  Review Process
Research:
• Background research paper prepared Fall 2003
  involving a literature search related to curriculum
  development.
• Focussed benchmarking of the Ontario curriculum
  against other provinces and countries (e.g. Alberta,
  British Columbia, Quebec, England, New South
  Wales, Japan)
• Extensive use of well researched sources (e.g.,
  N.C.T.M.)
              Review Process
Synthesis:
• A content analysis of information from the
  technical analysis, the focus group sessions,
  focused benchmarking of Ontario’s curriculum,
  and research on the curriculum review process was
  prepared

• Research, data and consultation input were
  summarized and used as a basis for
  recommendations for revision to the Mathematics
  curriculum policy documents
               Review Process
Revision and Feedback Consultation
• Parallel English/French writing teams of educators
  from across Ontario, with curriculum expertise,
  drafted revised documents based on the
  recommendations

• Early feedback from educators informed
  preparations for broader feedback process

• Feedback Consultation on proposed revisions in
  fall 2004
            Review Process
Post Feedback Activities
     • Analysis of feedback surveys
     • Two post-feedback consultations
     • Extensive consultation and feedback with Early
       Math/Junior Math team
     • French alignment meetings
     • Subject/Division Meetings
     • Editing, Fact Check, Bias Check
          Stages of Review Process for
                  Mathematics
Sept.             Sept.         Sept.       Sept.   Sept.
2003              2004          2005        2006    2007




        1 - 10                   
        11 - 12                             

    Analysis and Synthesis

    Revision and Feedback Consultation

    Editing, Publication and Distribution

   Implementation
    Opportunities and Routes for Input
                Technical   Focus         Other
   Subject /    Analysis    Groups     Consultations
   Division                             and Input
 Associations

                Analysis / Synthesis
Achievement
      Charts

                  Revision Teams

                     Feedback
                    Consultation
               ACHIEVEMENT
INTRODUCTION
                  CHART

 PATHWAYS         EXAMPLES
  REVIEW
     SAMPLE     APPLIED /
    PROBLEMS    ACADEMIC

  PROCESS      OVERALL/SPECIFIC
EXPECTATIONS    EXPECTATIONS

                             24 16
    RESOURCES/INITIATIVES


• Some provincially available resources or
  initiatives for mathematics education are…
Some Recent Initiatives
Key Messages from Revision

•Curriculum Expectations
•Learning
•Teaching
•Assessment/Evaluation
•Learning Tools
•Equity
Areas adapted from N.C.T.M. Principles and Standards
           for School Mathematics, 2000
The Curriculum
Curriculum Expectations
           The specific
          expectations for each
          grade should be seen
          in the context of the
          overall process of
          building mathematical
          knowledge and skills
          from grade to grade.
               From The Ontario Curriculum Grades 1-8 Mathematics, 1997
                                        Page 3
Curriculum Expectations
         A coherent and
         continuous program is
         necessary to help
         students see the “big
         pictures” or underlying
         principles of
         mathematics.
         From The Ontario Curriculum Grades 9 and 10, 1999
                              Page 4
        Curriculum

The revised curriculum is
coherent, focused on important
mathematics, and well
articulated across the grades.
Learning
Learning
It is important …that
students have opportunities
to learn in a variety of ways
– individually, cooperatively,
independently, with teacher
direction, through hands-on
experience, through
examples followed by
practice…
From Notable Strategies: Closing the Gap
Research and Literature Review - Page 1
          Learning
The revised curriculum supports
students learning mathematics
with understanding and actively
building new knowledge from
experience and prior knowledge.
Learning Tools
                              Learning Tools
                                        Manipulatives that are
                                        used well are central to
                                        effective instruction and
                                        have the capacity to
                                        greatly improve and
                                        deepen student
                                        understanding.
                                        Technology is not meant
                                        to replace mathematical
                                        thought but to expand it.
From Teaching and Learning Mathematics - the Report of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario
                                               Pages 25 and 28
       Learning Tools
The revised curriculum promotes
the use of technology and
manipulatives as tools for
teaching and learning
mathematics.
Assessment & Evaluation
Assessment & Evaluation
       Quality assessment
        includes a variety of tools
        and strategies that assess
        both the processes and
        products of mathematics
        learning and serves a
        variety of purposes:
        diagnostic, formative,
        and summative.
    From Targeted Implementation and Planning Supports
                        Page 21
Assessment & Evaluation

     Assessment should reflect
      instruction. Teachers
      need to adapt their
      assessment plans to
      ensure that the needs of
      all learners are met.

      From: Leading Math Success
               Page 33
  Assessment and Evaluation

The revised curriculum supports
assessment for the learning of
important mathematics and to
furnish useful information to
both teachers and students.
Teaching
Teaching
Effective instructional
strategies in
mathematics
emphasize the ability
to think, to solve
problems, and to build
one’s own
understanding
 From: Leading Math Success
          Page 31
          Teaching
The revised curriculum supports
effective mathematics teaching
that requires understanding
what students know and need to
learn and do.
Equity
         Equity
    Ontario schools
    should offer an
    educational program
    that …. provides all
    students with the
    learning opportunities
    and support they need
From Building Pathways to Success, Grades 7 – 12
                   Page 11
           Equity
This curriculum supports equity
by promoting excellence in
mathematics education for all
students
Working Toward Alignment



        INTENDED         DELIVERED
       CURRICULUM       CURRICULUM
          Ministry        Instructional
         Curriculum         Program
        Expectations         In The
                           Classroom



                ACHIEVED
               CURRICULUM
                  What Is
                  Being
                 Assessed
MINDS ON!
                     REVISED

A Problem To
Ponder

               DISTRICT
               TRAINING
                SESSION
     MAKING CONNECTIONS
     Student action should focus on solving
                   problems.

•The teacher helps students make connections
within mathematics and between mathematics and
the world and develop lifelong learning skills.
•The more that connections are made among a
network of ideas, the stronger will be the student’s
understanding and the less pressure will there be
on the student to memorize and to worry about
forgetting.         Leading Math Success - Page 46
        A Rich Learning Task
• On your table is a large sheet of paper. It
  holds a learning task, plus a place for
  reflecting on the six key messages.

• We will be coming back to the six key
    messages throughout the next two days.

           On with the task!!
         A Rich Learning Task
• You will begin by reading and representing the
  problem using the connecting cubes. That is: you
  will make a physical model that represents the first
  5 terms of the sequence.


• Discuss your models with one another.



          Work with a partner!
   MAKING CONNECTIONS
• One model of the first three terms of a
  sequence are modeled in the picture below.
• Create physical models for these 3 terms
  and the next 2 terms in this sequence for a
  total of 5 terms.
MATHEMATICAL MODELS
  Graphical   Numerical
    Model       Model
  MATHEMATICAL MODELS
                 Algebraic
                   Models



N = 2(n-1) + 1

                 N = (n - 1) + n

                                   N = n2 - (n - 1)2
MATHEMATICAL MODELS
Graphical         Numerical
  Model             Model



              ?    Physical
Algebraic           Model
  Model
 N = 2n - 1
   MATHEMATICAL MODELS
                 Algebraic
                   Models



T = 2(n-1) + 1    T = (n - 1) + n T = n2 - (n - 1)2




            T = 2n - 1
MATHEMATICAL MODELS
                  Numerical
Graphical           Model
  Model



              ?    Physical
Algebraic           Model
  Model
 T = 2n - 1
   RICH LEARNING TASKS
An extension to this problem:
 Which model (algebraic,
 numerical, etc.) would you use
 to determine the total number
 of cubes needed to make the
 first 50 terms?
 * Discuss your choice with a
 neighbor.
MATHEMATICAL MODELS
               It takes 52
               or 25
               cubes to
               make the
               first 5
               terms so it
               takes 502
               or 2500
               cubes to
               make 50
               terms.
   RICH LEARNING TASKS
Other extensions to this problem:
How would this problem change if:
- The students started with a $5 donation?
- The cost was $2 per car wash?
- One student charged $1 and the other
  charged $2?
- … and so on.
    RICH LEARNING TASKS
• A problem solving approach encourages
  students to reason their way to a solution or
  a new understanding….
• The communication and reflection that
  occurs during and after the process of
  problem solving helps students not only to
  articulate and refine their thinking but also
  to see the problem they are solving from
  different perspectives.
                 Draft Introduction Mathematics 9 and 10, 2005
       LEARNING TASKS
• “When developing detailed courses of
  study from this document, teachers are
  expected to weave together related
  expectations from different strands…”
• “Problem solving is central to learning
  mathematics.”
• “A balanced mathematics program at the
  secondary level includes the
  development of algebraic skills.”

                Draft Introduction: Curriculum Document 2005
RICH LEARNING TASKS

				
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