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….

• 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

GOALS OF THE TRAINING

Throughout the training…..

- E + NING

PARKING LOT

A staged process to review Kindergarten to Grade 12 curriculum documents by discipline area that:

• ensures that the curriculum remains current and relevant

• builds on the quality curriculum foundation already in place, and

WHAT IS SUSTAINING QUALITY CURRICULUM?

• ensures ongoing high quality education and continuous improvement in student achievement

RATIONALE FOR SUSTAINING QUALITY CURRICULUM

• sustains the effectiveness of Ontario’s curriculum for students in a knowledge-based society

• assures curriculum coherence and age- appropriateness from Kindergarten through Grade 12 in all disciplines

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

• 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

WHAT REMAINS THE SAME ?

Review Process

• 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

Analysis included:

Review Process

• 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

Analysis included:

Use of Technology and Manipulatives 3

Prominent Role of Mathematical Processes like Problem Solving and

Communication

Broad Range of Mathematical Topics

Elements of a Developmental

Continuum

Overall and Specific Expectations

Emphasis on Real Life Applications

1

2

4

5

6

Focus Groups: Strengths

Improve Concept Development and Grade

Appropriateness 2

Eliminate Gaps and Redundancies

Strengthen Link Between Expectations

and Achievement Chart

Reduce Number of Expectations

Cluster Expectations More Appropriately

Using Big Ideas

Improve Balance Between Expectations

Related To Facts/Procedures and

Those Related To Conceptual

Understanding

1

3

4

5

6

Focus Groups: Suggestions

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

• 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

Synthesis:

Review Process

• 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

Revision and Feedback Consultation

• 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

Post Feedback Activities

Review Process

Stages of Review Process for Mathematics

Implementation

Revision and Feedback Consultation

Analysis and Synthesis

Editing, Publication and Distribution

Sept.2003

Sept.2004

Sept.2005

Sept.2006

Sept.2007

1 - 10

11 - 12

Opportunities and Routes for Input

Revision Teams

Feedback Consultation

Achievement Charts

Subject /Division

Associations

Focus Groups

Other Consultations

and Input

Technical Analysis

Analysis / Synthesis

24

PROCESS EXPECTATIONS

OVERALL/SPECIFIC EXPECTATIONS

ACHIEVEMENT CHART

APPLIED / ACADEMIC

SAMPLE PROBLEMS

PATHWAYS REVIEW

EXAMPLES

INTRODUCTION

16

RESOURCES/INITIATIVES

• Some provincially available resources or initiatives for mathematics education are…

Some Recent Initiatives

Key Messages from Revision

•Learning

•Teaching

•Assessment/Evaluation

•Learning Tools

•Equity

•Curriculum Expectations

Areas adapted from N.C.T.M. Principles and Standards for School Mathematics, 2000

The Curriculum

From The Ontario Curriculum Grades 1-8 Mathematics, 1997

Page 3

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.

Curriculum Expectations

From The Ontario Curriculum Grades 9 and 10, 1999Page 4

A coherent and continuous program is necessary to help students see the “big pictures” or underlying principles of mathematics.

Curriculum Expectations

Curriculum

The revised curriculum is coherent, focused on important mathematics, and well articulated across the grades.

Learning

From Notable Strategies: Closing the GapResearch and Literature Review - Page 1

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…

Learning

Learning

The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior knowledge.

Learning Tools

From Teaching and Learning Mathematics - the Report of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario

Pages 25 and 28

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.

Learning Tools

Learning Tools

The revised curriculum promotes the use of technology and manipulatives as tools for teaching and learning mathematics.

Assessment & Evaluation

From Targeted Implementation and Planning Supports

Page 21

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.

Assessment & Evaluation

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

Assessment & Evaluation

From: Leading Math SuccessPage 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

From: Leading Math Success

Page 31

Effective instructional strategies in mathematics emphasize the ability to think, to solve problems, and to build one’s own understanding

Teaching

Teaching

The revised curriculum supports effective mathematics teaching that requires understanding what students know and need to learn and do.

Equity

From Building Pathways to Success, Grades 7 – 12Page 11

Ontario schools should offer an educational program that …. provides all students with the learning opportunities and support they need

Equity

Equity

This curriculum supports equity by promoting excellence in mathematics education for all students

DELIVEREDCURRICULUM

InstructionalProgramIn The

Classroom

INTENDEDCURRICULUM

Ministry Curriculum

Expectations

ACHIEVEDCURRICULUM

What IsBeing

Assessed

Working Toward Alignment

MINDS ON!

DISTRICT TRAINING SESSION

REVISED

A Problem To Ponder

MAKING CONNECTIONSStudent 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 MODELSGraphical Model Numerical Model

MATHEMATICAL MODELS

N = 2(n-1) + 1

N = (n - 1) + n

N = n2 - (n - 1)2

Algebraic Models

MATHEMATICAL MODELSGraphical Model Numerical Model

Algebraic ModelPhysical Model

N = 2n - 1

?

MATHEMATICAL MODELS

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

Algebraic Models

T = 2n - 1

MATHEMATICAL MODELSGraphical Model

Numerical Model

Algebraic Model

Physical 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 MODELSIt 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