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

Introduce your MATH-self to the others at your table M y name is…. A s a result of this training I hope…. T eaching is my chosen profession because…. H ome 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 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 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 Sept Sept Sept Sept

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 CurriculumExpectations 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, 1999 Page 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 Gap Research 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

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

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 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

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

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 – 12 Page 11 Ontario schools should offer an educational program that …. provides all students with the learning opportunities and support they need Equity

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

DELIVERED CURRICULUM Instructional Program In The Classroom INTENDED CURRICULUM Ministry Curriculum Expectations ACHIEVED CURRICULUM What Is Being Assessed Working Toward Alignment

MINDS ON! DISTRICT TRAINING SESSION REVISED A Problem To Ponder

RESOURCES/INITIATIVES List three or four provincially available resources or initiatives for mathematics education.

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 Model Numerical Model

MATHEMATICAL MODELS N = 2(n-1) + 1 N = (n - 1) + n N = n 2 - (n - 1) 2 Algebraic Models

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

MATHEMATICAL MODELS T = 2(n-1) + 1 T = (n - 1) + n T = n 2 - (n - 1) 2 Algebraic Models T = 2n - 1

MATHEMATICAL MODELS Graphical 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 MODELS It takes 5 2 or 25 cubes to make the first 5 terms so it takes 50 2 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

Timed Retell How does this activity support rich and meaningful learning in mathematics?