Principles and Standards for school math

Slide1 : “Higher Standards for Our Students... NCTM Presents Higher Standards for Ourselves”

Slide2 : 2 Adapted by the BC Association of Mathematics Teachers for Western Canadian Jurisdictions In cooperation with NCTM

Why Principles and Standards? : Therefore, school mathematics must continue to improve. Why Principles and Standards? The world is changing. Our students are different. School mathematics should work well for all students.

The World Is Changing : The World Is Changing In everyday life, we are exposed to an increasing amount of “mathematical” information. In the workplace, we are regularly challenged to learn new skills. Our lives are being reshaped by changing technologies.

Our Students Are Different : Our Students Are Different They are comfortable with and use technology. They have competing demands on their time. They are accustomed to visual stimulation and have easy access to information.

School Mathematics Should Work Well for All Students : School Mathematics Should Work Well for All Students Internationally, our students must strive to remain mathematically competitive LOWER 20 countries SAME 10 countries HIGHER 10 countries Canada Source: TIMSS-Canada Report: New Findings for a New Century (2000)

School Mathematics Should Work Well for All Students : School Mathematics Should Work Well for All Students Nationally, our students must strive to remain mathematically competitive LOWER 1 province SAME 3 Provinces and Canada HIGHER 1 province Source: TIMSS-Canada Report: New Findings for a New Century (2000) British Columbia

School Mathematics Should Work Well for All Students : School Mathematics Should Work Well for All Students Nationally, our students must strive to remain mathematically competitive LOWER 1 province SAME 3 Provinces and Canada HIGHER 1 province Source: TIMSS-Canada Report: New Findings for a New Century (2000) Alberta

School Mathematics Should Work Well for All Students : School Mathematics Should Work Well for All Students Nationally, our students must strive to remain mathematically competitive LOWER 1 province SAME 3 Provinces and Canada HIGHER 1 province Source: TIMSS-Canada Report: New Findings for a New Century (2000) Ontario

School Mathematics Should Work Well for All Students : School Mathematics Should Work Well for All Students Nationally, our students must strive to remain mathematically competitive LOWER 1 province SAME 3 Provinces and Canada HIGHER 1 province Source: TIMSS-Canada Report: New Findings for a New Century (2000) Quebec

School Mathematics Should Work Well for All Students : School Mathematics Should Work Well for All Students Nationally, our students must strive to remain mathematically competitive LOWER 1 province SAME 3 Provinces and Canada HIGHER 1 province Source: TIMSS-Canada Report: New Findings for a New Century (2000) Newfoundland

Wide Gaps between Subgroups Across the Nation : Wide Gaps between Subgroups Across the Nation 0 10 20 30 40 50 60 70 80 90 100 1993 1997 % Achieving Level 3 or Higher Year Canada Prov A Canada Prov A Prov B SAIP Mathematics Content Results (16-year-olds) Prov B

Therefore... : Therefore... We Must Continue to Improve Mathematics Education for All Students

Principles and Standards for School Mathematics : Principles and Standards for School Mathematics A comprehensive and coherent set of goals for improving mathematics teaching and learning in our schools. 14

Slide15 : Standards 15

How the NCTM Standards are Addressed by the WCP Framework : How the NCTM Standards are Addressed by the WCP Framework NCTM Standards Number and Operations Algebra Geometry Measurement Data Analysis and Probability WCP Framework Number Patterns & Relations Shape & Space Statistics and Probability

Number and Operations Standard : Number and Operations Standard Understand numbers, ways of representing numbers, relationships among numbers, and number systems Understand meanings of operations and how they relate to one another Compute fluently and make reasonable estimates Instructional programs from prekindergarten through grade 12 should enable all students to—

For Example:  • Compute fluently and make reasonable  estimates : Pre-K-2 Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use 6-8 Develop fluency in adding, subtracting, multiplying, and dividing whole numbers 3-5 Develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases 9-12 Develop fluency with basic number combinations for addition and subtraction For Example: • Compute fluently and make reasonable estimates 18

Western Canadian Protocol Emphasis Across the Grades : Western Canadian Protocol Emphasis Across the Grades Number Concepts & Operations Patterns & Relations Shape & Space Statistics & Probability K–3 4–7 8–10 11–12

Process Standards : NCTM Processes Problem Solving Reasoning and Proof Communication Connections Representations Process Standards WCP Processes Problem Solving Reasoning Communication Connections Estimation and Mental Mathematics Visualization Technology

Problem Solving Standard : Problem Solving Standard Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and in other contexts Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving Instructional programs from prekindergarten through grade 12 should enable all students to—

Slide22 : The Vision in WCP Mathematics: Examples from Principles and Standards 22

Resourceful Problem Solving : Resourceful Problem Solving How many different pattern block arrangements will cover a yellow hexagon?

One Student’s Solutions : One Student’s Solutions

Relevant Mathematics : Relevant Mathematics ChitChat Keep-in-Touch $20 per month NO monthly fee Only 10¢ for each minute

A Student’s Solution : A Student’s Solution No. of minutes Keep in Touch ChitChat $20.00 0 $0.00 $21.00 10 $4.50 $22.00 20 $9.00 $23.00 30 $13.50 $24.00 40 $18.00 $25.00 50 $22.50

Another Approach : Another Approach cost # of minutes

Principles : Teaching Assessment Technology Principles Features of high-quality mathematics programs Equity Curriculum Learning

Statement of Principles : Statement of Principles The Equity Principle Excellence in mathematics education requires equity– high expectations and strong support for all students.

Statement of Principles : Statement of Principles The Learning Principle Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.

For Example: Equity : For Example: Equity High expectations and worthwhile opportunities for all Accommodating differences to help everyone learn mathematics Resources and support for all classrooms and all students

Slide32 : Involvement 32

The Process of Developing Principles and Standards : The Process of Developing Principles and Standards Who was involved? Teachers School administrators Mathematics supervisors University mathematicians Mathematics educators Researchers

Highlights of Developing Principles and Standards : 1995 1996 1997 1998 1999 2000 Writers begin Review feedback from the field and Association Review Groups NCTM gathers information about possible revision Research Conference; Technology Conference Principles and Standards Discussion Draft released NRC Review and revision of discussion draft Release Highlights of Developing Principles and Standards 34

Highlights of Developing the WCP Framework : 1994 1996 1997… 2000 Jurisdictional Reviews of K to 9 WCP Draft Framework First Draft of WCP K to 9 Framework (developed using NCTM Standards) First & Second Drafts of WCP 10 to 12 Framework Western Canadian Jurisdictions implement WCP Mathematics 10 to 12 Framework Highlights of Developing the WCP Framework 35 1995 WCP K to 9 Framework is released WCP 10 to 12 Framework is released WCP jurisdictions conduct reviews of WCP 10 to 12 Framework – make minor adjustments Jurisdictional Reviews of 10 to 12 WCP Draft Framework

What is Needed to Implement a High Quality Mathematics Program? : 36 What is Needed to Implement a High Quality Mathematics Program? Participation of all constituencies Ongoing examination of the vision of school mathematics High-quality instructional materials Assessments aligned with curricular goals

Preparing Students for Tomorrow’s World : Preparing Students for Tomorrow’s World Recognize the importance of high-quality mathematics education Encourage your children to take learning mathematics seriously Advocate for mathematics programs that prepare all students for a changing world Work with teachers and others to provide quality mathematics programs

Principles and Standards: Better Mathematics Education for Our Children : Principles and Standards: Better Mathematics Education for Our Children What will my child learn? Mathematics with understanding The ability to use, explain, and justify mathematics Basics for today that prepare for tomorrow Flexible and resourceful problem-solving skills

Principles and Standards Web Site : 39 Principles and Standards Web Site standards.nctm.org

Ordering Principles and Standards : View the document or order it at Ordering Principles and Standards