The National Council The National Council of Teachers of of Teachers of

Mathematics (NCTM)Mathematics (NCTM)Principles and Principles and

Standards for School Standards for School MathematicsMathematics

Dr. Robinson, EEX 4251, Spring 2008

The PSSMThe PSSM

The The Principles and StandardsPrinciples and Standards desire desire to set forth a “comprehensive and to set forth a “comprehensive and coherent set of goals for coherent set of goals for mathematics for all students from mathematics for all students from prekindergarten through grade 12” prekindergarten through grade 12” (NCTM, 2000). (NCTM, 2000).

Who was Involved?Who was Involved?

– TeachersTeachers– School administratorsSchool administrators– Mathematics supervisorsMathematics supervisors– University mathematiciansUniversity mathematicians– Mathematics educators Mathematics educators – ResearchersResearchers

TimelineTimeline

1951 Max Beberman – UICSM Project1951 Max Beberman – UICSM Project

1957 SPUTNIK1957 SPUTNIK

1960 “New Math”1960 “New Math”

1963 FIMS – First International Mathematics Study1963 FIMS – First International Mathematics Study

1969 NAEP – National Assessment of Ed Progress1969 NAEP – National Assessment of Ed Progress

1973 1973 Why Johnny Can’t ReadWhy Johnny Can’t Read – Morris Kline “Back to Basics” – Morris Kline “Back to Basics”

1975 NACOME1975 NACOME

1980 1980 Agenda For ActionAgenda For Action – NCTM “Pragmatic – Problem – NCTM “Pragmatic – Problem Solving”Solving”

1982 SIMS – Second International Mathematics Study1982 SIMS – Second International Mathematics Study

1983 1983 A Nation at RiskA Nation at Risk

1987 J. R. Flanders analysis of textbooks – prior to algebra1987 J. R. Flanders analysis of textbooks – prior to algebra

TimelineTimeline

1989 1989 Curriculum StandardsCurriculum Standards – NCTM – NCTM

Everybody CountsEverybody Counts – Lynn Steen & NRC – Lynn Steen & NRC

1991 1991 Teaching StandardsTeaching Standards – NCTM – NCTM

1992 NSF-Funded Integrated Standards-Based Curriculums1992 NSF-Funded Integrated Standards-Based Curriculums

1995 1995 Assessment StandardsAssessment Standards – NCTM – NCTM

1996 TIMSS – Third International Mathematics and1996 TIMSS – Third International Mathematics and

Science StudyScience Study

1996 MAP 2000 – Mathematics Field Test1996 MAP 2000 – Mathematics Field Test

1998 National High-Stakes Test Debate – California1998 National High-Stakes Test Debate – California

2000 2000 Principles & Standards for School Math – NCTMPrinciples & Standards for School Math – NCTM

MAP & MSIP – MAP & MSIP – Show-Me Standards, CurriculumShow-Me Standards, Curriculum

Frameworks, Grade-Level ExpectationsFrameworks, Grade-Level Expectations

The PrinciplesThe Principles

The Principles highlight the basic The Principles highlight the basic characteristics of a high quality characteristics of a high quality mathematics mathematics instructional programinstructional program and provide guidance for making and provide guidance for making educational decisionseducational decisions. .

The Principles cont.The Principles cont.

Equity. Equity. Excellence in mathematics education Excellence in mathematics education requires equity—high expectations and strong requires equity—high expectations and strong support for all students.support for all students.

Curriculum. Curriculum. A curriculum is more than a A curriculum is more than a collection of activities: it must be coherent, collection of activities: it must be coherent, focused on important mathematics, and well focused on important mathematics, and well articulated across the grades. articulated across the grades.

Teaching. Teaching. Effective mathematics teaching Effective mathematics teaching requires understanding what students know and requires understanding what students know and need to learn and then challenging and need to learn and then challenging and supporting them to learn it well. supporting them to learn it well.

The Principles cont.The Principles cont.

Learning. Learning. Students must learn mathematics with Students must learn mathematics with understanding, actively building new knowledge understanding, actively building new knowledge from experience and prior knowledge. from experience and prior knowledge.

Assessment. Assessment. Assessment should support the Assessment should support the learning of important mathematics and furnish learning of important mathematics and furnish useful information to both teachers and students. useful information to both teachers and students.

Technology. Technology. Technology is essential in teaching Technology is essential in teaching and learning mathematics; it influences the and learning mathematics; it influences the mathematics that is taught and enhances students' mathematics that is taught and enhances students' learning.learning.

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Standards

9

• Number and Operations

• Algebra

• Geometry

• Measurement

• Data Analysis and Probability

• Problem Solving

• Reasoning and Proof

• Communication

• Connections

• Representation

The StandardsThe Standards

Five Standards describe the Five Standards describe the mathematical mathematical contentcontent that students that students should learn to be successfulshould learn to be successful

The Content StandardsThe Content Standards

1.1. Number and OperationsNumber and Operations

2.2. AlgebraAlgebra

3.3. GeometryGeometry

4.4. MeasurementMeasurement

5.5. Data Analysis and ProbabilityData Analysis and Probability

1212

Content Content StandardsStandards

Across the GradesAcross the GradesNumberNumber

Algebra

Geometry

Measurement

Data Analysis and Probability

Pre-K–2 3–5 6–8 9–12

Numberand Operation

The StandardsThe Standards

Five Standards highlight the Five Standards highlight the mathematical mathematical processesprocesses that that students draw on to acquire and use students draw on to acquire and use their content knowledge. their content knowledge.

The Process StandardsThe Process Standards

6.6. Problem SolvingProblem Solving

7.7. Reasoning and ProofReasoning and Proof

8.8. CommunicationCommunication

9.9. ConnectionsConnections

10.10. RepresentationRepresentation

The make upThe make up

Each Standard is broken up into four Each Standard is broken up into four grade-level bands:grade-level bands:– Pre-K to 2Pre-K to 2ndnd Grade Grade– 33rdrd Grade to 5 Grade to 5thth Grade Grade– 66thth Grade to 8 Grade to 8thth Grade Grade– 99thth Grade to 12 Grade to 12thth Grade Grade

Each of the Content Standards Each of the Content Standards includes a set of expectations includes a set of expectations specific to that grade band.specific to that grade band.

How were they made?How were they made?

NCTM was founded in 1920.NCTM was founded in 1920. In 1989 NCTM released In 1989 NCTM released Curriculum Curriculum

and Evaluation Standards for School and Evaluation Standards for School MathematicsMathematics

Outlined extensive goals for teachers Outlined extensive goals for teachers and policy makers for the school and policy makers for the school discipline.discipline.

How were they made?How were they made?

In 1991, NCTM published the In 1991, NCTM published the Professional Professional Standards for Teaching MathematicsStandards for Teaching Mathematics

Described the elements of effective Described the elements of effective mathematics teachingmathematics teaching

In 1995 NCTM released the In 1995 NCTM released the Assessment Assessment Standards for School MathematicsStandards for School Mathematics

Established objectives against which Established objectives against which assessment practices can be measuredassessment practices can be measured

How were they made?How were they made?

From 1995 to 2000, NCTM rewrote From 1995 to 2000, NCTM rewrote and revised its three previous and revised its three previous documents into one released in 2000:documents into one released in 2000:

The Principles and Standards for The Principles and Standards for School MathematicsSchool Mathematics

A single resource that can be used to A single resource that can be used to improve mathematics curricula, improve mathematics curricula, teaching, and assessment teaching, and assessment

1919

Principles

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Describe particular features ofhigh-quality mathematics programs

•Equity

•Curriculum

•Learning

•Teaching

•Assessment

•Technology

Statement of Principles

The Equity Principle

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Excellence in mathematics education requires equity– high expectations and strong support for all students.

The Curriculum Principle

A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades.

The Teaching Principle

Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.

Statement of Principles

The Learning Principle

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Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.

The Assessment Principle

Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.

The Technology Principle

Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.

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School Mathematics Is Not Working Well Enough for Enough Students

Internationally (TIMSS, 1994-1995), our students are not mathematically competitive 4th grade – average 8th grade – below average 12th grade – among lowest of 21

at 25th percentile, like FIMS & SIMS particularly poor in Geometry better in creative constructed

responses questions

LOWER7 countriesLOWER

7 countries

SAME14 countries

SAME14 countries

HIGHER20 countries

HIGHER20 countries

Source: US TIMSS Research Center, 1996–1998Source: US TIMSS Research Center, 1996–1998

US 8thUS 8th

US 12th

US 4th

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Students Can Do Basics, ...

347 + 453347 + 453 90% 73%

Source: NAEP 1996Source: NAEP 1996

864 – 38864 – 38

… But Students Cannot Solve Problems

Ms. Yost’s class has read 174 books, and Mr. Smith’s class has read 90 books. How many more books do they need to read to reach the goal of reading 575 books?33%

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What Does Research Tell Us? 1

What we can’t expect from research … Standards are not determined by research, but are

instead statements of priorities and goals What is “best” cannot be proven by research. Research cannot imagine new ideas.

What we can expect from research … Research can influence the nature of the standard. Research can document the current situation. Research can document the effectiveness of new ideas. Research can suggest explanations for success or failure.

1 Hiebert, J. (1999) Relationships between research and the NCTM Standards, Journal for Research in Mathematics Education, 30(1):3-19.

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Do Skills Lead to Understanding?

Can Drill Help Develop Increase Mathematical Reasoning?

Can Calculators & Computers Increase Mathematical Reasoning?

Steen, L.A. (1999). Twenty questions about mathematical reasoning. in L.V. Stiff & F.R. Curcio (Eds), Developing mathematical reasoning in grades K-12: 1999 Yearbook (pp. 270-285). Reston, VA : NCTM.