An Update:National Council of Teachers

of MathematicsUnited States Department of Education

MSP Regional ConferenceApril 1, 2009

Henry (Hank) Kepner, Jr.President, National Council of Teachers of Mathematics

Professor of Education and MathematicsUniversity of Wisconsin-Milwaukee

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First Things First

• A strong K–12 mathematics education for all students is important for our nation’s economic stability, future national security, and workforce productivity.

• Everyone must be mathematically literate and recognize the importance of mathematics learning. NCTM believes that teachers and what they do in the classroom are at the heart of making this vision a reality.

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Competitiveness

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From Secretary Duncan

• “Providing every child in America with a good education is both a moral imperative and an economic imperative. It’s also a matter of social justice. It is the civil rights issue of our generation—the one and only way to overcome the differences of wealth, background, and race that divide us and deny us our future.

• “I came to Washington with one goal—to give every single child in America the very best education possible.”

— Secretary of Education Arne Duncan

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Mathematics for all students

• NCTM supports programs and practices that encourage the acquisition of high-level mathematics skills by a wide range of overlapping populations:– children of poverty, – English language learners, – urban and rural students, – students of all races and ethnicities, – students with learning difficulties, – students who are female, and – students who are mathematically gifted.

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And yet…

• Important, but NOT for me– Parents are aware of the importance of

math, but remain complacent– Students pay lip service to the

importance of higher level math…

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NCTM Strategic Priorities

• Curriculum• Equity• Research• Professional Development• Advocacy

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Curriculum and Assessment

• Increase efforts to focus and align the PreK-8 curriculum to achieve coherence.

• NCTM supports developing stronger intervention programs and assessments, with an emphasis on the ongoing use of formative assessments.

an NMAP recommendation

an NMAP recommendation

Curriculum

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The Intent

To address:

• Long lists of mathematics learning expectations at the state level with little consistency across states

• Emphasis on breadth resulting in lack of depth, i.e. “mile wide, inch deep” curricula in mathematics

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Number of 4th-Grade Learning Expectations per State by Content Strand

Number&

Operation

Geometry

Measurement Algebra

Data Analysis,

Probability & Statistics

Total Number of Learning

Expectations

California 16 11 4 7 5 43

Texas 15 7 3 4 3 32

New York 27 8 10 5 6 56

Florida 31 11 17 10 20 89

Ohio 15 8 6 6 13 48

Michigan 37 5 11 0 3 56

New Jersey 21 10 8 6 11 56

North Carolina 14 3 2 3 4 26

Georgia 23 10 5 3 4 45

Virginia 17 8 11 2 3 41

Reys, et al., 2006

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The Rationale

• Identify key mathematical ideas across preK-8 that prepare students for future mathematics, particularly algebra

• Identify the mathematics that should be the focus of instruction and student learning at each grade level, preK-8

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NCTM Curriculum Principle

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

Principles and Standards for School Mathematics, p. 14

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NCTM Curriculum Principle

“…a well-articulated curriculum gives teachers guidance regarding important ideas or major themes, which receive special attention at different points in time. It also gives guidance about the depth of study warranted at particular times and when closure is expected for particular skills or concepts.”

Principles and Standards for School Mathematics, p. 16

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What’s a Focal Point?

• A major mathematical topic of emphasis for a grade level;

• More than a single objective, standard, expectation, or indicator;

• An important link in the chain of building mathematical understanding, preK-8;

• Not an element of a list of discrete topics to check off as mastered by students.

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34x 25

34x 25

17068 . 850

600 = 20x30

150 = 5x30

85020 = 5x4

80 = 20x4

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(3x+4)(2x+5) = (3x+4)(2x) + (3x+4)(5)

= (3x)(2x)+ 4(2x)+(3x)5+(4)5

2x

5

3x 4

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What do we know now?

Use status:

• Over half of the states• Most publishers• Teacher education programs, textbooks• Over 1,200,000 downloads later• Curriculum Center Survey results• Most popular NCTM publication – sales

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And…

• Focus on Grades PK-2• Focus on Grades 3-5• Focus on Grades 6-8• This month:

– Focus on Grade:•3•4•5

• And more to follow

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Concerns and Challenges

• Confusion – Understanding what is meant by a focal point – target, area of emphasis?

• What does it mean to focus?• Will states and school districts omit

curricular topics?• When will the state tests change?• What about high school?

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NMAP and Curriculum

• Increase efforts to streamline, focus and align the PreK-8 curriculum to achieve coherence.

• Validation

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NMAPConceptual Knowledge & Skills

• Curriculum focus and coherence PreK-8• Closure with topics• Major Topics of School Algebra

– Should be the focus of school algebra – however algebra is “presented.”

• Proficiency with the Critical Foundations– Whole numbers, fractions, particular

aspects of geometry and measurement.– Benchmarks

• Access to algebra• Teacher background

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13 yr olds 17 yr olds

7 8

24 37

28 21

27 15

14 16

Estimate:

12 7

13 8+

1

2

19

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I Don’t know

NAEP (NCTM)

•Algebra is more than a set of procedures for manipulating symbols.

Algebraic concepts and skills should be a focus across the PK-12 curriculum.

All students should have opportunities to develop algebraic reasoning.

Algebra when ready.Position of NCTM (Sept. 2008)

Algebra: What, When, and for Whom

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Early Algebra

1st Grade Story: Yolanda has 5 candies. Juan gives her some more. Now she has 12. How many did Juan give her?

• In Algebra 1 textbook:5 + x = 12

• Children should learn:5 + what = 12

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Curriculum

Focus in High School Mathematics Reasoning

and Sense MakingAnd Topic Books:

Algebra Geometry

Data Analysis & ProbabilityFall 2009

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NCTM’s Goal

• Guidance for schools and states in the design of curricula and assessment that target the most important topics.

• Focus for teachers that gives sufficient time for students to understand concepts and develop and apply skills necessary for future mathematics.

• Clear direction for students and parents on the importance of deep understanding of particular topics at each grade level.

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Equity

• Equity Position Statement• Equity Summits 2008 and 2009• Iris Carl Annual Equity Address• Equity and Publications

– Online issue of JRME– TCM focus issue

• Equity FOY for 2008-09• Equity theme of 2009 Annual Conference and

Exposition• And more!!!

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Linking Research and Practice

• Director of Research:Dr. Judith Quander

• Research Analyses, Briefs and Clips at nctm.org/research.aspx

NCTM ResearchNCTM ResearchClips and BriefsClips and Briefs

HomeworkHomework

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Briefs provide the research in more detail…

NCTM ResearchNCTM ResearchClips and BriefsClips and Briefs

Formative AssessmentFormative Assessment

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Linking Research and Practice

• NSF-supported Research Agenda Conference– Summer 2008;Report & Follow-Up 2009– Mathematicians, Mathematics

Educators, Supervisors, Teachers, Cognitive Psychologists, Policy Makers

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Professional Development

• E-learning programs reached 6 continents, 50 states, and 20 different countries

• 18 e-workshops, with over 700 sites connected• 4 NCATE online report compiler training sessions• Lesson Study course for teachers of grades 3-8, with

participants from 12 states• 7 Learn-and-Reflect sessions at NCTM Conferences

and Affiliate Conferences• To Come: Professional Development Continuum

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Professional Development

On the Web• Large-Scale Assessment tool• Intervention• President’s Messages• Position Statements (2008)

– Mentoring– Early childhood– Equity– Technology– Algebra

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Advocacy and Outreach

• Senate and House STEM Caucus• National Math Advisory Panel• Testimony before Congress – re: focus and

coherent curriculum; NMAP Report• Discussion with Obama transition team• Math Now legislation• Board meetings with

– Deputy Secretary Ray Simon (2008)– Patricia O’Connell Johnson (2009)

• U.S. Department of Education – Doing What Works

• Much more…

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Emerging Issues

• What algebra? When?• Early childhood mathematics education• Intervention• Elementary Mathematics Specialists• Special Needs: ELL and Special

Education• Urban-specific Needs• High School and College articulation

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What are Intervention Programs?

• Structured plans for providing instructional activities and materials to support students’ learning

• Additional instruction on content that has already been introduced in the classroom

• Intended to boost—not supplant or copy—regular classroom instruction

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Intervention:Instructional Actions

• Can occur in a variety of settings:-Whole-class -During school-One-on-one -Before/after

school-With a tutor -In summer

school

• Leads to follow-up assessment– Have the actions been successful?

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What is Remediation?

Actions taken to reverse established patterns of achievement by students who are already struggling or failing and who need intensive, long-term help.

• Supplemental instruction on content students are expected to have mastered but have not

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What is Intervention?

Plan of action implemented by an instructor on behalf of students who may need extra help or acceleration

• Students’ difficulties or strengths are in early stages

• Intervention ideally addresses weaknesses or strengths before they become a problem for the student

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nctm.org/intervention.aspx

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NMAP & Learning NMAP & Learning ProcessesProcesses

• Preschool background;• Need for the curriculum to develop conceptual

understanding, computational fluency, and problem solving;

• Importance of computational proficiency – facts, standard algorithms, and properties;

• Fractions;• Role of student effort;• Diverse learners;• Readiness.

We NeedElementary School

Mathematics SpecialistsNOW!

NCTM News Bulletin

Questions?

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f

hkepner@nctm.org