The National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics

1
The National Council of Teachers of Mathematics
(NCTM)Principles and Standards for School
Mathematics
Dr. Robinson, EEX 4251, Spring 2008
2
The PSSM

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

3
Who was Involved?

• Teachers
• School administrators
• Mathematics supervisors
• University mathematicians
• Mathematics educators
• Researchers

4
Timeline

• 1951 Max Beberman UICSM Project
• 1957 SPUTNIK
• 1960 New Math
• 1963 FIMS First International Mathematics
  Study
• 1969 NAEP National Assessment of Ed Progress
• 1973 Why Johnny Cant Read Morris Kline Back
  to Basics
• 1975 NACOME
• 1980 Agenda For Action NCTM Pragmatic
  Problem Solving
• 1982 SIMS Second International Mathematics
  Study
• 1983 A Nation at Risk

5
Timeline

• 1989 Curriculum Standards NCTM
• Everybody Counts Lynn Steen NRC
• 1991 Teaching Standards NCTM
• 1992 NSF-Funded Integrated Standards-Based
  Curriculums
• 1995 Assessment Standards NCTM
• 1996 TIMSS Third International Mathematics
  and
• Science Study
• 1996 MAP 2000 Mathematics Field Test
• 1998 National High-Stakes Test Debate
  California
• 2000 Principles Standards for School Math
  NCTM
• MAP MSIP Show-Me Standards, Curriculum
• Frameworks, Grade-Level Expectations

6
The Principles

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

7
The Principles cont.

• Equity. Excellence in mathematics education
  requires equityhigh expectations and strong
  support for all students.
• Curriculum. A curriculum is more than a
  collection of activities it must be coherent,
  focused on important mathematics, and well
  articulated across the grades.
• Teaching. Effective mathematics teaching requires
  understanding what students know and need to
  learn and then challenging and supporting them to
  learn it well.

8
The Principles cont.

• Learning. Students must learn mathematics with
  understanding, actively building new knowledge
  from experience and prior knowledge.
• Assessment. Assessment should support the
  learning of important mathematics and furnish
  useful information to both teachers and students.
  
• Technology. Technology is essential in teaching
  and learning mathematics it influences the
  mathematics that is taught and enhances students'
  learning.

9
Standards

• Number and Operations
• Algebra
• Geometry
• Measurement
• Data Analysis and
• Probability

• Problem Solving
• Reasoning and Proof
• Communication
• Connections
• Representation

9
10
The Standards

• Five Standards describe the mathematical content
  that students should learn to be successful

11
The Content Standards

1. Number and Operations
2. Algebra
3. Geometry
4. Measurement
5. Data Analysis and Probability

12
Content StandardsAcross the Grades
Pre-K2
35
68
912
Number and Operation

• Number

Algebra
Geometry
Measurement
Data Analysis and Probability
13
The Standards

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

14
The Process Standards

1. Problem Solving
2. Reasoning and Proof
3. Communication
4. Connections
5. Representation

15
The make up

• Each Standard is broken up into four grade-level
  bands
• Pre-K to 2nd Grade
• 3rd Grade to 5th Grade
• 6th Grade to 8th Grade
• 9th Grade to 12th Grade
• Each of the Content Standards includes a set of
  expectations specific to that grade band.

16
How were they made?

• NCTM was founded in 1920.
• In 1989 NCTM released Curriculum and Evaluation
  Standards for School Mathematics
• Outlined extensive goals for teachers and policy
  makers for the school discipline.

17
How were they made?

• In 1991, NCTM published the Professional
  Standards for Teaching Mathematics
• Described the elements of effective mathematics
  teaching
• In 1995 NCTM released the Assessment Standards
  for School Mathematics
• Established objectives against which assessment
  practices can be measured

18
How were they made?

• From 1995 to 2000, NCTM rewrote and revised its
  three previous documents into one released in
  2000
• The Principles and Standards for School
  Mathematics
• A single resource that can be used to improve
  mathematics curricula, teaching, and assessment

19
Principles
Describe particular features of high-quality
mathematics programs

• Equity
• Curriculum
• Learning

• Teaching
• Assessment
• Technology

19
20
Statement of Principles

• The Equity Principle

Excellence in mathematics education requires
equity high expectations and strong support for
all students.
21
Statement of Principles

• The Learning Principle

Students must learn mathematics with
understanding, actively building new knowledge
from experience and prior knowledge.
22
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

HIGHER 20 countries
US 4th
SAME 14 countries
US 8th
US 12th
LOWER 7 countries
Source US TIMSS Research Center, 19961998
23
Students Can Do Basics, ...
347 453
864 38
But Students Cannot Solve Problems
Ms. Yosts class has read 174 books, and Mr.
Smiths class has read 90 books. How many more
books do they need to read to reach the goal of
reading 575 books?

• Source NAEP 1996

24
What Does Research Tell Us? 1

• What we cant 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.
25
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.