Transcript MAE 4330 - Dr. Robinson

The National Council of
Teachers of
Mathematics (NCTM)
Principles and Standards
for School Mathematics
Dr. Robinson, EEX 4251, Spring 2008
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).
Who was Involved?
– Teachers
– School administrators
– Mathematics supervisors
– University mathematicians
– Mathematics educators
– Researchers
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 Can’t 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

1987 J. R. Flanders analysis of textbooks – prior to algebra
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
The Principles

The Principles highlight the basic
characteristics of a high quality
mathematics instructional program and
provide guidance for making educational
decisions.
The Principles cont.

Equity. Excellence in mathematics education requires

Curriculum. A curriculum is more than a collection of

Teaching. Effective mathematics teaching requires
equity—high expectations and strong support for all
students.
activities: it must be coherent, focused on important
mathematics, and well articulated across the grades.
understanding what students know and need to learn
and then challenging and supporting them to learn it
well.
The Principles cont.

Learning. Students must learn mathematics with

Assessment. Assessment should support the learning

Technology. Technology is essential in teaching and
understanding, actively building new knowledge from
experience and prior knowledge.
of important mathematics and furnish useful information
to both teachers and students.
learning mathematics; it influences the mathematics that
is taught and enhances students' learning.
Standards
• Number and Operations
• Algebra
• Geometry
• Measurement
• Data Analysis and
Probability
9
• Problem Solving
• Reasoning and Proof
• Communication
• Connections
• Representation
9
The Standards

Five Standards describe the mathematical
content that students should learn to be
successful
The Content Standards
1.
2.
3.
4.
5.
Number and Operations
Algebra
Geometry
Measurement
Data Analysis and Probability
Content Standards
Across the Grades
Pre-K–2
Number
and Operation
Algebra
Geometry
Measurement
Data Analysis
and Probability
12
Numb
er
3–5
6–8
9–12
The Standards

Five Standards highlight the mathematical
processes that students draw on to
acquire and use their content knowledge.
The Process Standards
6.
7.
8.
9.
10.
Problem Solving
Reasoning and Proof
Communication
Connections
Representation
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.
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.
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
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
Principles
Describe particular features of
high-quality mathematics programs
19
•Equity
•Teaching
•Curriculum
•Assessment
•Learning
•Technology
19
Statement of Principles
The Equity Principle
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.
20
Statement of Principles
The Learning Principle
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.
21
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
20 countries
US 4th
US 8th
SAME
14 countries
US 12th
Source: US TIMSS Research Center, 1996–1998
HIGHER
LOWER
7 countries
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Students Can Do Basics, ...
347 + 453
90%
864 – 38
73%
… But Students Cannot Solve Problems
33%
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?
Source: NAEP 1996
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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 :
25
NCTM.