The Changing Landscape
US Math Education
Hungary
Netherlands
Latvia
Slovak Republic
Japan
Luxembourg
France
Belgium
Canada
Norway
Germany
Macao
South Korea
China
Ireland
Hong Kong
China
Austria
Denmark
Finland
New Zealand
Iceland
Sweden
Poland
Czech Republic
Switzerland
Liechtenstein
Spain
Program for International Student Assessment
100%
75%
50%
32%
25%
%
Grade 8 Passing Rate
National Center for Educational Statistics -- 2007
60,000
46,286
45,000
30,000
15,000
11,533
0
Reading
Math
Georgia Grade 8 Students Not Passing State Test
www.doe.k12.ga.us -- 2008
100%
78%
75%
50%
25%
22%
0%
ELA
Math
Connecticut High Schools Not Making AYP
www.sde.ct.gov -- 2008
standards.nctm.org
Math Wars
TRADITIONAL
PROGRESSIVE
Procedures
Memorization
Worksheets
Text Books
Repetition
Concepts
Understanding
Manipulatives
Rubrics
Exploration
Math Wars, Latterell, Carmen M. -- 2005
Traditional Approach
Strengths
Easy Implementation
Systematic Instruction
Weaknesses
Not Very Engaging
Some Students do not Generalize
Math Wars, Latterell, Carmen M. -- 2005
Progressive Approach
Strengths
• Engaging Activities
• Emphasizes
Understanding
Weaknesses
• Hard to Implement
• Hard to Internalize
Principles
Math Wars, Latterell, Carmen M. -- 2005
Number of Topics per Grade
Top Achieving Countries
NCTM
39
37
35
34
24
25
24
25
20
17
15
18
16
8
3
1st
3
2nd
3rd
4th
5th
6th
7th
Grade
Center for Research in Math & Science Education, Michigan State University
8th
Grade 4 International
Test Question
80%
“There are 600 balls
in a box, and 1/3 of
the balls are red.
38%
How many red balls
are in the box?”
Percent Correct
Center for Research in Math & Science Education, Michigan State University
Changing Course
“Teachers face long lists of
learning expectations to
address at each grade level,
with many topics repeating
from year to year. Lacking
clear, consistent priorities and
focus, teachers stretch
to find the time to present
important mathematical topics
effectively and in depth.”
www.nctm.org/focalpoints
NCTM Now Recommends
Instruction should devote “the
vast majority of attention” to
the most significant
mathematical concepts.
Focus on developing problem
solving, reasoning, and critical
thinking skills.
Develop deep understanding,
mathematical fluency, and an
ability to generalize.
www.nctm.org/focalpoints
National Math Panel Report
“The manner in which
math is taught in the
U.S. is "broken and
must be fixed."
www2.ed.gov/about/bdscomm/list/mathpanel/reports.html
National Math Panel Recommendations
Math curricula should:
Be "streamlined and should emphasize a well-defined set of the
most critical topics in the early grades."
Emphasize "the mutually reinforcing benefits of conceptual
understanding, procedural fluency, and automatic recall of facts."
Teach with "adequate depth."
Have an "effective, logical progression from earlier, less
sophisticated topics into later, more sophisticated ones."
Have teachers regularly use formative assessment.
www2.ed.gov/about/bdscomm/list/mathpanel/reports.html
1. Screen all students and provide interventions
to students identified as at-risk.
2. Instructional materials for students should
focus intensely on in-depth treatment of whole
numbers.
3. Instruction during the intervention should be
explicit and systematic.
4. Include instruction on solving word problems
that is based on common underlying
structures.
5. Students should work with visual
representations.
6. Devote ten minutes in each session to fluent
retrieval of basic arithmetic facts.
7. Monitor student progress.
8. Include motivational strategies.
ies.ed.gov
For over a decade, research studies of mathematics education in high performing
countries have pointed to the conclusion that the mathematics curriculum in the
United States must become substantially more focused and coherent in order to
improve mathematics achievement in this country.
To deliver on the promise of common standards, the standards must address the
problem of a curriculum that is “a mile wide and an inch deep.”
These Standards are a substantial answer to that challenge.
www.corestandards.org
Kindergarten Standards
www.corestandards.org
100%
75%
50%
25%
13%
%
Colleges Providing Sufficient Training
www.nctq.org
Massachusetts Teacher Licensing
Teacher Candidates
Passing License Test
100%
75%
50%
25%
%
27%
“Education leaders said that the
high failure rate reflects what
they feared, that too many
elementary classroom and
special education teachers do
not have a strong background in
math and are in many ways
responsible for poor student
achievement in the subject, even
in middle and high schools.”
Boston Globe
Massachusetts Reading & Math
% of Proficient & Advanced Students
www.doe.mass.edu/mcas/2009/results/summary.pdf -- 2009