| Term |
What
they say |
What
they mean |
| Standards-based |
Based on high standards
that would achieve international competence. |
Not based on local,
state, national or international standards of excellence. Based
on National Council of Teachers of Mathematics (NCTM) Standards. |
| Research-based |
Based on high quality
research showing positive results. |
Based on research
conducted by the authors, and others who promote NCTM Standards,
without any EVIDENCE of success. |
| Brain-based |
Based on the latest
cognitive research conducted by modern brain scientists. |
Based on constructivist
psychology dating back to the early 1900's. Directly based
on 1960's theories by Jean Piaget. Cognitive biologists
do not agree with these theories. |
| Real-life Problem
Solving |
Application of mathematics
to real world situations. |
Long, irrelevant story
problems with very simple answers that are guaranteed to distract
students away from the math lesson. Students with reading
deficiencies, and English Language Learners, who could otherwise
achieve in math, are lost in the words. Method to prevent practice
of skills. |
| Balanced Instruction |
Include time for whole-group
instruction as well as small group, partner, or individual activities.
Balance teacher-directed instruction with opportunities for open-ended,
hands-on explorations, long-term projects and on-going practice.
|
Students 'discover'
math by themselves while the facilitator watches in the wings.
Takes time away from other subjects.
|
| Multiple Methods for
Basic Skills Practice |
Provide numerous methods
for basic skills practice and review. |
Play games (see below).
Enroll at Kumon.
|
| Emphasis on Communication |
Students are encouraged
to explain and discuss their mathematical thinking, in their own
words. |
Students read and
write about math rather than master math. |
| Enhanced Home/School
Partnerships |
Provide opportunities
for family members to participate in the students' mathematical
learning. |
Require parents to
teach the basics at home or pay $100/month to Kumon or Sylvan. |
| Appropriate Use of
Technology |
Learning is extended
and enhanced through the use of calculators |
Their words from the
Teacher's Manual:
"Sensible adults reach for calculators whenever they need
to multiply with numbers that are not 'easy'."
|
| Games |
Frequent practice
is necessary to attain strong mental arithmetic skills and reflexes. |
Enjoying math is more
important than learning math. |
| Invented Strategies |
Students should be
provided with opportunities to invent algorithms. |
Students should 'discover'
thousands of years of mathematics theory by themselves. They should
not be encouraged to use the strategies required in Algebra
and Calculus. Those strategies can be learned in remedial college
classes. |
| Algoritm |
A set of step-by-step
instructions for… carrying out a computation. |
Anything but
the accepted standard US algorithms. |