“If learning doesn’t happen, there

has been no teaching. The

actions of learning and teaching

are inseparable.”Fosnot, Dolk, 2001

“Enabling students to learn with understanding depends heavily on the opportunities that a teacher provides to his or her students.”

Fagan, 2005

“The assumption was that math facts had to be taught before problem solving could be. But the reverse approach, in fact, works. The techniques of teaching math facts in the context of real experiences is succeeding beyond anyone’s expectation.”

Berliner, 1990

“It boils down to this---

if you can’t talk about math, you are unlikely to do it well.

Story problems, anyone?”Newsweek 1996

“Math is not about numbers or the right answer.

Math is about discovery.and exploring different ways of

thinking.It’s about teaching your students that

they can solve anything.And giving them the tools to make it

possible.”Unknown

“There are two kinds of teachers:

the kind that fill you up with so much quail shot that you can’t move, and the kind that just gives you a little prod behind and you jump to the skies.”

Robert Frost

“The greatest sign of success for a teacher….

is to be able to say:

The children are now working as if I did not exist.”

Montessori

“HOW

a student learns

is as important as

WHAT

a student learns.

WHAT

a student learns depends on

HOW

the student learns it.”NCTM Standards

“Mathematics is no more

computation than typing is to literature.”

John Allen Paulos

“It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.”

Paul Halmos

“Arithmetic is being able to count up to twenty without taking off your shoes.”

Mickey Mouse

“What’s one and one and one and one and one and one and one and one and one and one?

I don’t know, said Alice. I lost count.

She can’t do addition, said the Red Queen.”

Lewis Carroll

“A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”

G. H. Hardy

“We cannot hope that many children will learn mathematics unless we find a way to share our enjoyment and show them its beauty as well as its utility.”

Mary Beth Ruskai

“Mathematics, in the common lay view, is a static discipline based on formulas…But outside the public view, mathematics continues to grow at a rapid rate… the guide to this growth is not calculation and formulas, but an open-ended search for pattern.”

Lynn A. Steen

“Calculators can only calculate – they cannot do mathematics.”

John Van De Walle

“Attitudes create a self perpetuating cycle:Children with positive beliefs about math perform well, which makes them like math and feel good about themselves; students with negative beliefs fall farther behind, which reinforces their low expectations and sense of failure.”

Nancy Kober

“Children do not learn by doing…

They learn by

thinking,

discussing,

and

reflecting

on what they have done.”Dr. William Speer

“Learning Mathematics:In reality, no one can TEACH

mathematics.Effective teachers are those who can

stimulate students to LEARN mathematics.

Educational research offers compelling evidence that students learn

mathematics well only when they CONSTRUCT their own

mathematical understanding.”Everybody Counts

“Connections are crucial. They are the bridges between informal and formal understandings. Some are formed through conversation, some through writing, some through drawing. All are formed by the mind of the learner, often with the guidance of the teacher.”

Unknown

“The soundest way to convince students of the relevance of math is not by saying so, but by offering a curriculum that is relevant to today’s job and life demands, one that builds students’ problem-solving skills, challenges their powers of reasoning, and incorporates technology.”

Nancy Kober

“Skills are to mathematics what scales are to music or spelling is to writing. The objective is to write, to play music, or to solve problems – not just master skills.”

Everybody Counts