1
If learning doesnt happen, there has been no
teaching. The actions of learning and teaching
are inseparable. Fosnot, Dolk, 2001
2

• Enabling students to learn with understanding
  depends heavily on the opportunities that a
  teacher provides to his or her students.
• Fagan, 2005

3

• 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 anyones
  expectation.
• Berliner, 1990

4

• It boils down to this---
• if you cant talk about math, you are unlikely to
  do it well.
• Story problems, anyone?
• Newsweek 1996

5

• Math is not about numbers or the right answer.
• Math is about discovery.
• and exploring different ways of thinking.
• Its about teaching your students that they can
  solve anything.
• And giving them the tools to make it possible.
• Unknown

6

• There are two kinds of teachers
• the kind that fill you up with so much quail shot
  that you cant move, and the kind that just gives
  you a little prod behind and you jump to the
  skies.
• Robert Frost

7

• 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

8

• 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

9

• Mathematics is no more
• computation than typing is to literature.
• John Allen Paulos

10

• 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

11

• Arithmetic is being able to count up to twenty
  without taking off your shoes.
• Mickey Mouse

12

• Whats one and one and one and one and one and
  one and one and one and one and one?
• I dont know, said Alice. I lost count.
• She cant do addition, said the Red Queen.
• Lewis Carroll

13

• 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

14

• 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

15

• Mathematics, in the common lay view, is a static
  discipline based on formulasBut 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

16

• Calculators can only calculate they cannot do
  mathematics.
• John Van De Walle

17

• 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

18

• Children do not learn by doing
• They learn by
• thinking,
• discussing,
• and
• reflecting
• on what they have done.
• Dr. William Speer

19

• 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

20

• 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

21

• 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 todays
  job and life demands, one that builds students
  problem-solving skills, challenges their powers
  of reasoning, and incorporates technology.
• Nancy Kober

22

• 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