Illustrated Math Dictionary

## Tuesday, 3 December 2013

## Saturday, 30 November 2013

## Friday, 29 November 2013

## Thursday, 28 November 2013

## Wednesday, 27 November 2013

## Tuesday, 26 November 2013

## Monday, 25 November 2013

The focus of the Math Specialist In
International Schools (MSIS) project is to build teacher conceptual
understanding of mathematics. Thanks to last weeks rich engaging discussions of
the Amman cohort, I decided to share some thoughts on the importance of
what they (all of the cohorts) are doing.

Recently, a parent asked me why her child was
not being taught math the way she had learned it. I was troubled by the
next statement of this young mother ….this “new” math….. Troubled
because this is not “new” math! Teaching math conceptually (teaching for
understanding) has been around for a long time! More recently, in the
Principles and Standards for School Mathematics (2000). NCTM, one of the six
principles states: “

**Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge**.”
In 2001, The National Research Council in its
document Adding It Up: Helping Children Learn Mathematics used the term
mathematical proficiency to describe the successful learning of mathematics.
They broke down mathematical proficiency into five components. Conceptual
understanding, procedural fluency, strategic competence, adaptive
reasoning, and productive disposition.

Sadly, after decades of studies on the
learning of mathematics, rote learning still appears to be the norm. Rote
learning is not the answer in mathematics. Learning only to perform mathematics
procedures (algorithms) allows students to find answers to a set of rules. This
is not the essence of mathematics.

For example take division, How did you learn
to divide whole numbers? Fractions, decimals, integers? Did you learn a
particular rule or did you learn division as a mental process that can be
completed using any number of strategies? Division problems can be solved many
ways, repeated subtraction, repeated addition, using a number line, using
objects, and models. For example the procedure using for dividing fractions,
“invert and multiply” is only one of many procedures. The concept of division
and the procedure of solving division problems are not the same thing!

It is important we teach for understanding.
This does not mean that procedures are not learned. They are learned, but not
without conceptual understanding. A great benefit of knowing a procedure (How
it works) and understanding the concept (Why it works) is that if you forget a procedure,
understanding why it works helps in reconstructing the forgotten procedure. On the other hand, if procedural
knowledge is the limit of one’s learning, there is no way to reconstruct a
forgotten procedure. Conceptual understanding in mathematics, along with
procedural skill, is much more powerful than procedural skills alone.

Yes, our goal is to make certain
students acquire procedural fluency (the How), the conceptual
understanding (the Why), and equally important to experience rich problem
solving (Where it works)

## Sunday, 24 November 2013

## Saturday, 23 November 2013

## Friday, 22 November 2013

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