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Topic: Other Issues for Grades 4 and 5
Replies: 131   Last Post: Oct 25, 2006 7:55 PM

 Messages: [ Previous | Next ]
 Cynthia Garland-Dore Posts: 68 Registered: 12/3/04
Re: How it works?
Posted: May 5, 2001 1:19 PM

Knowing how to drive a car and fixing a car are very different. Using
a computer and fixing something wrong on the computer are very
different skills. What do you need to know to drive a car or use a
computer? What decisions do you need to make very day?

In mathematics, students have learned to compute by specific sets of
rules for years. The part that's been difficult for some of these
children has been when they have to make decisions on what procedures
to use and when to apply them in any other settings other than
isolated computation. They often made errors using the procedures
which led them to incorrect answers and they didn't even realize it
because they lacked number sense.

Children do need to know how the basic operations work to really have
the knowledge to use them meaningfully. They need to develop a
variety of operational procedures to solve a problem. It's important
to realize the relationships between operations. They need to be sense
makers to make decisions about how to solve the problems. That requires more than knowledge of procedures.

I've only addressed number operations so far. I guess because it seems
to be the topic most associated with mathematics. However, I
think the same for all areas of mathematics and learning. Students
need a variety of spatial experiences to understand geometry ideas.
They need experiences with data to understand how it's collected and
interpreted. Many of the ideas explored in these experiences then link
to other mathematical experiences. It's not that all children are
being trained to be formal mathematicians. We all need these skills
in real life. We use logical reasoning skills developed through
mathematics every day when we try to solve problems. To know means to
think and reason.

I think we use sense making when we use our cars and computers too.
We make connections and learn more with our many varied experiences. Our knowledge base grows through these experiences so we
are not just following a set of procedures. We are generalizing and
applying knowledge we have acquired through a variety of experiences.
Computers and cars work no better than the operator using them. If the
operator can think and reason, then they have many more options in the
ways they can drive a car (drive in different settings like the city,
or when it snows; drive cars with automatic or standard transmissions;
become a bus driver or truck driver) or use a variety a computer can
provide (use a word processor; send email; search the internet; build
a database; developing web sites; set up a mailing list). Learning
never stops, even when it comes to cars and computers. I think what
makes learning engaging and some times even fun is learning how things
work.

mathematical learning:

Developing Computational Fluency with Whole Numbers in the Elementary
Susan Jo Russell
http://www.terc.edu/investigations/relevant/html/CompFluency.html

The Mathematical Miseducation Of America's Youth By Michael T.
Battista
http://www.pdkintl.org/kappan/kbat9902.htm

Modes Of Teaching And Ways Of Thinking
Anne Goodrow
http://www.terc.edu/investigations/impact/html/eval-2.goodrow.html

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