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From: They're Counting on Us: A parent's guide to mathematics education
Basic Facts
Are
today's children expected to know their number facts? Absolutely!
Knowing basic facts is as important today as it was in our school days.
While we may have learned them with flash cards and proved it with
timed tests, there are many other ways to learn basic facts.
When
a third-grade teachers asked her students how they knew their
multiplication facts so well, the students told her that it was from
playing Circles and Stars—a game that students play by rolling number
cubes. As students play this game, they have many changes to learn that
6 circles filled with 4 stars each is 24. They also learn that 4
circles filled with 6 stars each is also 24. They record their results:
6 x 4 = 24 or 4 x 6 = 24.
Another way that students learn their
facts is by using objects. Making a rectangular arrangement of colored
tiles that is 6 tiles in one direction and 4 tiles in another provides
students another way to learn that 6 x 4 = 24. This method is helpful
because it allows students to visualize the multiplication facts,
making them easier to remember.
Students also learn from
real-life situations. If each of six friends gets four cookies, how
many cookies do you need altogether? Very young students can act out a
problem like this, or model it with blocks and beans, or draw pictures
to show their solutions.
As they learn mathematical games, make
physical models, and solve real-life problems, students learn number
facts in a way that is enjoyable and builds confidence in using basic
facts.
But basic facts are not enough. We also want our children
to grow up being able to solve complex problems. A well-conceived,
well-taught mathematics program has to address both goals if our
students are to be competent, confident mathematical thinkers.
Computation
Besides
knowing the basic facts, students need to calculate: to understand and
use addition, subtraction, multiplication, and division. Accurate
calculation is another goal that supports complex problem solving.
We
used to think that students had to be proficient in computing before
they were able to solve complex problems. But we have seen that
students can learn to compute while problem solving. New instructional
materials (see Materials for Making Sense of Math) include problems
such as this one: Suppose Emilio and then of his friends want to share
147 jelly beans. How many should each one get? In years past we would
not consider posing this problem until students were able to divide 147
by 11. Now the study of division might begin with such a question.
We've found that children use a variety of ways to solve this and in
doing so develop an understanding of how to divide. As students examine
the different ways this problem can be solved, they find that the
traditional long division format is just one way to solve it.
Older
students also work with mathematical ideas tied to meaningful
situations. As middle-grades students explore the ways that numbers
grow by doubling, they begin to learn about exponential growth and how
that differs from growth that increases by the same amount each time.
If your allowance on the first day of each month is one penny and
doubles every day of that month, will you be better off than if you
were given a monthly allowance of $1 per day? Connecting mathematics to
situations provides a purpose for learning mathematics. Students who
experience mathematics in meaningful situations will be able to apply
mathematical ideas and skills to a range of problem-solving situations.
By
studying a curriculum that develops skills and computation, and that
also has regular opportunities to solve complex and interesting
problems, students gain a deeper understanding of what they are doing.
Beyond Arithmetic
Often,
when we talk about the basics, we talk only about basics as they relate
to number. The word "basics" triggers thoughts about number facts and
procedures. But mathematics is much more than that. Today's basics
include a broad understanding of geometric ideas, knowing how to
interpret and display data and how to use the technology used in the
workplace. The scope of what is basic needs to be regularly reexamined
to meet the challenging demands the world puts on its citizens, and the
workplace puts on its employees. We're preparing our students for that
world and the school vision of basics must match the expanded vision of
the workplace.
Circles and Stars
- The first roll tells how many circles to draw.
- The second roll tells how many stars to draw in each circle.
- The winner for the round is the one who drew thee most stars.
(In the "official" version, the winner of the game is the one who drew
the most stars altogether in seven rounds. This give addition practice
as well.)
From Math by All Means: Multiplication, Grade 3 by Marilyn Burns.
©1991 Math Solution Publications. Used with permission.
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This Page was last updated: Friday, February 27, 2004 at 12:02:07 PM
This page was originally posted: 5/23/2001; 3:18:29 PM.
Copyright 2008 cmcmath
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