From Math by All Means: Multiplication, Grade 3, by Marilyn Burns
Return to Handbook.
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 teacher 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 chances to learn that 6 circles filled with 4 starts 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 .
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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 of the round is the one who draws the most
stars. (In the "official" version, the winner of the game is the
one who drew the most stars altogether in seven rounds. This
gives addition practice as well.) From Math by All Means: Multiplication, Grade 3, by Marilyn Burns |
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.
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 ten 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.
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.
| Last Updated: 18 Aug 09 |