so many of them signed the petitions. By the time the teachers were told anything about the secret campaign, it was all over. The women, supported and organized by the extreme traditionalists, had scared enough parents and convinced the school board that the teachers must go back to teaching traditionally. Now desks are in rows, teachers lecture, students silently copy methods and then practice with lots of examples, and the problem solving that students used to love is no longer in evidence. The teachers at the school were demoralized and defeated.
There were two types of books that were at the center of this. Both introduced students to the same mathematical methods and procedures, but the IMP books attempt to do so in a way that made the mathematics more meaningful for students. Consider, for example, the way that the IMP book and the traditional book (brought in by the parent activists) introduced algebraic variables to the students. The traditional book begins with a brief example of rental charges at an ocean shop and then has the following text:
The letter h stands for the hours shown in the table: 1, 2, 3, or 4. Also, h can stand for other hours not in the table. We call h a variable.
A variable is a symbol used to represent one or more numbers. The numbers are called values of the variable . An expression that contains a variable, such as the expression 4.50 × h, is called a variable expression . An expression that names a particular number, such as 4.50 × 4, is called a numerical expression , or numeral.
Another way to indicate multiplication is to use a raised dot, for example, 4.50 • 4. In algebra, products that contain a variable are usually written without the multiplication sign because it looks too much like the other x, which is often used as a variable. 7
The traditional book gives two pages of explanations like these before presenting twenty-six “oral exercise” questions and forty-nine “written exercise” questions, 8 such as:
Simplify 9 + (18 – 2) and 2 • (b + 2)
In contrast, the IMP book introduced students to variables through a particular situation—that of the nineteenth-century settlers who traveled from Missouri to California to set up life on the West Coast. The students are told, “You will encounter some very important mathematical ideas—such as graphs, different use of variables, lines of best fit, and rate problems—as you travel across the continent.” 9 They are then given various exercises that require them to represent the settlers’ situations using mathematical tools such as graphs and variables. For example, the students are told about families and some general conventions, such as “anyone more than fourteen years old is considered an adult.” 10 They are then introduced to variables through this question:
The Hickson household contains 3 people of different generations. The total age of the 3 family members is 90.
a) Find reasonable ages for the 3 Hicksons.
b) Find another reasonable set of ages for them.
One student in solving this problem wrote:
C + (C + 20) + (C + 40) = 90
What do you think C means here?
How do you think the student got 20 and 40?
What set of ages do you think the student came up with? Try this question, it can be solved in many ways. 11
In the IMP curriculum, students are gradually introduced to the concept of a variable—one of the most important concepts in the mathematics curriculum—before being asked to interpret and use variables in representing a situation mathematically. The students are also encouraged to discuss variables, exploring their meaning and when they are used, and generally to raise any questions or problems they have. The traditional curriculum, by contrast, tells students what variables are on page 1 of the book and then leads students through seventy-five practice questions. In requiring that students consider situations and that they discuss the meaning of concepts such as variables, the IMP curriculum
There were two types of books that were at the center of this. Both introduced students to the same mathematical methods and procedures, but the IMP books attempt to do so in a way that made the mathematics more meaningful for students. Consider, for example, the way that the IMP book and the traditional book (brought in by the parent activists) introduced algebraic variables to the students. The traditional book begins with a brief example of rental charges at an ocean shop and then has the following text:
The letter h stands for the hours shown in the table: 1, 2, 3, or 4. Also, h can stand for other hours not in the table. We call h a variable.
A variable is a symbol used to represent one or more numbers. The numbers are called values of the variable . An expression that contains a variable, such as the expression 4.50 × h, is called a variable expression . An expression that names a particular number, such as 4.50 × 4, is called a numerical expression , or numeral.
Another way to indicate multiplication is to use a raised dot, for example, 4.50 • 4. In algebra, products that contain a variable are usually written without the multiplication sign because it looks too much like the other x, which is often used as a variable. 7
The traditional book gives two pages of explanations like these before presenting twenty-six “oral exercise” questions and forty-nine “written exercise” questions, 8 such as:
Simplify 9 + (18 – 2) and 2 • (b + 2)
In contrast, the IMP book introduced students to variables through a particular situation—that of the nineteenth-century settlers who traveled from Missouri to California to set up life on the West Coast. The students are told, “You will encounter some very important mathematical ideas—such as graphs, different use of variables, lines of best fit, and rate problems—as you travel across the continent.” 9 They are then given various exercises that require them to represent the settlers’ situations using mathematical tools such as graphs and variables. For example, the students are told about families and some general conventions, such as “anyone more than fourteen years old is considered an adult.” 10 They are then introduced to variables through this question:
The Hickson household contains 3 people of different generations. The total age of the 3 family members is 90.
a) Find reasonable ages for the 3 Hicksons.
b) Find another reasonable set of ages for them.
One student in solving this problem wrote:
C + (C + 20) + (C + 40) = 90
What do you think C means here?
How do you think the student got 20 and 40?
What set of ages do you think the student came up with? Try this question, it can be solved in many ways. 11
In the IMP curriculum, students are gradually introduced to the concept of a variable—one of the most important concepts in the mathematics curriculum—before being asked to interpret and use variables in representing a situation mathematically. The students are also encouraged to discuss variables, exploring their meaning and when they are used, and generally to raise any questions or problems they have. The traditional curriculum, by contrast, tells students what variables are on page 1 of the book and then leads students through seventy-five practice questions. In requiring that students consider situations and that they discuss the meaning of concepts such as variables, the IMP curriculum
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