Archived: The Educational System in the United States: Case Study Findings

Methods of Teaching Math and Science
Teachers discussed and exhibited a variety of teaching practices, ranging from
teacher controlled to learner centered. These included lecturing, a ‘‘question-and-
answer’’ format, group work, ‘‘hands-on’’ activity, and individualized instruction.
Examples of each will be described.
Observations of the teaching of math and science revealed, in general, that prac-
tices did not differ notably across grade levels and across sites. In most instances,
teachers were in charge and controlled the interaction. They lectured and asked
questions on a particular topic, expecting students to ‘‘fill in the blank,’’ i.e., pro-
vide the precise answer they were looking for, so that the logic of the argument
they were building could be demonstrated. Some teachers did this with remark-
able skill; they appeared to be thoroughly grounded in their subject and presented
material in an interesting, logical, and sometimes entertaining manner. This was
particularly true when experienced and dedicated teachers were teaching students
who were considered ‘‘advanced.’’
Lectures. 
At Uptown High, I observed a chemistry class taught by Mr. V. He had
taught for over 35 years and was planning to retire soon. There were 23 students
in the class, 19 of whom were Asian American. All sat on stools at lab tables. The
teacher remained at the front of the class during the period, pacing back and forth
and writing on the board as he spoke. During his interview, Mr. V. told me that
he was from the ‘‘old school’’ and liked to lecture. The observation proved to
be a case in point; there was more teacher talk—for example, asking and answer-
ing his own questions—in the example that follows than was the case in most
of the classrooms observed.
Teacher: Suppose I wrote the equilibrium this way:
SO
2
+ 1/2 O
2
= SO
3
SO
3
= SO
2
+ 1/2 O
2
If I only know this, how do I write the relationship?
Student: It’s a reciprocal.
Teacher: Yes, when we reverse, the constants change and become a recip-
rocal.
What’s the relationship in terms of their K? [K is an equilibrium constant.]

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He writes an elaborate formula on the board. For the most part, the teacher
talks and develops the argument. Occasionally he will ask a question that can
be answered in a word or brief sentence.
He then shows how the formulae look with gases, and then presents a ‘famous
equation.’
PV = nRT [the ‘‘ideal gas law’’]
P
=
nRT
V
[Note: In this equation, P = pressure, V = volume, T = temperature, and
R = ideal gas constant.]
At the teacher’s question, a student explains that (n) indicates moles per liter
at equilibrium. The teacher then describes chemical equations that utilize the
ideal gas law. After writing the assignment on the board, he explains homo-
geneous equilibrium.
For most of the lessons the teacher lectures, both asking questions and answering
them in rhetorical fashion. He is well versed in his subject and ‘‘getting it right’’
is important to him. However, the fact that he uses this mode of instruction sug-
gests that he is primarily concerned with subject matter. Most students are atten-
tive and try to follow the logic of his argument.
Initiation-response-evaluation. 
In this sequence, a teacher asks a question (initi-
ation), a student provides a response (response), and the teacher then evaluates
its merits (evaluation). Teachers may also provide an explanation. One example
will suffice:
An eighth-grade algebra class: The problem is 3 x 
· 
4 = y.
Teacher: How do I get it over here? If 4 is being subtracted here, how do
I get it to the other side?
Student: Add it.
The teacher writes the correct answer on the board: 3 x 
· 
y = 4.
Teacher: OK, add it. Number 15?
y 
· 
2 = 4 x + 20
+ 2
+ 22
So how can I get it in my general linear equation form?
Student: 4 x 
· 
y = 
· 
22

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Teacher: Yeah, because added here, we have to subtract to get it to the other
side. (King Junior High School female math teacher in her thirties)