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

Hands-on learning. 
In some cases, teachers stressed the importance of ‘‘hands-
on’’ learning. Others, however, expressed doubt or, at least, uncertainty that stu-
dents would actually derive what they needed to know from working with mate-
rials. A third-grade teacher at Midtown Elementary described the dilemma:
I’ll put out the manipulatives. OK, it’s time to play a little bit, but then I’m
not sure they’re getting the idea. You know . . . . The ones that probably
need to use the manipulatives are the ones that need to work faster. So, I
don’t know. I have to work the system out somehow.
Perhaps conveying a more generalized ambivalence, another teacher in this school
said that when math manipulatives had been introduced 2 years earlier, the teach-
ers had referred to them as ‘‘projectiles.’’
At East Elementary School, a fourth-grade teacher had developed a science curricu-
lum that contained a ‘‘hands-on’’ component. In this school, the two teachers at
this grade level specialize; one teaches science and math, and the other language
arts and social studies. The math/science teacher valued the fact that she could
concentrate on two subjects and prepare them well, and she had amassed a great
many materials. She also provided ‘‘double period’’ science for each group.
On the day I observed the teacher first engaged the students in a discussion of
matter and the elements. They then watched a video on matter, the weight of
matter, and change of state. It lasted 15 minutes and was presented in simple
English with demonstrations of all concepts (such as melting, evaporation, con-
densation, and freezing). After discussing what they had seen, the teacher ex-
plained that they would be using nuts and bolts to construct their own ‘‘mol-
ecules.’’
She wrote the following ‘‘elements’’ on the board and told the children that
they are to use two or three of each.
Long bolt
Lo
Short bolt
Sh
Wing nut
Wg
Hex nut
Hx
The children work intently. As they finished, the teacher told them to ex-
change their molecule with another group and to write the formula for that
molecule. She went around the room to check. The children came up with
the following formulas:
LoShHx
2
Wg
Lo
2
Wg
3
Hx
Wg
2
HxLoSh
Lo
2
HxLoSh

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197
Lo
2
Hx
3
Wg
2
ShHx
2
Wg
At 1:40 p.m. the children were told to take their molecules apart. A student col-
lected the bags. The teacher asked if they now felt confident about writing for-
mulas. She discussed some of the difficulties she had witnessed, such as children
writing superscripts rather than subscripts or making the numbers rather than the
letters large. Finally, she distributed a worksheet and went over the terms.
Teacher: What are the two groups that would classify elements?
After a few wrong answers (charged, not charged; positive and negative):
Child: Metal and nonmetal.
Teacher: Elements are made of . . . .
Child: Atoms.
Teacher: Tell me about a nucleus.
After they went through all of the terms, the children were given a brief
assignment that involved organizing the terms that had been covered.
This teacher had gone to a special program dealing with elementary leadership
in math and science for 3 weeks during the summer, and for 1 week the follow-
ing summer as well as meetings throughout the year. She said she got ‘‘state-of-
the-art’’ training in math. Then the principal asked her to teach science. At first
she was apprehensive: ‘‘The old district science curriculum was awful, and the
new one is just as bad . . . . It doesn’t follow any published curriculum, and no
support or materials are provided. The books are useless.’’ She started out borrow-
ing the fifth-grade books. She said that after attending the special program she felt
she was able to teach science and math in an interesting and constructive manner.
Individualized instruction. 
Rockefeller Elementary was well known for the staff’s
efforts to individualize instruction. The teacher-made curriculum in mathematics
in this school is organized around nine topics, each of which is signaled by a dif-
ferent color (e.g., numeration (blue), addition (pink), subtraction (yellow), mul-
tiplication (green)). There are nine levels to numeration, six each for addition,
subtraction, multiplication, and division, and eight for mixed operations. Impor-
tantly, the levels have nothing to do with grade levels. For example, second-grad-
ers will do levels three and four in addition. The central idea behind the approach
is that children work independently on what they need and where they are. The
‘‘Notes to Teachers’’ underscores this fact. This is a school ‘‘where individualized
instruction is a reality. Children’s needs come before a planned curriculum.’’ The
guide provides ‘‘materials developed for children by teachers who teach chil-
dren.’’

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198
In the example below, there were 21 children in a 4th-grade class, although only
17 were present. Two ‘‘special education’’ teachers were also in the room, work-
ing one-on-one with two boys. A math resource teacher had just finished working
on factoring.
I am writing as she leaves and fails to notice the shift in to individualized
instruction.
The children have pulled out spiral workbooks and begun working. The regu-
lar classroom teacher sits with a small group of children (the children are
grouped into clusters formed by having four or five desks pushed together)
and speaks softly with them. Throughout the session, she moves from cluster
to cluster but sits each time and looks over children’s work. The workbooks
are different colors. Yellow is the book on subtraction; orange is division, and
purple for mixed operations.
At 10:10 a.m., the teacher announces a multiplication speed test. There is
some movement and talking while forms are distributed. At 10:13 a.m., the
teacher asks if they have their names on their papers: ‘‘I’m getting ready. Are
you ready? GO!’’ The students have 2 minutes. After this time, the teacher
says, ‘‘STOP! Now count the number you did.’’ Some children are excited that
they did better than before, while others moan that there is no improvement.
Although it is true that the staff in this school subscribed to an individualized ap-
proach to learning, there appeared to be a good deal of discussion about the
work, and periods of individualized instruction were balanced with other, still
more interactive sessions. Moreover, a critical component of math instruction was
what might be characterized as the thrill of competition with oneself (e.g., the
reference to ‘‘your personal best’’ above) or with another group (e.g., the ‘‘chal-
lenge’’ that one class made to another).
In sum, five types of teaching methods were observed during the course of this
study-lecturing, a type of question-and-answer interaction involving initiation, re-
sponse, and an evaluation (I-R-E) of the response by the teacher, group work,
‘‘hands-on’’ activity, and individualized instruction. The predominant mode was
the I-R-E sequence in which the teacher controlled the interaction, asking ques-
tions, evaluating answers, and frequently providing the explanation as well.