A study in England attempted to determine the "right" method for teaching mathematics. A random sample of 248 students was chosen from the school at large. The students were randomly assigned to one of two classes. At the beginning of the research, the students had experienced the same mathematical approaches, they demonstrated the same levels of mathematics achievement, and there were no differences in gender, ethnicity, or social class.

In one class, teachers taught mathematics through lectures and textbooks. This was the traditional group. Discipline standards were very high, and the students were tested often. In the second class, students worked on open-ended projects, and teachers used a variety of methods for teaching. Discipline was extremely relaxed for this group. This was the non-traditional group. At the end of the project, students were tested on Britain's National School-Leaving Exam. The mean for the traditional group was 473 while the mean for the non-traditional class was 582.

Explain how the researchers employed the principle of control in the design of the study. Select all that apply. Note: This question is not about the control group.

I. The two groups had no differences in gender, ethnicity, or social class.
II. The study used a sample of 248 students.
III. The students were randomly selected.
IV. The students were all tested on Britain's National School-Leaving exam.
V. The students had all experienced the same mathematical approaches and demonstrated the same mathematics achievement before the study began.
VI. The students were randomly assigned to the groups.


A) I and II (this one because these don't affect the experiment)
B) II and IV
C) I, IV and V
D) II, III and VI
E) IV and V

Explain how the researchers employed the principle of replication in the design of the study. Select all that apply.

I. The two groups had no differences in gender, ethnicity, or social class.
II. The study used a sample of 248 students.
III. The students were randomly selected.
IV. The students were all tested on Britain's National School-Leaving exam.
V. The students had all experienced the same mathematical approaches and demonstrated the same mathematics achievement before the study began.
VI. The students were randomly assigned to the groups.

A) I and V (this one)
B) II
C) III and VI
D) IV

Explain how the researchers employed the principle of randomization in the design of the study. Select all that apply.

I. The two groups had no differences in gender, ethnicity, or social class.
II. The study used a sample of 248 students.
III. The students were randomly selected.
IV. The students were all tested on Britain's National School-Leaving exam.
V. The students had all experienced the same mathematical approaches and demonstrated the same mathematics achievement before the study began.
VI. The students were randomly assigned to the groups.


A) IV
B) I and V
C) II
D) III and VI (this one)

1 answer

1. Definitely NOT II.

2. How did they know that the students started with the "same levels of mathematical achievement"? Was Britain's National School-Leaving Exam given previously?

3. Right.