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. 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.
In the given study design, the researchers employed several principles to ensure control, replication, and randomization. Here's how each of these principles was incorporated:
Control: The principle of control refers to the elimination or minimization of differences between groups, except for the variable being studied. In this study, the researchers ensured control by:
I. The two groups had no differences in gender, ethnicity, or social class. This eliminates any potential bias or confounding effects from these variables and increases the internal validity of the study.
V. The students had all experienced the same mathematical approaches and demonstrated the same mathematics achievement before the study began. By ensuring similar pre-existing levels of mathematics achievement and exposure to the same mathematical approaches, the researchers controlled for these factors that could otherwise influence the results.
Therefore, the correct option for the principle of control is A) I and II.
Replication: Replication involves conducting the study with a sufficiently large sample size to increase the generalizability and reliability of the findings. In this study, the researchers ensured replication by:
II. The study used a sample of 248 students. By including a reasonably large sample size, the study increases the likelihood that the findings reflect the characteristics of the larger population.
Hence, the correct option for the principle of replication is B) II.
Randomization: Randomization involves randomly assigning participants to different groups to ensure that any potential confounding variables are equally distributed between the groups. In this study, the researchers ensured randomization by:
III. The students were randomly selected. This indicates that the sample was selected in a random manner, further increasing the generalizability of the findings.
VI. The students were randomly assigned to the groups. By randomly assigning students to either the traditional or non-traditional group, the researchers avoided selection bias and ensured that any differences observed in the outcome (National School-Leaving Exam scores) could be attributed to the different teaching methods.
Therefore, the correct option for the principle of randomization is D) III and VI.
To summarize the correct options:
- Control: A) I and II
- Replication: B) II
- Randomization: D) III and VI