Question

Does Tutoring Improve Geometry Scores? Part 1

A Geometry teacher checked the tutoring logs for the last test and found that the 12 students who did tutoring had an average test score of 87, while the 18 students who did not do tutoring had an average test score of 79.

1. Identify the explanatory variable and the response variable.

2. Is the situation described an observational study or an experiment? Explain.

3. The students were not required to do tutoring and signed up for it voluntarily. Do you think that may impact the scores? Explain.

4. Identify as many other possible variables as you can that may explain why the Geometry test scores are higher for those who did tutoring than for those who did not do tutoring.

5. Based on this study, can you conclude that tutoring caused the students’ Geometry test scores to increase? Why or why not?

6. Design an experiment that would allow us to determine if tutoring causes an increase in Geometry test scores. Be as thorough as possible.

Answer 1

1. The explanatory variable is whether or not the student did tutoring. The response variable is the student's Geometry test score.
2. This situation is an observational study because the students were not randomly assigned to do tutoring or not.
3. Yes, because the students who voluntarily signed up for tutoring may have been more motivated to do well on the test than those who did not do tutoring.
4. Other variables that may explain the difference in test scores include the student's prior knowledge of Geometry, the amount of studying done outside of tutoring, and the quality of the tutoring.
5. No, we cannot conclude that tutoring caused the increase in Geometry test scores because there may be other variables that caused the difference in scores.
6. To design an experiment, we would need to randomly assign students to either a tutoring group or a non-tutoring group. We would also need to make sure that both groups are similar in terms of prior knowledge of Geometry and motivation to do well on the test. After the test, we would compare the test scores of the two groups to see if there is a significant difference.

Answer 2

1.

The explanatory variable is whether or not the student received tutoring. The response variable is the student's Geometry test score.

2.

The situation described is an observational study. In an observational study, the researcher does not control the variables. In this case, the researcher did not control whether or not the students received tutoring.

3.

Yes, I think the fact that the students were not required to do tutoring and signed up for it voluntarily may impact the scores. Students who are motivated enough to sign up for tutoring may be more likely to be high achievers in the first place.

4.

Some other possible variables that may explain why the Geometry test scores are higher for those who did tutoring than for those who did not do tutoring include:

• The amount of time spent tutoring
• The quality of the tutoring
• The student's prior knowledge of Geometry
• The student's motivation
• The student's study habits
• The student's learning style

5.

Based on this study, we cannot conclude that tutoring caused the students' Geometry test scores to increase. The study is observational, and there are many other possible explanations for the difference in test scores.

6.

To design an experiment that would allow us to determine if tutoring causes an increase in Geometry test scores, we would need to do the following:

• Randomly assign students to either a tutoring group or a control group.
• Provide the tutoring group with tutoring for a specific period of time.
• Give both groups the same Geometry test at the end of the study.
• Compare the test scores of the two groups.

If the tutoring group scores significantly higher than the control group, then we can conclude that tutoring caused the increase in test scores.