Strong Correlation Between Students’ Efforts and Accomplishments

In working at Pasadena Unified’s Center for Independent Study (CIS) since January, I have noticed the relationship between the number of hours students put into learning the online curriculum and the number of assignments they complete. 

By Scott Phelps

I wanted to see if the relationship was a robust one across all of my students, so I made a scatter plot of the number of hours my thirty students put into their online work (including  answering the questions successfully, persevering while getting put in recovery mode after answering questions incorrectly, and having to try the fundamentals again), vs. the number of assignments they completed. I compiled the data for March, but it is likely that the results would be similar for other months or for the semester as a whole. The scatter plot shows a strong positive correlation between those two variables:

As the graph shows, the more hours students were logged in to the online curriculum, the more they accomplish. There are of course individual differences. For example, some students leave themselves logged in while clicking over to other tabs, playing on their phones and doing other things. Still, the correlation is strongly positive, with a correlation coefficient of 0.86, and a coefficient of determination of 0.75, meaning that 75% of the variation in the number of assignments completed can be explained by changing the number of hours worked along a straight line drawn through the points. The slope of this line is 4.4, meaning the straight line model predicts that 4.4 assignments are completed for each hour worked, i. e., that it takes less than 15 minutes to complete one assignment. This is a reasonable amount of time, so the good news is that it is entirely possible that students can be more successful if they put in the time. Of course, this may require that they have been taught to stay with the assignments for some time, to pay attention to the videos, to pause them and take notes, to take the time to figure out difficult questions on paper, etc. But it is possible!

It is well-known that disparities between the accomplishments of different students are highly affected by many factors outside of the school’s control, such as parental education level, family income, etc. Most studies put the outside of school effect as at least 80% of the total effect on students’ accomplishments in school. The differences in the out of school lives of wealthy and poor families are well known, and many wealthy families provide a much higher level of help outside of school, such as hiring private tutors for their children.

This data from the students’ independent study courses cannot be explained by that reality, given the demographics of my students. For example, the student who completed the most assignments, and the student who worked the most hours, both come from families of low to moderate resources and from a historically underrepresented ethnic group. Also, the time available for these students to do their assignments is much greater than it is for students at in-person school. They can do them all day. (Of course some of them have extra family duties, but the great majority do have the time.) The differences in accomplishments can’t be attributed to some not having enough time outside of the school day to do their work.

Some other phenomenon must be at work here. As Jaime Escalante is reported to have said, at least in the movie about him, you need to have the ganas, the desire to succeed. The students who have put in more time and have completed more assignments, have a stronger desire to succeed. In several cases, it was after they reached a low point in their lives that they found this increased ganas. In many cases, a strong parent or godparent is involved. It is clear that it is something inside the student that is driving their accomplishments. Brava to them! I hope we can all help awaken that in more of our students.