Consider the following example:
- Justin and Anna are both math teachers at a High School
- Anna is a new teacher and Justin has been teaching for 10 years
- Their classes have 20 students each
- The topic of the week is Calculus I.
Below is a fictional survey results after a week of Calculus I.
Figure 1: Fictional survey results
The desired result is to have all 20 students understand the course material, which is measured by passing the final exam. Maximal effectiveness would be achieved if all students pass.
Recall that effectiveness can be expressed as: Actual Outputs/ Desired Outputs.
In this case effectiveness can be expressed quantitatively (although this is not always the case!) as:
Actual number of students that passed the exam/ Desired number of students that passed the exam
Justin: (10/20) = 50%
Anna: (15/20) = 75%
Result: Anna is a more effective math teacher than Justin
Recall that efficiency can be expressed by Actual Outputs / Actual Inputs.
In this case, the output is the number of students who pass the exam, while the resource being expended (input) is the teacher’s time.
Maximal efficiency for each teacher can be achieved if students can pass the course, using the least amount of the teacher’s time.
This can be expressed as number of students that passed the exam / time spent teaching
Justin: (10)/(5+1+1) = (10/7)
= 1.43 students pass the exam per hour of Justin’s teaching time
Anna: (15)/(5+5+2) = (15/12)
= 1.25 students passed the exam per hour of Anna’s teaching time
Result: Justin is more efficient than Anna in that more students pass the final exam, per hour of teacher’s time used.
If Anna is more effective, and Justin is more efficient, who should the school hire?
Which teacher is the most productive?
Recall that productivity is defined as the combination of effectiveness and efficiency.
If effectiveness is expressed numerically, to get a better idea of overall productivity (assuming we give both qualities equal weight), we can use the formula:
Productivity = Effectiveness x Efficiency
Justin: 50% x 1.43 = 0.71
Anna: 75% x 1.25 = 0.94
Thus, overall, Anna is more productive than Justin.