Completing Your Data

As an undergraduate student studying botany, I got quite good at using dichotomous keys. Mine is still on my bookshelf and the $40.00 price tag is still attached (it was among the most expensive books I bought during my studies). It is almost 800 pages of plant descriptions along with either or questions. Does the specimen contain this characteristic? If the answer is “yes,” then it belongs in this group. One continues to narrow down the identification until only one species is left and the plant is identified (correctly we hope).

Humans like making either/ or decisions and—when identifying plants—it is very useful. I have found dichotomies to be far less useful when dealing with teaching and learning issues, however.

When we move into the social interactions, dynamic situations, and nuanced language of schools and classrooms, few situations can be easily or clearly or accurately described by answering questions with “yes” or “no.” Despite this, we continue to seek and, in many cases, insist that things be identified and grouped with dichotomies.

For all their rhetoric about being “data-driven,” educators seem to be unaware that dichotomies are rarely the comparisons that matter. Closer inspection suggests many dichotomies can be made into a simple matrix and these lead to deeper insights and more valuable information.

Case #1: A leader at a very innovative charter school (one that enrolled students from a pool of applicants) was describing the results of his school. He comments that their students were similar (in the demographics commonly reported) to the greater population, but that their students scored higher on the assessments given to all students. He concluded their program caused the differences.

This is misleading. There are really four groups of interest in this story, and I suggest we cannot know the true impact of the school’s program without knowing all four:

 EnrolledNot enrolled
AppliedStudents who applied and were taught the programStudents who applied but did not experience the program
Did not apply Students who didn’t apply and did not  

When using dichotomous thinking, we assume “experiencing the program” was the most relevant factor, with a matrix, we see more interesting groups and questions.

  • We assume the students who did not experience the program are all the same, but the matric shows us the students who did not enroll comprises two groups. Perhaps it is A factor that causes the students to apply that accounts for the increased performance rather than the curriculum they experienced.
  • We also see there is a group that contains no students. If they do not apply, they do not get the chance to experience the curriculum. If we could find out how the curriculum affected these students, then we might be able to draw some conclusions about program. Of course, it is very difficult to create ethical methods for gathering this data.

Case #2: Teachers are people who self-select to enter the field and who complete the requirements for becoming licensed. This requires completing higher education, internships, and other commitments. Teachers also include those who had a positive experience in school and those who had a negative experience. These two groups have different motivations and purposes for becoming teachers.

Adults can be divided into four groups:

Positive & TeacherPositive & Not a teacher
Negative & TeacherNegative & Not a teacher

Especially today, when schools face looming shortages, understanding why people who had a positive experience in school did not become teachers may be very important. For a long time, those who had negative school experiences but became teachers have been excellent teachers who bring much needed perspective to school. Those who had negative experiences and did not become teachers are perhaps the most important group, but alas, we have little hope of accessing their experience.

When we adopt matrices as opposed to dichotomies when we are considering relevant data, we learn whose voice or what factors we are missing. This missing data is more important for many decisions than the data we have.