Feedback for Effective Education

Richard A. Beldin, Ph.D.

Everyone has an opinion about education reform. So do I. Are my opinions any better than anyone else's? You be the judge.

Let's begin by making an analogy with activities that people learn to do well. For example, consider shooting at a target with bow and arrow or a rifle. We know that shooters can develop great skill with practice.

The shooter chooses his target, aims, fires, and then examines his outcome. The distance and direction of his shot from the bull's eye tell him how to correct his next shot.

Now, think about the analogy with a teacher. First, what is the target? In our society, we ask teachers to shoot at so many targets that it is hard to know exactly which is the most important. Let's simplify matters by thinking about just one of those targets, success in the first college course of mathematics, required of every student on the Mayaguez campus of the University of Puerto Rico.

The high school math teacher who wants to teach students so that they will be successful in their first math course in college has a clear target. He or she then can design a course plan that promises to aid students in this way. That is like aiming at the target.

The teacher delivers the course according to the plan, making some necessary adjustments for the specific group of students and how they react to the course. This is like shooting.

Finally, the teacher tries to determine how successful the students were in their first college math course. Whoops! Colleges don't tell high school teachers the results of their students in college! The teacher is thwarted in the attempt to correct his or her teaching by the lack of feedback in our educational system.

Now, I've just been talking about mathematics and the gap between high school and college, but the same is true of any subject and any two institutions of any level.

What about within a given school or school system? Suppose a principal wished to evaluate teachers by the subsequent success of their students? That seems like a reasonable thing to do. If teacher A has more successful students (in later courses) than other teachers under similar conditions, then maybe teacher A is a better teacher?

We can't (or at least don't) evaluate teachers that way. Instead we use checklists of criteria which we assume lead to better teaching, but we never test the assumptions. Admittedly, it would require a lot of data manipulation to evaluate teachers based on results. Years ago, that would have been impossible, but today, the computing power we have is more than sufficient for the task if we just decide to use it.

My conclusions are:
1. Teachers can't evaluate their teaching methods for lack of feedback about how well their students do in subsequent courses.
2. Principals can't evaluate their teachers for the same reason.
3. It is within our means to keep student records in a form that will permit us to satisfy the unmet needs of points 1 and 2.

I obtained the high school of origin of all freshmen who took Precalculus for the first time during the fall term of 1997-8 and their final grades in the course. Then I sorted the data by school and rated the schools by the percentage of their students who were successful.

Five schools were so successful that at least 90% of their students were successful in Precalculus. These schools are:
1. Southwestern Educational Society in Mayaguez,
2. Academia Santa Maria in Ponce,
3. Colegio Marista in Guaynabo,
4. Colegio San Antonio in Isabela, and
5. Colegio San Jose in San German. These schools are rated "A" for successful students.

Three schools had more than 80% but less than 90% of their students successful in Precalculus. These schools are
1. Colegio San Carlos in Aguadilla,
2. Colegio Catolico Notre Dame of Caguas, and
3. Academia Maria Reina in Rio Piedras. These schools are rated "B".

Ten schools had more than 65% but less than 80% of successful students. They include:
1. Colegio San Agustin of Cabo Rojo,
2. Josefina Leon Zayas of Jayuya,
3. Dr. Carlos Gonzalez of Aguada,
4. Colegio Pablo Casasus of Mayaguez,
5. Colegio Ntra. Senora del Carmen of Hatillo,
6. Colegio La Milagrosa of Mayaguez,
7. Academia La Inmaculada Concepcion of Mayaguez,
8. CROEM of Mayaguez,
9. Academia San Luis of Lajas, and
10. Colegio Evangelico Capitan Correa of Arecibo. These schools are rated "C".

Only one school is rated "D", with between 60% and 65% of successful students. This school is Colegio San Benito of Mayaguez.

Fifteen schools are rated "F", with fewer than 60% of their students being successful in their first college math course. These schools include:
1. Pedro Perea Fajardo of Mayaguez,
2. Segundo Ruiz Belvis of Hormigueros,
3. Jose de Diego of Mayaguez,
4. Monserrate Leon de Irrizary in Cabo Rojo,
5. Lola Rodriguez de Tio in San German,
6. Eugenio Maria de Hostos in Mayaguez,
7. Luis Munoz Marin of Anasco,
8. Aurea Quiles of Guanica,
9. Academia Adventista del Oeste in Mayaguez,
10. Ines Maria Mendoza of Cabo Rojo,
11. Efrain Sanchez Hidalgo of Moca,
12. LiBlanca Malaret of Sabana Grande,
13. Leonides Morales Rodriguez of Lajas,
14. Patria La Torre Ramirez of San Sebastian, and
15. Luis Munoz Marin of Yauco.

Other schools were not included because the numbers of students enrolled in Precalculus as freshmen during the period were too few for statistical analysis.

There is no desire on my part to criticize any of these schools or their teachers or administrations. There may be many reasons for these facts, but the facts should be made public.

If we are going to have meaningful educational reform, it must be based on the principle that we will pay attention to facts, not just theories or untested assumptions.