Keep your heart with all vigilance,

for from it flow the springs of life.

Understanding Accountability

Teacher evaluations haven't been getting much good press lately. I, for one, am not in favour of the way teacher evaluations are carried out though I do see the need for accountability. Teaching is both a science and an art but we lack the data, knowledge, understanding and wisdom to examine both effectively. But this post isn't about the current state of affairs. Rather, it's an attempt to better understand the purpose, use and limits of teacher evaluations and appraisals. 

Understanding Conditional Arguments

Before we begin, some understanding of valid and invalid arguments using conditionals is required. It is important to state at the start that I've had no formal training in logic. What I have is the accumulated knowledge in the few Philosophy modules back in university and the rest is self taught. Much of what follows must be credited to Yap E.M. who took the time to share and teach me. Any error or fault, however, is mine to own.

The first thing we need to know is what a conditional statement is. For example:

If he's a good teacher, then his students learn.

Being a 'good teacher' is the antecedent while 'students learn' is the consequent, it's what follows if he is a good teacher. Conditional statements such as the example above can be expressed as:

If A, then B.

A is the antecedent while B is the consequent. Conditional statements usually exist as assumptions which we use to navigate the world around us. Some examples would be:

  • If it's 10pm, the sky would be dark.
  • If she likes me, she will go out with me.
  • If he's angry with me, he will punch me.

Valid Arguments: Modus Ponens & Modus Tollens

Conditional statements are particularly useful as it can be used to establish a fact or truth when only part of the information is available. For example, I've been stuck in an underground bunker the entire day and my watch shows that it is 10pm. I can know for sure that it is dark because:

Premise 1: If it's 10pm, the sky would be dark.
Premise 2: It's 10pm.
Conclusion: The sky is dark.

In other words, given that if it's 10pm, the sky would be dark. I see that it is 10pm, therefore the sky is dark. This is an argument, specifically modus ponens which can be expressed as:

P1: If A, then B
P2: A
C: B

Conditional statements are also useful to tell us when something isn't the case. For example, I am out at the beach and the sun is shining. I can know for certain that it isn't 10pm because:

Premise 1: If it's 10pm, the sky would be dark.
Premise 2: The sky is not dark. (The sun is shining)
Conclusion: It isn't 10pm.

In other words, given that if it's 10pm, the sky would be dark. I see that the sky is not dark, therefore it isn't 10pm. This argument is known as modus tollens, which can be expressed as:

P1: If A, then B
P2: Not B
C: Not A

Invalid Arguments: Affirming Consequent & Denying Antecedent

The problem with conditional statements begins when we use them in a way that, though it is invalid, we still hold it to be true. The first such invalid argument is known as affirming the consequent:

Premise 1: If it's 10pm, the sky would be dark.
Premise 2: The sky is dark.
Conclusion: It is 10pm.

In other words, given that if it's 10pm, the sky would be dark. I see that the sky is dark, therefore it is 10pm.  Such an argument can be expressed as:

P1: If A, then B
P2: B
C: A

We can see that the argument is invalid, 10pm isn't the only time that the sky is dark. Another type of invalid argument can be seen in the following example.

Premise 1: If it's 10pm, the sky would be dark.
Premise 2: It isn't 10pm.
Conclusion: The sky is not dark.

In other words, given that it it's 10pm, the sky would be dark. I see that it isn't 10pm, therefore the sky is not dark. This invalid argument (what if it's midnight?) is known as denying the antecedent which can be expressed as:

P1: If A, then B
P2: Not A
C: Not B.

In summary, we have two types of valid arguments:

  • Modus Ponens
  • Modus Tollens

And two types of invalid arguments:

  • Affirming the Consequent
  • Denying the Antecedent

Invalid Evaluations & Appraisals

Evaluations and appraisals have been the source of much unhappiness around the world and Singapore is no different. Part of the reason stems from the poor understanding about the need and use of evaluations and appraisals as well as its limits. Both teachers and school management are at fault though the faults are different for each group. Let us take the following conditional statement

If he's a good teacher, then his students learn.

For the sake of keeping the discussion focused, let us assume this statement to be true. We need not further clarify what key terms such as 'good' and 'learn' mean as well as the relationship between both. At some level, all of us probably agree that good teachers bring about student learning.

The problem is that we often fall into the error of affirming the consequent. In other words, given that if he's a good teacher, then his students learn. His students are learning, therefore he must be a good teacher. When this error is committed by school management, they mistakenly assume success to be a certain indication of the teacher's ability. Teachers, including myself, commit the same error. We see that our students are learning and think therefore we must be good teachers. 

On the other hand, if students are not learning, the teacher in question cannot be a good teacher - modus tollens. In other words, given that if he's a good teacher, then his students learn. His students are not learning, therefore he mustn't be a good teacher. This argument can be a difficult one for many to swallow.

There are two takeaways for teachers and school management. For teachers, if there is no evidence that your students aren't learning, there is a need to take a hard look and examine and reflect. I find John Hattie's statement that every student has the right to a year's worth of learning - one year invested yields one year of learning - to be true. We've been given a part of the students' time by the management, parents and the students themselves. They at least deserve to receive a certain amount of learning for the time invested. Schools and teachers must be accountable for the time and money parents and students invest through us.

School management and policy-makers need to recognise that no matter how comprehensive and holistic an evaluation is, whilst it is good for maintaining accountability, it isn't a very good tool for identifying whom to raise and be given responsibility. The more explicit the system of evaluation, the more likely people within will game the system - students cheat, teachers teach to the test, schools search for valuable students instead of creating valuable students. 

Conclusion

Teacher evaluation and appraisals are necessary. Just as a doctor must be accountable to his patient, or the soldier to his nation, teachers likewise need to be accountable that the students placed in our care are receiving the right to learn.

Although evaluation and appraisals are necessary, we need to recognize that these tools are far from perfect. It neither rightly measures nor measures rightly. For example, most schools only know how to measure student learning through test and exams. While tests and assignments may be frequent, examinations are heavily weighted. In the end, a student's learning is measured primarily by the answers on a stack of paper filled over 2 hours. Even with the data available, school managers lack the training and knowledge to make full sense of it. This is evident in how we only calculate for averages in examination scores, disregarding other statistical information such as mode, median and spread - to name a few.

In conclusion, teachers should welcome evaluation and appraisals as a means to ensure we are giving our students what they deserve. School management and policy-makers need to recognize how inadequate and imperfect evaluation and appraisals are and not use or extend beyond its limits.

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