Are Common Assessments Valuable?

As we prepared for the start of the new year, my colleagues and I got into a discussion about common assessments and their value.

Our math department does quite a good job collaborating and using common assessments, and we were lauded as a good example by our administrators and others during the school-wide training meetings that happen the week before students come back. This was fine, but then we were informed that we did not meet AYP due to our math scores. In fact, we had a 47% pass rate for 2006 and a 34% pass rate for 2007. If I understand correctly, we were supposed to have improved by at least 10%, not dropped by 13%.

This was the news that prompted a few of us to start talking about what to do and how the results of the common assessments should be used. One fellow math teacher pointed out that as long as we are giving common assessments we should also be using the results of these assessments to guide our instruction. As we discussed the different approaches we are taking in our Algebra 1 classes she mentioned that having a common assessment may prove more valuable now that different approaches are being taken, as long as the results are being reviewed. If it turns out that one class does much better on the common assessments then we should consider the approach that teacher and class took, and the rest of us should adjust our teaching accordingly.

I am excited to see what happens. Last year we gave common assessments and, once they were given, we decided that the majority of students were doing poorly. Those of us teaching Algebra 1 were taking the same approach to teaching and getting the same results. We did nothing to change what we were doing, we just kept going because that was the way it worked. The common assessments didn't do much for us because we didn't do anything to respond to the results they showed. This year we will be looking at the results and seeing what was happening that made the difference between the successful classes and the less successful classes.

What is a 'Teacher'?

I was reading a little bit in 'E-Learning by Design' by William Horton, and came across a question that made me wonder about my role as a teacher. The question was one of a list meant to help the reader decide whether to skip the first chapter. The question reads, in part, "Do you lack either education and experience in instructional design? Perhaps you are a subject-matter expert or instructor..." So which am I, as a teacher? Am I a subject-matter expert? An instructor? An instructional designer? What does it mean to be any of these? Does an instructor have to be a subject-matter expert and/or an instructional designer?

My initial answers to these questions is that each of these are separate things. To be one is not necessarily to be the other. College professors, for example, may be subject-matter experts in their chosen field, but may not be able to instruct others in similar pursuits, and may not be able to design quality instruction. Is there value in becoming a professional with training in all of these areas? If one did obtain such training, would they be able to more effectively help students learn? Should all teachers receive specific training in each of these areas, or should teachers team up based on their strengths and have specific tasks assigned them? Should there be teachers working behind the scenes to create lessons for those who are actually in the classroom?

Chinese Philosophy and Math

I have been reading Fung Yu-Lan's book 'A Short History of Chinese Philosophy'. In the introductory chapter the author is talking about the spirit of Chinese philosophy. In the latter portions of the chapter he addresses why it is that Chinese philosophy is often written in brief and disconnected ways when compared with the Western philosophy and its more articulate style. In Chinese philosophy aphorisms, allusions, and illustrations are used to create this brief and disconnected style. Their use leads to suggestiveness, and Fung points out that this suggestiveness is less limiting than a more articulate approach. There are ideas that are suggested and understood that could not be articulated well without limiting the scope of thought.

It seems to me that the traditional methods of teaching math, namely memorization, drill, and practice, are more articulate (there is a certain way to solve this type of problem, and that method should be used to finish some set of exercises). Once a student has completed the exercises they should have a grasp on the mathematics.

A problem that is to be used to teach mathematics cannot be this articulate. There needs to be more suggestiveness, thus allowing the students to use whatever mathematically accurate approaches they see fit. Having a classroom discussion on the ideas that come from the various solutions will help the students define certain mathematical concepts in ways that will be beneficial to themselves.

Fung quotes a passage from the Chuang-tzu, a significant book of philosophy, which may help distinguish between ideas suggested and methods articulated, and how ideas suggested can be the more powerful of the two.

"A basket-trap is for catching fish, but when one has got the fish one need think no more about the basket. A foot-trap is for catching hares; but when one has got the hare, one need think no more about the trap. Words are for holding ideas, but when one has got the idea, one need no longer think about the words." (pg 12)

Later on Fung says that 'words are something that should be forgotten when they have achieved their purpose. Why should we trouble ourselves with them any more than is necessary?' (pg 13) It seems to me that the traditional methods of teaching math are having our students deal with the words. The formulas they memorize and the specifically formatted equations they learn to solve are the words used to describe the ideas of mathematics. Our students, however, don't get to experience the ideas of the mathematics because we are spending so much time focusing on the words.

The last paragraph of the first chapter of Fung's book says the following.

"Kumarajiva, of the fifth century A.D., one of the greatest translators of the Buddhist texts into Chinese, said that the work of translation is just like chewing food that is to be fed to others. If one cannot chew the food oneself, one has to be given food that has already been chewed. After such an operation, however, the food is bound to be poorer in taste and flavor than the original."

Do we assume our students are not capable of chewing the food of mathematical ideas? Are we continually chewing this food for them? I think we are. It is no wonder that our students are not enjoying math classes as much as we would like them to, or even as much as they would if we would let them.