tests raise as many questions as they do answers

For my assessment class I have to write a weekly journal entry organizing my thoughts around my opinions and ideas of testing and assessment. While all my entries are in rough draft form and will require some revisions, I thought I would share one here as a little bit of insight into what I'm studying for those of you interested. This entry begins by discussing the TIMSS assessment, which is administered by the International Study Center where I am now doing my assistantship.

As we discussed the validity of the TIMSS study in last week's class, we broached the idea that if a math test is assessing the math taught, and is reliable, then it is ultimately fairly valid to make inferences about the math students have learned. From this discussion, I acknowledged that we can fairly reliably and validly assess what it is that we have taught, but I wondered how we know if we are teaching the "right" thing. The assessment assumes already that the curriculum is appropriate.

Generally, math skills are considered to be important for three main reasons. The first is that they help people function effectively in the "real world." That is, in daily life, they will use skills in arithmetic and other basic math areas to survive. The usual examples are budgeting, paying taxes, and grocery shopping. In the US, we usually focus on the second reason math is important: that it will result in greater success in college and in the workplace. This reason is likely less truthful than it is idealistic. Realistically, people do not need very strong math skills in the workplace, and many people finish college without taking any math classes. Yet colleges and companies set minimum standards in math skills, because they believe their employees and students should have a certain ability level in math. Whether or not this is a valid requirement, I will not address. Finally, our third reason for learning math is that people proficient in advanced math will likely contribute greatly to the field of math itself, or to the many fields of engineering and science that continue to make our nation globally competitive. From a political perspective, this is perhaps the most important reason to learn math, whether or not it is the most noble. If the first reason were our driving force, we would learn a lot less math than we actually do. If the third were, we would focus more of our energy on those students destined to be gifted in math, and less in those with lower aptitude. Because the second is our focus, we stay on a middle ground. Furthermore, as part of our national culture, education has become a right of citizens, so beyond the material motivations to learn math, we also treat it practically as a human need. If we truly put faith in this idea, then we are doing a great injustice to our students. They are quickly learning to hate math.

Chinese Taipei consistently scores well on the TIMSS assessment. In a summary of their national curriculum, a key word appears that likely appears in none of the state curricula of the US: beauty. Written into their curriculum is the overarching goal that students will learn to appreciate the beauty of mathematics. In the US, we seem to have replaced that word with "utility." In his book Outliers, Malcolm Gladwell also references the great success Asian countries have traditionally had on math assessments. While he hypothesizes various reasons, one of the most interesting ideas is that Asian languages often name numbers in a more logical fashion (think two-ten-five, instead of twenty-five). Even in the very concrete arena of arithmetic, a focus on the structure inherent in numerical patterns seems to be more successful than meaningless labels. Just as lower levels of thinking seem to come easily if we teach for higher levels of thinking, maybe the application of math in the "real world" will come easily if we teach math for math's sake, not for its utility.

Ultimately, the importance we have placed on math education is just another paradigm of our times. It is based on the idea that math is necessary for success in careers, and that that success is more important than other aspects of our well-being. While I would not be able to begin assessing the truth behind these assumptions, I still think it is worth the investigation. If we can bring ourselves to painfully examine the real reasons we need math education, without the pressure of tradition, maybe we can begin simultaneously to identify more effective ways to teach it. Maybe the key to doing well on math assessment, is assessment of math instruction itself.