The Daunting Task of Evaluating Math

According to the Merriam Webster Online Dictionary, Evaluate means “To determine the significance, worth, or condition of usually by careful appraisal and study”. Such definition entails powerful words like significance, worth and appraisal. A couple of months ago I had an interesting conversation with famous Canadian professor James Stewart, who has authored a considerable amount of books related to Mathematics. He declared that “there is a worldwide crisis of Algebra”. The statement is a loud cry shared by Math teachers around the world. Students do not have solid knowledge of Algebra. That is a fact. However, there is the other side of the coin--the student side which may cry out loud that “There is a worldwide crisis of how teachers evaluate Math proficiency. “ Which means, that many students feel discouraged on the way teachers grade their work; especially analytic procedures.
I am a Math teacher in a country that ranks 82 out of 180 in literacy rate, according to the United Nations Development Programme. The School Life in Mexico is 11.5 years (below countries with smaller GDP such as Namibia, Botswana, Cuba, Peru, and Lebanon based on data from the CIA World Factbook). Politically, fiscal and security issues are far more important in Mexico than Research, Technology, and Patent Queries.
Every country has the right to focus its efforts where it pleases. However, Education in Mexico suffers a terrible stagnation by political and economic interests (such as predatory unions) that produce teachers who are barely paid, and need to bear classes of more than 50 students in rural areas. It would be logical to think that the least worry for such teachers is evaluating their students in an efficient and significant matter; thus discouraging students to study science and Mathematics.
I may infer that this situation happens in many countries around the world—students who feel frustrated by teachers who do not appreciate their analytical efforts. Personally, during my High School and College years I truly hated Math teachers who only evaluated math proficiency by taking a look at the answer, and considered the whole procedure wrong. Moreover, by not being able to solve a specific exercise, did not mean that I did not know about how variables and Algebra works. I just didn’t arrive at the answer the teacher was expecting. So, Math students need to ALWAYS arrive at the conclusions teachers are expecting? Several mathematicians may shield themselves by saying that “It is not what teachers expect, but what mathematical procedures dictate”. That would be a reasonable answer, but the fact is that we are trying to encourage students to push the human race forward. We are trying to make them become fascinated by the fact that Mathematics describes the world around them, and if properly applied their efforts may revolutionize our world.
The main problem with Math evaluation techniques is that discussion tends to be forgotten, in favor of proven forms, functions and methods. Not only discussion and debate are almost non-existent in Math classes around the world, but procedures are evaluated by poorly designed exams which result in a frustrating experience for students. How could a teacher inspire students if what they learn in class is poorly and rigidly evaluated? The rigidity comes later in life. It is something that students will sooner or later experiment and learn from it. The purpose of a Math class is not to discourage people, but to enthrall them in a world of mistakes and wonder. Where is the appraisal of the value of a procedure if you only look at the answer, and not at the whole picture?
Personally, it has been TRULY favorable whenever I recommend students to at least TRY to solve an exercise or problem, and I reward them for taking risks.
To all Math Teachers who are reading this, and feel that rigidity and an overloaded discipline is the right path to teach Math, I encourage you to at least try once to evaluate even the tiniest effort. Your students will appreciate it, and your attendance rate will definitely increase. In the wide picture, more and more students will become attracted to Math, and mankind as a whole will benefit from it.

image: gettyimages.com