“The student thinks they understand the lesson, but when they cannot solve the problem, they start looking for the fault in their own intellect.”
These words were stated by Natəvan Fərzəliyeva, winner of the "Young Teacher of the Year" competition and mathematics teacher, in a statement to AzEdu.az.
She also noted that the biggest flaw of textbooks is the failure to maintain the balance of transition from simple to complex:
“There are some topics in textbooks whose presentation alienates students from mathematics. I particularly agree with students on these three topics.
In the topic of trigonometric transformations, dozens of formulas are given consecutively in textbooks. Instead of understanding the logic of these formulas, students are forced to memorize them. This removes mathematics from the thought process and turns it into a “memory test.”
In logarithmic functions, the transition from exponential function to logarithm is presented very abruptly in textbooks. There are not enough necessary visual and logical transitions for the student to master this new “mathematical language.”
Spatial geometry (stereometry) is a topic that requires 3D thinking, but it is still explained with 2D (planar) images in textbooks. The student cannot visualize the figure, yet we demand proof from them.
The biggest flaw of textbooks is the failure to maintain the balance of transition from simple to complex. The simplest examples are shown in the topic explanation, but in the exercises section, suddenly, questions of an Olympiad level or excessively complex structure appear. This “leap” damages the student's self-confidence. The student thinks they understand the lesson, but when they cannot solve the problem, they start looking for the fault in their own intellect.”
She stated that many of the problems in our textbooks are far from the interests of modern youth:
“Problems like "pipe filling a pool" or "train traveling on a road" still prevail. In my opinion, we should present derivatives not with the concept of speed, but with the speed at which a social media post goes "viral", and probability theory by linking it to the decision-making mechanism of artificial intelligence. Mathematics should move from "dusty book pages" into the phone in the student's pocket.
In the era of modern programming and mass computation, some topics have become an academic burden. Complex computational trigonometry - artificially complicated trigonometric equations and identities - should be reduced. Also, archaic algebraic calculations, such as long division of polynomials or manual simplification of multi-digit irrational expressions, should be minimized.
Instead, more statistics, data analysis, and algorithmic thinking should be taught. The student should not be a calculating machine, but an individual capable of analyzing results.
As a result, we are trying to teach children mathematics with 19th-century methodology to manage 21st-century technology. In textbooks, the principle of "how" to teach should change, rather than "what" to teach."
