Ironically, the “learning of percent” is one of the most problematic aspects of
school mathematics.
In our view, these difficulties are not associated with the arithmetic aspects of
the “percent problems”, but mostly with two methodological issues: firstly,
providing students with a simple and accurate understanding of the rationale
behind the use of percent, and secondly - overcoming the psychological
complexities of the fluent and comprehensive understanding by the students of the
sometimes specific wordings of “percent problems”.
Before we talk about percent, it is necessary to acquaint students with a much
more fundamental and important (regrettably, not covered by the school syllabus)
classical concepts of quantitative and qualitative comparison of values, to give
students the opportunity to learn the relevant standard terminology and become
accustomed to conventional turns of speech.
Further, it makes sense to briefly touch on the issue (important in its own
right) of different representations of numbers.
Percent is just one of the technical, but common forms of data representation:
p% = p × % = p × 0.01 = p × 1/100 = p/100 = p × 10-2
"Percent problems” are involved in just two cases:
I. The ratio of a variation m to the standard M
II. The relative deviation of a variation m from the standard M
The hardest and most essential in each specific "percent problem” is not the
routine arithmetic actions involved, but the ability to figure out, to clearly
understand which of the variables involved in the problem instructions is the
standard and which is the variation. And in the first place, this is what teachers
need to patiently and persistently teach their students.
As a matter of fact, most primary school pupils are not yet quite ready for the
lexical specificity of “percent problems”. ....Math teachers should closely, hand in hand with their students, carry out a linguistic analysis of the wording of each
problem ...
Schoolchildren must firmly understand that a comparison of objects is only
meaningful when we speak about properties which can be objectively expressed in
terms of actual numerical characteristics.
In our opinion, an adequate acquisition of the teaching unit on percent cannot
be achieved in primary school due to objective psychological specificities related
to this age and because of the level of general training of students. Yet, if we want
to make this topic truly accessible and practically useful, it should be taught in high
school.
A final question to the reader (quickly, please): What is greater: % of e or
e% of Pi
