Mathematics: Teach to Memorise

The irresponsible experiments on the national system of education of the last 30 years have created a set of fundamental problems in the Portuguese school system, which may only be solved in the medium and long perspective. The most important of these is the absolutization of thinking and creativity, to the detriment of memorization and memory development, during the entire school experience of the pupil. This is the topic of this Chapter.

Memorize – what for?

The promoters of the above-mentioned educative experiments would categorically insist that there is no knowledge that must be memorized or learned by heart, that it is sufficient to understand how the things work, and after that the pupil can think logically to deduce any missing pieces. Let us remind the TV interview shown shortly after the tsunami in Indonesia, featuring a British girl who memorized at school and quickly recalled the symptoms of a tsunami coming, promptly communicating her logical conclusions to her parents, as a result, not only she herself and her family survived the tsunami, but also all the other guests staying at the same hotel. At the same time, there were thousands of other people present at the beaches, who had no memorized knowledge of tsunami, in absence of which their creative and independent thinking turned out to be completely useless in saving their own lives.

We therefore conclude that the two components, memorization and creative thinking, must be developed in harmony, as in order to be able to use the knowledge already accumulated by humanity we have to resort to memorization, on the other hand, the memorized knowledge is also needed as a base for new knowledge, to be created by our own creative and independent thinking.


We need a criterion to assess the memorization capacity of our pupils. Well, Mathematics is a subject fundamental for all the exact knowledge that can be expressed numerically, including Science and Technology. Mathematics deals with abstract objects, non-existent in Nature in their pure form, first defining them, and then studying their properties, for future practical usage. The simplest example of such objects are natural numbers, as for example, 17. Thus, to start using Mathematics, one needs to know – that is, needs to memorize – the respective definitions of the objects which we are working with. Indeed, without knowing the definitions and the properties of the arithmetic operations, studied in the primary school, we shall make little use of sines and cosines – for which we must also know the definitions, in order to give practical usage to the respective formulas. Thus, the memorization ability is indispensable for Mathematics, equally, a pupil with good systematic memorization ability will not fail in Mathematics.

Thus, we shall use the results of the National Exams in Mathematics to assess the systematic memorization capacity of our pupils. The average grades of these exams are usually around 6 or 7 (note for the non-Portuguese reader: the grading scale used runs from 0 to 20, 10 being the minimum positive grade). Thus, an average pupil, who managed to arrive to the final phase of his school learning experience, has hardly mastered 1/3 of the competences in Mathematics he should have acquired. However, the lack of competences in Mathematics implies, first and foremost, the very serious problems with the memorization ability, which should have been developed at School, by way of constant, systematic and persistent memory-developing exercises. Without exercise, the memorization ability degrades, in the same way as any other unused human ability: the patients who stay in bed for a long time forget how to walk.

Thus, we give a "Bad" (Fail) grade to our pupils for their systematic memorization ability.


The lack of systematic memorization ability reveals fatal in teaching of Mathematics, and equally in teaching of all the other subjects that require the capacity of abstract thinking, the development of which primarily depends on Mathematics. Among such high-failure subjects we shall note Physics, which no-one likes, as it has a lot of abstract fundamental notions, such as "the material point". Other subjects, such as Psychology, depend mostly on the day-to-day experiences, and thus are well-loved by the pupils.

Many pupils "study for the tests", resorting to indiscriminate memorization, to try to avoid scholar failure. They learn by heart entire book pages of the subject matter that will appear in the test, without understanding any of it, subsequently copying from the memory onto the test paper, expecting to include something relevant into their replies. Regrettably, such type of memorization ability lends no help to the pupils: they are unable to use such indiscriminate knowledge on future occasions, studying from zero for each test, as he lacks systematically memorized knowledge. Such pupils are unable to establish any relation of the matter they are currently studying with what they have already learned in the other subjects, or in the previous years of study.

A very frequent excuse that such pupils provide is "I don't remember any of this; we studied it a long time ago, already in the primary school", clearly revealing the most severe and extremely common deficiencies in the systematic memorization ability of our pupils.


The pupils fail to develop their systematic memorization ability, because all the exercises necessary for such developments had been excluded from the curricula of all of the subjects studied in school. This causes of scholar failure of the majority of pupils, caused by clearly inadequate study curricula and the wrong underlying teaching principles.

Here we must especially note that this single monumental pedagogic folly contributes much more to the universalised scholar failure than the insufficient teacher competence and all the other factors, taken together.


The teaching in the Primary School (1st Cycle of the Basic School) should be based on the usage and development of the systematized memorization ability of the pupils. The elements of critical and creative thinking should be introduced into the curricula gradually, along the learning experience of the pupils, growing in importance as the pupils grow and develop their intellectual capacities, and eventually becoming predominant in the Secondary School.


Thus, all the pupil textbooks and teacher manuals in all the subjects of all the years need to be revised and republished, to include the exercises for the development of the systematized memorisation ability. This includes poems for the lessons of Portuguese, arithmetical tables , definitions and formulas in Mathematics and Sciences, names of Kings of Portugal and historical dates, National Anthem, and all the other subject matter that can not be deduced logically but needs to be studies and known, for future use.

Additionally, we must stop loosing time uselessly by trying to explore the "critical and independent thinking" in the pupils of the 1st and 2nd cycles of the Basic School, given that the respective intellectual capacities get only developed later, in older pupils.


We understand by systematically memorized knowledge any knowledge that has been memorized, understood, and properly related to other knowledge already in the pupil's memory.


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