No one can pretend the levels of difficulties in mathematics don´t exist. However, although it can be said we have problems, what we don´t need is to think about it as something throned. It makes it problematic. The word problem itself means ” to be thrown”, an obstacle in the way. For instance, there are variations of the “bleme” affix we can use as a tool to think about obstacles in the terrain: the astrobleme.
In social life, as we go through the dense terrains of sociocultural relations, our movements, both physical and mental, occurs due to lexical (vocabulary) and ethological (semiotic) possibilities, given by the socio historical circunstancies.
problem (n.)late 14c., “a difficult question proposed for solution,” from Old French problème (14c.) and directly from Latin problema, from Greek problema “a task, that which is proposed, a question;” also “anything projecting, headland, promontory; fence, barrier;” also “a problem in geometry,” literally “thing put forward,” from proballein “propose,” from pro “forward” (from PIE root *per- (1) “forward”) + ballein “to throw” (from PIE root *gwele- “to throw, reach”).
https://annemichael.wordpress.com/2018/02/02/cosmogenic-questioning-play/
Meaning “a difficulty” is mid-15c. Mathematical sense is from 1560s in English. Problem childfirst recorded 1920. Phrase _______ problem in reference to a persistent and seemingly insoluble difficulty is attested from at least 1882, in Jewish problem. Response no problem “that is acceptable; that can be done without difficulty” is recorded from 1968.
As the degree of awkwardness or easygoingness people go on socializing vary, to many, a mathematical problem could be compared to getting stuck in the middle of a astrobleme crater, a situation where they don´t know how to move and where to go.
Instead of throwing something at the students, we could let them explore the terrain and find the way . The structure and patterns of the proposed elements lays in a terrain´s topology as exercise.
The magic moment. The ones we go with class in awe, as teachers right way how to solve the question on the blackboard. The “ah!” exclamatory moment when people who don´t knew where and what to look, got it. Nevertheless, preceding this moment we must teach students to think first they have an obstacle.
In order to see the landscape, they need to resolve the problem by removing the obstacle. Students experience the other way around., they thrown themselves on this mental field effort to find out a landscape. Many paths to one structure: the answer.
It is possible to say that:
1) to know how to observe the landscape ( its dimensions, regions, paths and rules) is spacial reasoning and
2) to know where to go means how to move covered by operator rules to places, the numbers you need
3) to get there operators takes contextual (topological knowledge) skills as an unproblematic perspective.
4) by reducing the movement of field efforts directing rules to terrain characteristics
Along with the verb “to count”, that allows us to perceive that number are words, the “bleme” affix, shows the notion of a movement to put something in a given situation. So words are elements in a mental space. Are tools to explore and describe the mathematical landscape. The relative liberty of the language games of Wittgenstein´s approach floats on a contract that holds meaning on the rules.
Likewise, in the “The Unreasonable Effectiveness of Mathematics in the Natural Sciences ” might embed the same dimensions, as whatever the numbers can create, the material physics theories can test it.
To be able to see the same principles from the world in the words we use to describe it. The physical, abyssal anxiety that some experiment, with no ground can be seen as a barrier to freely move in a unknown environment.
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