¢https://www.researchgate.net/publication/318635333_Inculcating_higher-order_thinking_skills_in_mathematics_Why_is_it_so_hard
Higher thinking processes are concepts of educational reform that rely on educational classifications such as Bloom's. [] This idea is based on the fact that there are some types of learning processes that require more cognitive and cognitive training than other species, but also have more general benefits than those types. For example, in Bloom's classification, skills include the process of analysis, assessment, and authorship (creating new knowledge). All these skills are thought to be higher thinking requirements, which require different learning and teaching methods than ways of learning facts and concepts. Higher levels of thinking include the process of learning complex assessment skills, such as critical thinking and problem solving. Higher thinking is a difficult process of learning and learning.
Higher thinking processes are concepts of educational reform that rely on educational classifications such as Bloom's. [] This idea is based on the fact that there are some types of learning processes that require more cognitive and cognitive training than other species, but also have more general benefits than those types. For example, in Bloom's classification, skills include the process of analysis, assessment, and authorship (creating new knowledge). All these skills are thought to be higher thinking requirements, which require different learning and teaching methods than ways of learning facts and concepts. Higher levels of thinking include the process of learning complex assessment skills, such as critical thinking and problem solving. Higher thinking is a difficult process of learning and learning.
Dear Mr Turki Fahed Almasaeid ,
First of all, your question has two focuses, that is, two meanings (please forgive my English is not my first language).
First, the meaning of sentences is that it is difficult to instill high-level mathematics. Both the computer and the human brain naturally reject more detailed and unique ideas. They are called loads. However, human beings must bear these increasing loads for the survival of the population. In fact, because of many defects and deficiencies in human physiology, it is necessary to constantly bear the load and survive better. However, to understand the fact that these loads become easier when they are continuously trained. It is as though why a generation is more likely to accept harder knowledge than a generation of humans.
The second is to think of "why is it so difficult" as a process in which higher-order mathematical thinking is instilled. First, clarify such a difficult scope, and then classify and discuss different levels of difficulty and different conditions. Finally, you can find out why it is so difficult or what is so difficult..
I hope the answer will help you.
sincerely,
Lanzco CHENG
In the early 1970's a psychologist named Julian Stanley instituted a program a Johns Hopkins to understand youth gifted in mathematics.
https://en.wikipedia.org/wiki/Julian_Stanley
Being a lowly grad student at the time a couple of us were assigned to work with Stanley to develop courses that would help him test his hypothesis. To do that we developed courses in mathematics that would test abstract reasoning but did not require a lot of background and teach them. Basic algebra, number theory, projective geometry were such topics.
He created a center a Hopkins to study "gifted youth."
https://en.wikipedia.org/wiki/Julian_Stanley
If you look at the alumni of this program - it is quite impressive Rhodes Scholars, a Fields Medalist, founders of Facebook and Google. Not to mention Lady Gaga.
Anyone that has ever taught mathematics at the college level knows the challenges of having one person that does all the problems (assigned or not) and wants more that you get periodically, then the group of blank stares no matter how the material is presented and the group in the middle. Teaching is an art form. It is also a balancing act - not to hold back the best and the brightest and keep them challenged while doing all you can to impart the knowledge and skill to the greatest number. It is often said that some are born with a mathematical intuition while some never develop one. The question for mathematics is how to we impart the all important mathematical intution..
Would have Charles Fefferman's talents wilted on the vine if not for the University of Maryland welcoming him with open arms at 14 and taking him in although he had not graduated from high school? In fact I am not sure if Fefferman technically ever graduated from high school but at 22 he was a full professor of mathematics at the University of Chicago - the youngest person to achieve a full professorship appointed in the US.
https://en.wikipedia.org/wiki/Charles_Fefferman
To inculcate thinking - leaving apart higher order or lower - it is necessary to establish connect between mathematics and the real world. This link is to be provided in the class room right from the primary school level. Then as the pupils climb up to higher schools of learning, they think in terms of how the different theorems, axioms, postulates or formulae are applied in real life or business or engineering situations. Some students find trigonometry difficult to learn, while some other find Calculus (both differential and integral) difficult, for some probability theory is a hard nut to crack. First, teachers have to learn how to connect mathematics with real world. Then the teaching-learning process becomes fun and triggers the other orders of thinking.
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