In my opinion, there are two main obstacles in math teaching and studying:
1st MAIN OBSTACLE. From all other sciences, mathematics has the largest degree of coherence and inter-connectivity between all its branches. From the first years of studying mathematics, it is obvious that each math lesson is essential to understand all other later math lessons. In contrast, in physics for example: you can understand very well mechanics without knowing electricity; you can understand optics without knowing electricity or mechanics and so on. Because mathematics demands a marathon-like effort on many years to understand it, a maximum tenacity in daily or periodical study (which is very time consuming), the "natural" selection is harsh, because just a small percent of people are sufficiently motivated by "the science and art of counting" (which math is) to get over this first obstacle.
2nd MAIN OBSTACLE. The poverty of methods and digital resources (images, animations and software) which is used to teach math from the first grades: it's only in the last 20 years that digital resources in math exploded and were implemented recently in teaching (and that is not sufficient time for extensive and diverse implementation in math pedagogy).
MY THESIS
In the "reference frame" of exact and "almost-exact "sciences, math may appear as a very important domain and language: which is true. However, my thesis is that the human being are based on not one, but three types of logic and metalogic, which logics are not reducible one to another:
1. rational logics (all "governed" my mathematics) which may be all integrated in a rational metalogic (rML) ("governed" by meta-mathematics)
2. emotional logics (studied by arts, aesthetics, psychology, philosophy, religions etc) which may be all integrated in an "emotional metalogic" (eML);
3. "volitional" logics (also studied by psychology, neurobiology and medicine in general, sociology, philosophy, religions etc), which may be all integrated in a "volitional metalogic" (vML), which I also conjecture to not be reducible to any of the first and second types of metalogic (rML and/or eML).
I have extensively presented my aforementioned thesis in my papers:
https://www.researchgate.net/publication/313478425
https://www.researchgate.net/publication/313847195
MY "META-THESIS"
My "meta-thesis" would that mathematics and rML in general aren't sufficiently "powerful" (and would never be) in the "humanity reference frame" (which is almost infinitely larger than the "reference frame" of exact sciences) to gain more interest than eML and vML. My prediction (and conjecture) is that rML may only imitate eML and vML, but can never replace them. I also argued in my (previously mentioned) papers that eML and vML (which are conjectured to be irreducible to rML, which rML may be only an "imitator" of both eML and rML, but not their "replacer").
See also other URLs of my work:
https://www.researchgate.net/publication/320740914
https://www.researchgate.net/publication/327022481
See also general URLs:
https://en.wikipedia.org/wiki/Metalogic
https://en.wikipedia.org/wiki/Logic
https://en.wikipedia.org/wiki/Mathematics
https://en.wikipedia.org/wiki/Metamathematics
This discussion was inspired by Prof. Patrick Dasgupta, who is full professor since 2004 in Physics and Astrophysics Faculty from University of Delhi (https://du-in.academia.edu/PatrickDasgupta), when he kindly invited me (directly or using the Academia.edu robot?) to participate to a session on his article called “On Reasonable Effectiveness of Pedagogy in Mathematical Physics”
Draft paper URL:
https://www.academia.edu/38551383/On_Reasonable_Effectiveness_of_Pedagogy_in_Mathematical_Physics
Session URL (on which I’ve also pasted this large discussion-comment):
https://www.academia.edu/s/387493a781/on-reasonable-effectiveness-of-pedagogy-in-mathematical-physics#
Regards!
Andrei-Lucian this is a very good question and require a sensitive answer. Let me see if I can show a little sympathy here. The first main obstacle is not that math does not have momentum, but are the instructors excited motivators of this science. It is hard to get excited or may I say enthused about math if the instructor does not give his students a momentum. I am ambivalent. I love math and I loved literature. I can teach the science of math as well as converse with literary concepts. Every instructor I had in High School gave me a momentum. They excited me about the concepts that is why I have never forgotten the basics and was able to mature to the next level. A positive momentum is very important if you are an instructor. However, if you come in with a negative momentum you will have a negative result from the class. Now to discuss the 2nd main obstacle Andrei, I agree that we should try to stay up with the times and make this science digital. I know Einstein used the blackboard, but come on now we should be able to use the computers as well as the blackboard to explain this science. Now Andrei this is the sad part about this science and I am going to try to be as sensitive as I possibly can. Most people who follow this science sooner or later develops cancer of the brain that has no cure and they die. I am not saying literature is better, which is the road I chose in life, it has its mishap too, but I am glad I did not go farther into math. I do not have brain cancer today. God Bless you.
Dear Mrs. Bays,
1a. Math teaching surely needs "momentum", but in large quantities and the teachers who share constant big enthusiasm in math teaching are rare: however, I am glad that you are one of those enthusiastic teachers.
1b. I am also "ambivalent" in your sense: passionate on both exact and humanistic sciences, in sciences, arts and religions. However, I tend to be more oriented to the scientific rigorous approach.
2a. Besides starting from the earliest grades with many math-based games (like origami for example), I think that digital animations and constant teaching and learning using a math software (like Mathcad for example, which also has the possibility to implement programming routines built on lines of code, but also to generates graphs and animations) would be an ideal way to further continue the math learning and teaching. Learning basic programming (and a basic math software) in parallel with math is essential for every child to create his own math experiments and to very himself after working on paper.
2b. I don't think that mathematicians are (statistically and significantly) more predisposed to brain cancer than the rest of the population: this is a "hard claim". Do you have any scientific proof on this claim? Knowing one or two cases of mathematician who developed brain cancer isn't a proof: I also know examples of persons passionate by literature who developed brain cancer. I hope you didn't share this false claim with your children! I am waiting for proofs on this last claim of yours: as a pediatrician specialist (with experience in adult medicine too), I assure you there is no published evidence about mathematics predisposing to brain cancer.
Regards!
Hello Andrei, as I formerly stated I realize that this is a sensitive issue. However, like I said everyone I knew that was mathematicians died of brain cancer. Unlike you I do not know any humanitarians that died from this ailment. My B.S. degree was in Elementary Education with a minor in English. My Master's degree is a Master's of Divinity in General Studies. Like I said I suffer, but not with brain cancer or brain problems. I am a truth speaking problem, I donot lie. God Bless!!!
Dear Mrs. Bays,
It is far from me the intention of acusing you of lying. However, it is wrong to generalize and to "induce" a supposed causal effect between that person studying math and his/her diagnosis of brain cancer. There are many risk factors and many demonstrated causes of brain cancer but studying math isn't among them and isn't cited in any manual of medicine (or oncology, to be more specific). At the contrary, math games (like Sudoku for example) were demonstrated to prevent degenerative brain diseases (like Alzheimer’s disease for example). In conclusion, you are on very thin ice when you generalize a rule from a single case you have witnessed.
Regards!
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