The best method of teaching or learning math.

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The STUPID MATH “finally“ became SWEET!

Posted on 29 May 2020 | 4:50 pm by

You see,most students and people hate math.Do you wonder why?Don't worry,this is about the best method of teaching or learning mathematics.


For some decays,people in math education had been thinking that the reason students hate math and don’t learn it good enough is because it’s not “cool”.So,they ‘ve started using things as colorful pictures,mathematical games, and phrases as “math is sweet” in teaching to make it appear cool,but still most students don’t like it much and learn it well .
So,here we’ll see how we could teach math in classroom,textbooks,… so students learn it by love, easily ,and effortlessly.This is also applicable for self study,as in the homeschooling.

                                                                      MY OWN STORY
     About 16  years ago when i was in school and for the first time had an algebra course,my dear math teacher first taught us the mathematical operations on monomials & polynomials like adding & multiplying,also some of the algebraic identities like the perfect square identity,and solved  for us some examples,also gave us much of  homework.It took about 4,5 sessions.On the next class,he started teaching us “factoring  polynomials” this way;
     “O.k. students,let’s start the new  lesson,factoring. Factoring  is the opposite of multiplying”, and he explained it by an example.Then he’d started  teaching us the methods of factoring.
     I think at this point the unconscious mind of a typical student would like to kill itself,thinking  unconsciously that,for 4 sessions the teacher was talking about multiplying the expressions,and the identities,and we did a lot of  homework,and now all of a sudden he’s talking about doing the opposite of  all of what we had so far,all of the work and effort we had in doing  the homework,WITHOUT giving us a good reason of why we should do the opposite now,after all the things.On the next  sessions my teacher  continued teaching the methods,and required us to do homework,and some  of them were hard. [Please,consider that almost  all the math teachers around the world teach the subject in the style of my teacher]
    The disadvantage of this style of teaching or  learning,besides of it’s crazy beginning,is that at some point over the  lesson(here factoring) when students try to solve a higher level  problem,some thing inside their heads asking them unconsciously ((what  are you doing?)),((what’s all the effort for?)), and that’s the point when they start disliking the subject,become disappointed, and give up.This  is not just for the story i told you,but it is in every thing.For  instance,consider teaching multiplying polynomials and the  identities,themselves.Here, there may not be a crazy beginning like for my story with factoring,but again at some point when students try to solve a  problem,some thing inside their heads asking them the mentioned  questions.                                                     
                                                    The Best Method
    There are two types of teaching or learning right now.The first one is like my teacher’s,talking about the non sense abstract stuffs.The second one is similar to the first one,but  the instructor FINALLY gives the students some reasons(or applications)  of the non sense stuffs he/she has taught.
    THE BEST METHOD,is not  like the two above,but to teach that way,for instance in teaching  factoring,the instructor after defined factoring,should talk about the most  important cases in which we need factoring(which may take at least 1 or 2  sessions), and then teaches the methods of factoring.
    The benefit of  this method is that the instructor satisfies the unconscious minds of  the students at the beginning,that what are you learning here is not non sense and useless,but it is important.I believe that by this  method,first of all,students learn by love which is very  important,they’re curious to learn more about the subject(here factoring),and doing homework would not be annoying and make them dislike the subject,because they know that we need to factor for some useful reasons the instructor gave them at first. That would be way better if the cases be touchable, came from practices(like an example in building a car in which we need to for instance,factor), and cover more areas of science and engineering.
     I’ve got a free tutorial  channel at youtube,in which i teach some mathematical subjects in a way close to the best method. Here are some of my courses ;
1.Factoring polynomials
3.Integral calculus
4.Sequences & Series
Please,check them out to feel the method.
    I don’t mean that an instructor should give the students all the cases in which we need the subject(here factoring) at the beginning,but my point  is that we should give them enough of the most important cases at first to make them realize that what are you learning in this session and the later ones is important, and we could give them another most important cases or just cases later.
Whatever i told you above is also for self learning,and not just for math but also for science.

    As  another subject,consider integral calculus.In a typical course or  textbook,the instructor starts by defining integrals,and may be some theorems,then the methods of integration,and FINALLY some cases in which we need integrals,like calculating the volumes of objects and the  length of curves,you know,after well raping the brains of students by talking about the non sense abstract stuffs.
The disadvantages are;
    1.After  some point when students try to integrate a complicated function,some  thing inside their heads asking them unconsciously ((what are you  doing?)),((what’s all the effort for?)),And that’s the point when they  start disliking the subject, and become disappointed.
    2.The cases in  which we need the integrals are non sense.They just say that for calculating the length of curves we need integrals,without mentioning why we should care about length of curves,who needs to calculate it? Again,my method here is that,after we defined the integrals we should talk about  the most important cases in which we need integrals(not at the end),  and then we should teach the methods.Also,we should give the students more details for the cases like calculating the length of curves .                                  
                                                 If i ran a school,i would…
    So far,I’ve talked about how we should teach or learn math & science in the current educational system & syllabuses,for the best,but if i had a school or college in which i was able to make my own educational system & syllabuses,i would run it in a manner even better than the best method above.
I’d like to explain it,again by my own story;
    Many years ago when I was studying in elementary school(2nd or 3rd grade),my dear teacher started teaching us multiplication,this way;
    She drew 3 rows of apples,each row contained 5 of them.Then,she said “here we got 3 five apples or 3 times 5 apples.Lets count the number of them [she did it].So,3 times 5 equals to 15”.Then,she solved more counting problems for us,gave us home works,and required & helped us to memorize the multiplication table.Later,in the same grade or the next ones,they taught us how to multiply fractions,also how to multiply decimal numbers.

    The way my elementary school teachers taught us(which is still the usual teaching method) is just focusing on teaching the tools not the real thing,or some times even forgetting about the real things. Multiplication or generally mathematics,are tools for real things,as designing a car, bridge,…, surveying,discovering the laws of nature. In my owned school my teachers should not teach like that,I mean focusing on less important things like the tools,instead of the most important things like the real things i mentioned.So,in my owned schools,when the teachers want to teach multiplication to the students who are going to learn it for the first time(may be 2nd graders),the teachers like my 2nd or 3rd grade teacher,may start by the counting the number of objects problems,then the multiplication table,and at this moment stop teaching multiplication itself,but start teaching or talking about the most real & practical things in which we need to multiply, as calculating the area of a rectangular farm,but in good details that why do we need to calculate it?who needs it?...

    I may go even further,and make my school do not have a course titles as mathematics,but my students would learn the necessary math in their other courses,courses like “how to design a building”.

     Here,i just talked about math,but to see how i think we should teach or learn science,also for more information please watch my three videos below;

If i ran a school,i would... 1

If i ran a school,i would... 2

If i ran a school,i would... 3

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