I think Maths is very interesting subjects but if some students find it difficult its may be because of the lack of interest. Also Maths need to be understand as Maths is a subject that you can not memorize it as it contain long questions of different types. Hence if a teacher become able to develop the interest of the students will enhance to make the subject easy for the students.
I think Maths is very interesting subjects but if some students find it difficult its may be because of the lack of interest. Also Maths need to be understand as Maths is a subject that you can not memorize it as it contain long questions of different types. Hence if a teacher become able to develop the interest of the students will enhance to make the subject easy for the students.
I think the way which most of teachers use to teach mathematics makes it seems hard, boring, and irrelevant; they key factor is how we teach mathematics.
I had an advantage that I could see that math was useful because my dad used it in his research.
Partly it is that math is not much fun as it is taught. Why do I have to do 20 problems every night? Why are the problems stupid? How is any of it relevant?
It doesn't help when the computer used to do the math problems has the wrong answer. Sometimes the computer wants a very specific answer and (x+3)*(x+5) is wrong while x2+8x+15 is correct. Sometimes it tells you what form is needed (and we just didn't read the question carefully enough) and other times we play guess the answer.
The problems start in pre-k and elementary school, and propagate. Having parents that hate math is a disadvantage.
At any time of life it is difficult to see all the skills that you will need 20 years hence.
Basically math is the teacher at the front of the class working out a problem. The students go home and work 20 similar problems. Next class period repeat.
One problem my daughter brought home was to take two points that were the rate of decline in marriage over the last few years, calculate the slope and then predict the rate 20 years from now. It was not appreciated when I calculated that marriage would be abolished in 2075, and thereby showing the problem with extrapolating values beyond the existing data.
Last year my daughter took chorus. She tried out for "All State Chorus" and practiced once. She made the first of three cuts, but her cumulative score was not enough to make the second cut. A year later, she is practicing at home. She is in the advanced chorus, made the cut for elite chorus, and has passed the second round for All State and did so well that she will try out for the elite chorus for All State. Part of it is that she has music teachers that are inspiring, have drive, and love the subject.
How do you get the same thing from a math teacher? I realize that this is a two-way street. The music teacher has a room with kids that like the subject and are there because they want to be there. The math teacher has a room with kids that would mostly prefer to be anywhere else and they will complain to each other about the stupid homework. By labeling it stupid, they have already made it harder to learn the simple stuff so that they can get to real problems.
Basic mathematics can be learned easily, usually and by applying it to simple and real questions, taken from everyday life. (if to make a cake I need 3 eggs, how many eggs will be served for 30 cakes etc ..)
Over time both the mnemonic part, the logical part and the abstract part are involved.
There are different types of brain.
The tendency is to give many formulas, one for each solution, often losing the concept. The concept of unscrewing is translated into a screwdriver. I give an example.
They taught me a formula for the area of the
square= L * L,
rectangle L * H,
triangle L * H / 2,
trapezium, H * (Lmax + Lmin) / 2.
They did not teach me the unified vision. The unique formula is that of the trapezium area: Area = H * (Lmax + Lmin) / 2.
Indeed:
Square: Lmax = Lmin = H: Area = H * (H + H) / 2 = H * H
Rectangle: Lmax = Lmin = Lmax: Area = H * (Lmax + Lmax) / 2 = H * Lmax
Triangle: Lmin = 0; Area = H * (Lmax + 0) / 2 = H * Lmax / 2
Trapezium: Area = H * (Lmax + Lmin) / 2.
In this way I would have learned a single fomula and reasoned from time to time.
Prefer the "case-> formula" method or the "formula -> case" method, depends on the type of brain you have.
This, in my opinion, is the problem of teaching mathematics, it is not related to the type of cognitive logical structure that must accommodate it. In practice it is not adapted to the subject, it is lowered from above.
In this case, a possible solution, for me, is to expose both methods and leave the choice to the brain that has to use them.
To better explain:
depending on the problem there are brains that think better RISB and brains that think better CISB (in analogy with the RISC or CISC processors).
RISB = Reduced Instruction Set Brain,
CISB = Complex Instruction Set Brain.
The classification is not absolute. Fortunately, our operating system manages, depending on the problem, the RISB or CISB mode or a mix of both.
Dear Gioacchino de Candia , yes, these are some of the problems i think. However, what are the way forward? We need to overcome these problems because of the future generation.
Solution; teaching mathematics as story telling (Teaching Mathematics as Storytelling Rina Zazkis and Peter Liljedahl; https://www.sensepublishers.com/media/1019-teaching-mathematics-as-storytelling.pdf)
Often the issue is abstraction and lack of contextualization. Anchoring math in meaningful scenarios especially in the forms of interactive games can help
I am of the opinion that the challenge is cyclical. From many conversations with all levels of K12 teachers, it appears that many of those introducing the concepts of mathematics (at the elementary level) are not really fond of the subject in the first place. When a young person is introduced to something new (like mathematics) they observe and absorb everything the educator is doing, how they act, and begin to mimic their educator. If the educator does not like math, this feeling becomes ingrained in the psyche of the student. Fortunately, some elementary school teachers love math and the more that do, the better the mathematical educational experience students have as they progress through the primary grades. Unfortunately, many educators at the elementary level do not love (or even like) math and can not hide their disdain for the subject and possibly they do not put the same effort in educating their students as they do with other subjects. I say this challenge is cyclical, as many of those students that do successfully attain a high school diploma that do not like math, did like the experiences they had with the educational process and end up as teachers themselves. Additionally, K-6 educational programs do not require much math for teachers to get their teaching certificate. In Florida, the General Knowledge test really does not require a very high level of mathematical understanding and the cycle repeats itself. Please let me know what your opinion is about my thoughts. I would greatly appreciate it.
Maybe the first step is to identify the features of math that are so disagreeable. Learning math should be easier than learning English, except that we use language almost constantly while we use math relatively infrequently. I say easier because there is nothing in math like "i before e except after c or when sounded as a as in neighbor or weigh" with a few exceptions like science. Of course if such convolutions make things easier we can always have rules like the sum of the angles of a triangle equal 360 but only if you are on a flat surface using degrees and not radians and so long as you are using numbers base 10. I suppose one could try the sum of the angles of a triangle are pi radians so long as the pie is made from plums, but larger if made from blueberries.
More seriously, a part of the problem is the materials used in teaching. A small problem is that there are often mistakes in the teaching materials. The other problem is that the computerized teaching/testing system is a pain in the butt. So the problem gives (2,4) and an equation of y=3x+2 and asks for a line parallel to the equation that passes through the point. To figure this out I need to write (y-4)=3(x-2) and then reorganize to get y=3x-2. The student answers the latter getting no points and finds that the correct answer is the former. A human teacher would give at least partial credit and maybe take a point or two off for not reading the question carefully enough. However, the student giving the answer clearly knew how to do the problem. Of course having the homework program periodically crash or reset does not help. The child wanted to do good and started math after getting home. They expect that it will take 30 to 40 minutes but clever resets drags this out for four hours. Life is not fair, but is a math assignment really the right place for a lesson in fairness to make students like math?
In my opinion, there are two main reasons for negative attitudes towards learning Maths: 1. Maths teachers are very often uninterested in teaching (they call themselves ''mathematicians'', not Maths teachers) and this ''teaching through stories'' isn't something that they care about. 2. Curriculum requirements are sometimes too high for students. There are two (and more then that) theories that teach us about cognitive capacities of our students: Piaget's and Vygotsky's. Both of them convince us that formal logic operations are something that depends on developmental stage. E.g. Piaget's fourth stage appears at 12, and that stage in thinking operations is necessary for understanding of many concepts.