I share the view of Miguel that there is no particular method that can be considered as the "best method to teach mathematics". A teacher can use a good method to teach mathematics, but if the teacher is not a good one, then the outcome could be very bad. On the other hand, teacher can use a relative good method to teach mathematics, but if the teacher is a very good one, then the outcome could be very good or even excellent. A good teacher can use not a very good method to teach mathematics, but the outcome of the teacher's work could be a good one or better than others using a more sophisticate methods to teach mathematics, if he/she follows some principles. Some of this principles are the following:
1- Explain first the theory, Axioms, Theorems, Properties, etc., as deep and clear as the teacher can, and later put some practical examples.
2- Put the students to think while the teacher is teaching the main elements of the theory.
3- Demonstrate the main theorems and properties that the teacher is explaining in any given part of the theory.
4- Do not waste the time of the students in making too many exercises on the same topics. Convince the students to give time to understand the theory explained.
5- Explain the theory in a logic manner and do not jump any impotent topics.
6- Allocated time for the participation of the students in a class and in a debate of any specific topic.
Although there is not A best way of teaching mathematics, I would suggest the most beneficial way is to know what your students think. Many of the workshops and teacher education programs that i have conducted as well as in my research, I see that knowing your students thinking, understanding patterns in their thinking and connecting it with the existing curriculum, representation used in the class are the most useful tasks of teaching. Ball & Bass (2002) list 7 essential tasks of teaching mathematics and they are comprehensive in nature. I would suggest you to go through those. Let me know if you need access to that paper.
There is no one method that can be applied to all pupils. It is a complex interwoven issue that do not haw a straight forward answer. There are a number of variables that need to be address and looked into in order to be able to suggest one best way of teaching mathematics.. We can talk about best practices in teaching mathematics.
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