Just my thoughts.
In the methods of pedagogy, it is imperative that first and
foremost, the methodologies, tactics, and manner of communication
must be appropriate as determined by the age, character / behavior
as well as the existing level of understanding by the student on
the subject.
Secondary, there should in ideal, be the existence of a Reward and
Punishment System in force so as to manage and influence over
matters concerning learning.
On the subject of Mathematics, the ideal structure of teaching
should divided into 3 phases.
Firstly, the introductory phase, where students are brief first on
i) the technical structure of a formula or equation, and ii) the
areas of application, eg, the use of a frequency chart in
determining statistics.
Second, the method of teaching should be instructional, with
emphasis on step by step derivation of all processes involved in
the computation process of the selected examples. In this phase, it
is crucial that unique examples requiring alternative manner of
treatment for a similar equation should also be walked thru with
the student.
Often, a student will encounter problems especially in algebra,
where a regular contributor to failure of understanding lies in the
students inability to flexibly identify a combinative set of
sub-equations, as a common symbol in the overall macro
equation.
Think along e =mc2 vs 1+10+(35x2) = [(1.8+1.2) x 3] to the power of
2 which is essentially the same, and youll get what I
mean.
Third, to ensure that the student fully understand on the essence
of what had been taught, apply the fundamental of the mathematical
topic into a simple and common real life example that the students
age group may easily related to.
And need not I say, of course visual tools and simple to understand
notes will prove to be very useful in the enriching of
understanding for the students.
On the teaching of English on the other hand, a different approach
should be used instead.
Unlike the teaching of Mathematics, the approach has to be
facilitative and mildly thought provocative.
The use of compare-and-contrast methods between simpler and more
exotic choice of language used on one same situation should be
presented to the students for their own assessment and reflection
on the different choice of words used on a same set of
conditions.
In addition to the grammar, vocabulary and spelling of the subject
which has to be taught and guided thru in a more structured manner,
the facilitation of the students awareness to notions and concepts
of elements both sensory, physical, illusionary or objective in
nature will also have to be gradually introduced and encouraged
upon.
Take a student who may be artistically talented.
In the coaching of English across to the student, more can be
absorbed and understood by the student if he / she had been
reminded and encouraged to pepper his / her work with factors such
as imagination, sensory or colorful description, and
emotions.
Take a different student who is in contrast, very much strong in
structural learning, but sadly lacking of artistic skills now for
the same example.
Clearly the sensory approach will be as clear as Greek to this
student.
What should be encouraged for this student instead, should ideally
be the arrangement of events or scenes in the students essay in
a Step-by-step manner, whereby the student would have encountered
significantly less barrier to expression using the breakdown
approach.
On the use of Rewards and Punishment, flexible varieties may be
used on the students, so long as they do not publicly harm a child,
either physically (i.e. body) or psychologically (i.e pride).
The primary aim is to i) motivate and encourage repetitive actions
desired and to ii) effectively disencourage and discontinue any
unconstructive or wayward trends.
Last but not least, patience will also be a must.
While it is understandable that temperature may rise when a student
consecutively fail to understand a logic or concept, it also has to
be understood that if one already knows the taught concept well -
then he / she wouldnt even be in school in the first place.
