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 student’s 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 you’ll 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 studentÂ’s 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 studentÂ’s 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 student’s 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 wouldnÂ’t even be in school in the first place.