Successful spellcasting
[1] requires, in the purest sense, only two things. Magical strength and properly focused will. The existence of wandless, wordless magic seems evidence enough of that. A gestural component does appear to make magic easier; even wandless magic seems to involve hand motions more often than not.
Wands are of course the most common gestural instruments. While the use of a wand in general, and particularly a wand specifically suited to the witch or spell being cast, greatly lowers the degree of strength and focus required, it adds complications - the gestures must be precise, or the spell will produce an unintended effect, or - less often - no effect at all.
A verbal incantation reduces the strength and focus required even further, though it introduces similar avenues to miscasting as a wand does; stress on the wrong syllable, timing mistakes and other errors can change the effect produced, sometimes drastically. In this sense, the spoken words become a surrogate for mental focus, the act of speaking them with precision somehow avoiding the necessity for as firm an understanding of the effect to be produced - this is demonstrated by the fact that spells may be successfully cast with only a vague idea of the intended effect, as well as by miscasts which produce an unintended effect, most of which would be by definition not specifically expected by the witch involved.
A fundamental element of properly focused will is expectation, and determination. It is the mental state in which the witch both intends to force the world to change in the way she wishes, and the expectation that it will do so. These factors can directly influence the strength of the resulting effect, above and beyond simple success.
Magical strength, as a function of both the ability to perform more demanding magics, as well as the capacity to perform magic repeatedly, appears to be inherited
[2], but also increased through both practice and simple physical maturation. A witch who attempts a spell beyond her maximum magical strength will either fail outright or produce a very limited version of the true effect, no matter how perfectly she performs it otherwise. Additionally, magical strength is correlated with physical stamina, but seemingly only in one direction, to wit: a witch with unusually good physical conditioning does not evidence more magical strength or stamina, but use of overly powerful spells or too many spells may result in physical as well as magical exhaustion.
Beyond these common factors, a variety of individual spells have their own additional unique mental focus requirements, including the Killing Curse, the Cruciatus Curse, the Patronus Charm, and the Anti-Boggart Charm, among others.
Based on verbal feedback from my Professors, from their own direct observations, my gestural elements and incantations appear to be of sufficient quality to achieve success, and neither my wand nor my physical or magical health appear to be impaired. The only variables remaining are magical strength and properly focused will.
If my difficulties were due solely to an inherently low magical strength - which might not be unexpected as I was born to non-wizards, and had no opportunity to practice magic prior to my arrival at Hogwarts - one might then expect my failures to be proportional to the strength required for the spells. However, based on my own records, my failure rate is constant across all spells I have been told a first-year should be able to cast, even though some of them are known to be less powerful or demanding than others. Further, as noted below, other 'muggle-born' do not show the same difficulty.
I must therefore conclude that the source of my difficulties lies in an inconsistently focused will. Of the components of will, I do not believe my determination is lacking - I have a very strong interest in being able to reliably use magic, and my failures to date have produced unpleasant feelings to which I had not previously become accustomed, and that I would very much prefer to avoid. Thus it behooves me to examine in detail my expectations.
My failures over time have forced me to accept that, lacking some change in my technique, my spells will often fail to produce any effect. Though this might be called a ‘lack of confidence’, I believe it is only an effect and not a subsequent cause
[3], where less confidence produces more failures which lowers confidence further, and so on. Further, my failures occurred similarly at the beginning of the year, even including my first attempts, when I had not yet had enough evidence to anticipate failures, but while I did have evidence
[4] that it was indeed possible for me to use a wand to produce effects in general.
Thus I must consider the question of, what about my mental state when spellcasting differs from that of other students who do not have similar difficulties? It cannot simply be that I was ‘muggleborn’ or ‘muggle-raised’ - there are enough first-year students in my year with similar backgrounds who are not showing the same difficulties to discount that. One obvious element which differs is the breadth and level of education I have obtained in muggle backgrounds and disciplines, particularly the sciences. One might posit a ‘reverse-placebo’ effect, wherein I strongly believe the muggle rules of science - which offer very little explanation whatsoever for magic, and are often entirely contradicted by even simple spells - and thus my belief in the efficacy of magic is diminished sufficiently to cause my attempts to use it to fail.
And yet, I do have an approximately 30% success rate. I certainly have not 'stopped believing' in the laws of physics during 30% of my attempts, and given that, if the reverse-placebo hypothesis was fully explanatory, one would expect my failures to be universal, rather than intermittent. It is possible my limited success is based simply on my empirical acceptance that, despite my inability to explain it scientifically, magic does obviously function reliably for the vast majority of the wizarding community. It is not ephemeral or a magnet for rationalization as are muggle pseudo-magical traditions - wizarding magic is subject to falsifiable predictions of genuine physical effects, which hold up under observation.
What avenues, then, are left to me, if I wish to correct the problem? If I could somehow have my scientific education removed, that would presumably solve the problem, but I would not permit such a thing, even assuming it was possible magically. I want to understand
all of the world, not just one half or the other. Plus, such a drastic change to my memory would effectively make me not me anymore...it is only a solution to my problem in the same sense killing me and raising a new girl named Violet without educating her as much would be, which is to say, not much of a solution at all.
It is possible, if I were able to sufficiently reconcile magical reality with my own scientific understanding of the world, that my mental dissonance would diminish or vanish and my failure rate would decline proportionally. Though efforts in that direction seem less than promising, given that they have occasionally been tried by others before with little success, that magic itself interferes with most muggle equipment which would help to obtain necessary data, and that my own unreliability in spellcasting would make personal experimentation inefficient.
I could also abandon my study of magic and return to my muggle education. I suspect that avenue would cause me lasting emotional harm, however. I might feel unfulfilled, knowing that on one hand, the supposedly universal muggle sciences are blind to a vast swath of reality, and on the other that magic has as much or more potential to relieve human suffering as scientific understanding, but may never see that potential realized without enough individuals with both the necessary viewpoint and the apparently quite rare
[5] capacity to use magic at all.
ArXiv: Violet's Scholarly Output (homework/papers)