Stage 1 (up to about 10 wpm): The code is memorized as a code, not a language, and is stored in Short Term Memory “look-up table.” Faster than that, the next letter is sent sooner than the short term memory can be accessed. (Old Novice license, 5 wpm)
Stage 2 (up to about 18 wpm): Consistent frequent usage causes the mind to elect to move the learning into long-term memory. This has a quicker access time. The transfer occurs subconsciously during one’s sleep. Once this occurs, strangely, the learner suddenly finds they can copy faster, and continued practice quickly leads to improvement up to the new speed ceiling. this is why the speed of 13 wpm was selected for the old general class license. You can not copy 13 wpm until the transfer into long term memory has taken place. Hence the speed choices for General (13 wpm) and Extra (20 wpm, just above the next plateau).
Stage 3 (up to about 27 wpm): Further continued usage at higher speeds causes the whole process to move from long term memory into the language center of the brain. This is a more complex change and may take longer. It will happen more quickly for some who is still in the neurological developmental stage for language development (younger than 15). This is much faster, but note that the sender is still SPELLING at you. You do not hear words.
Stage 4 (generally up to your Haas (echo suppressor) limit, likely between 45 and 55 wpm): In this stage of learning you begin to interpret whole syllables and even words at the same time. Now you genuinely copy code as another language. Once into this stage, you can, with practice, increase speed readily until limited by the brain’s built-in echo suppressor, known as the Haas Effect. About 10% of people don’t have this at all, they are not limited in this way, but will have difficulty understanding speech in a eho filled hallway.
With this understanding you will grasp better just what is going on. Note that those who devised Farnsworth and Kock methods did NOT understand the above, though they were aware of the plateaus.
You will also recognize what Farnsworth is trying to do, which is to get you to hear letters as a sound rather than an interpreted cipher from a look up table. I frankly doubt if you can have success learning code without learning the cipher first. I can not imagine interpreting code and not knowing what the cipher actually is, and i may be wrong. I personally think that one isn’t really ready for Farnsworth until they have the code memorize, and probably already in long term memory, but that’s an opinion.
You have it in long term memory, so I would think you are ready for Farnsworth, but in my opinion, not for Koch, and you need to be writing down the letters to interpret words later.
You pass from stage 2 into stage 3, using the language center, by frequent (not necessarily long episodes of) practice. Many five minute episodes in a day is worth MUCH more than one hour long episode. All in the world that is happening, is convincing your brain that this is in regular use, and might as well transfer into the language center.
Going from stage 3 to stage 4, true language, copying syllables and words that transform in your head into meaning, the goal of the Koch method. My opinion is that this can not take place until already in stage 3, but others have more experience with the Koch method than I and might disagree. Regardless…
Once IN stage, easily recognized by being able to readily copy on paper, usually by printing, 20-25 wpm, though sweating a bit and concentrating plenty, THEN a trick that I find helps for moving on to the highest stage is this…
There is a reason you are printing. That is, you are copying discrete letters. I found when I learned way back when that I could NOT force myself to use script which is obviously faster. After a while, and I wasn’t getting faster, I decided that I must FORCE myself to script the copy. Lo and behold, within moments of starting by golly writing in script, B-A-N-G, I was copying over 3 wpm, and within a week was copying 40 wpm, and equally amazing, I could begin to sit back and hear someone talk to me!
P.S. That all important practice…
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frequent short sessions is more valuable than one long one
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SENDING is just as effective as receiving. You still have to THINK of the letter and form it. I used to be walking down the street, and I would spell in Morse things I saw, signs I saw, under my breath of course 
Hope this is helpful to many!