Translation:I went to school, and then studied.
When referring to a series of actions all done in the past Within the Same sentence, only the last verb at the sentence will be turned into past tense. Here this particular lesson teaches us how to connect and string a series of actions into a single sentence. It may be correct grammatically, but speaking in two short sentences like this;
makes us sound very unnatural
There are two different ways to join sentences by changing verb endings to mean, essentially 'and'. One way is to put the verb in て form (verb stem plus te base) - がっこう に いって、それから べんきょう しました。- I went to school and then studied. The other way is to use the verb stem plus base 2 of the verb - in this case い (the verb stem of the verb いく - to go) and き base 2 of いく from which we get the original sentence がっこう に いき、それから べんきょう しました - both sentences basically mean the same - in both cases both forms of the verb iku mean "go ....and....." and serve to join two sentences together. Personally, I think both are as common as the other - iki might sound slightly more poetic, if anything.
I was taught that it is the way that Japanese children learn Japanese. The verbs are split into 3 groups - ichidan, godan, and irregular and then they learn the bases that are attached to the stem - so for 行く for instance the first five are か、き、く、け、こ and then the te and ta bases are the last two and then they learn the uses for all the bases and what if any endings are attached to them for other uses. So logical and regular - even the two irregular verbs 来る and する.
I feel like you both don't understand Japanese verbs very well. ~masu is a polite Japanese verb ending. It has nothing to do with the verb stem. Perhaps what you are trying to ask is about joining sentences with ～まして instead of the te form or verb stem plus base 2? (using 行くas a model this would be 行きまして、行って and 行き respectively). Presuming you are asking about using the verb ending ~まして to join sentences - yes, this is possible but it is only used for very very formal occasions - for instance, I worked as an interpreter at Japanese Weddings and we would use ～まして and 下さいませ so this should give you an idea of the degree of formality/politeness involved. As for Tae Kim's guide I couldn't tell you anything about it, sorry.
The verb form used in the first clause here (行き), called the ren'yōkei 連用形 in Japanese, is often called the "masu stem" in English because it's the stem that -masu attaches to. It sounds like it's what you're calling "verb stem plus base 2 of the verb" in other comments on this page?
(Incidentally, in case you don't know this, to have more than one paragraph in a Duolingo comment you need to add two spaces to the end of each non-terminal line.)
Iki is the stem of that verb and in this case, it is used sort of like a conjunction? You can think of it like a this than that type of action form. When you have thr stem form of a verb ans then the sentence goes on like a list with another action directly following, it's a sequential set of actions.
Often times when people complain about a sentence being annoying without the kanji, its kanji that havent been learned in this series yet.
In this case we learned the kanji for school way back in the lessons, so to not have it here IS actually annoying.
Of course, if they used furigana all the time this wouldnt be an issue and you could both read it and learn new kanji at the same time.
Your sentence is not exactly the same as the one from the exercise. Yours implies only that the act of study came (somewhere in time) after you went to the school. You could have gone to the school AND have returned home AND finally have studied.
The sentence from the exercise though implies a chain of events, one coming just after another.
I understand that was a stem of ます, but how on earth would anyone think that was a past tense?
Sorry if this question has already been addressed here, but I wonder if the English translation goes against the grammatical no-no of splitting predicates: http://simplewriting.org/worst-punctuation-mistake/
Kanji is almost universally accepted in the course, and if it isn't an error report is usually enough to get it added. But if it's a "type what you hear" question, there's an issue with the programming of duolingo which is only set to accept one "correct" answer, and the Japanese language which has multiple ways to "spell" the same correct answer. A contributor explains the problem in the comments in this thread.