[quote=@RomanAria]
[@Keyguyperson] Oh, key, it's not quite that bad.
But wait, [@Dedonus] I'm not entirely sure that I get it? Why is "house" accusative? Is it because it's like the object of an implied preposition or something? I'd almost think it would be dative to be the direct object...
[/quote]

The first thing we have to address is that doceo is more of an exception.  Usually, when you have a verb of showing, telling, or giving, you have an accusative direct object and a dative indirect object.

-I give the ball (accusative) to you (dative).
-I told the secret (accusative) to you (dative).
-I will show the house (accusative) to you (dative).
-etc.

For [i]doceo[/i], instead of a dative indirect object, as you would expect, you get a second accusative.

-I taught the grammar of Latin (accusative) to you (accusative) (or I taught you the grammar of Latin).

Now to get back to the factitive sentence pattern.  [i]Doceo[/i] is usually brought up because it is an example of a double accusative that is [b]NOT[/b] a factitive sentence.  How I see factitive sentences are like active linking sentences (if that makes any sense).

-I will paint the house (accusative) purple (accusative). FACTITIVE
-The house (nominative) is purple (nominative).  LINKING

-The Roman people elected our friend (accusative) Consul (accusative). FACTITIVE
-Our friend(nominative) is a Consul (nominative).  LINKING

-The Romans considered Romulus (accusative) a god (accusative). FACTITIVE
-The Romulus (nominative) is a god (nominative).  LINKING

Linking verbs are like equal signs (=).  They establish the relationship between two nouns (or a noun and an adjective) and show that they are "equal".  In a linking sentence, these two nouns (or adjective) must both be in the nominative case (kind of like noun-adjective agreement).

Just like in linking verbs, factitive sentences also establish a relationship between two nouns (or adjective).  However, there is a third party that is making this connection.  Since all these nouns that form a factitive sentence take an accusative object, the complement (i.e. purple, Consul, god) must also be in the same case (the accusative).  Therefore, in the example sentences above, both the factitive and linking sentences are giving the same information.  The factitive just gives [b]MORE[/b] information (i.e. who made the accusative the way it is).

Does that help?

Edit: One of the biggest problems I see in teaching Latin is that, even though most of my students are native English speakers, some people don't know English grammar very well.  I'm not saying this about you, but one problem is that how we usually teach Latin is that we kind of assume that our students have a basic understanding of English grammar (direct objects, indirect objects, active and passive voice, et cetera).  Honestly, I feel that Latin (and Greek) actually helps with understanding English grammar because you have to look at way things are and not just accept that things are because it feels natural.  

For instance, my junior year in high school (even though I went to a pretty well-off school, grammar was basically an afterthought in the majority of my English classes), I did not fully understand when to use the correct relative pronoun (who, whom, whose, et cetera), but when we went over relative pronouns in Latin, it made a whole lot more sense because of noun-adjective agreement.  The relative pronoun (in Latin) must match its antecedent (I usually have to explain this too) in gender and number, but its case (i.e. usage) is determined by its role in the relative clause.  Through learning Latin, I understand that you use [i]whom[/i] when it is the direct object, [i]whose[/i] when its a possessive pronoun, and [i]who[/i] when its the subject.

Edit2: Sorry for derailing the thread.  Latin (and Greek, in my case) nerds just nerding out here.  Move along.  Nothing to see here. :D