What does 敎其子以齊語 mean?

In "Du's Handbook of Classical Chinese Grammar," the following sentence and translation is given:

敎(교)其(기)子(자)以(이)齊(제)語(어)
Taught his son the language of Qí.

"Du's Handbook" has explained that 以 (이) can be used as a direct object marker, which seems to be how it was translated here. 齊(제) was an ancient kingdom of China during the Spring and Autumn Period. And 語 (어) means "language." Therefore, the sentence seems to make sense, but couldn't the sentence also be translated as follows?

敎(교)其(기)子(자)以(이)齊(제)語(어)

Taught (敎) his (其) son (子) using (以) the Qí (齊) language (語).

以 (이) can mean "to use," "to take," "with," "in order to," and a few other things, so I am suspicious of 以 being used simply as "a marker."

I do not know the story from which the sentence was taken, but if the person had wanted to express the meaning "Taught his son the Qí language" instead of "Taught his son using the Qí language", I think he would have written it one of the following two ways:

敎(교)其(기)子(자)齊(제)語(어)

Taught (敎) his (其) son (子) the Qí (齊) language (語).

 

以(이)齊(제)語(어)敎(교)其(기)子(자)

Took (以) the Qí (齊) language (語) [and] taught (敎) [it to] his (其) son (子).

The first sentence simply uses the standard Chinese "indirect object"-then-"direct object" order to clarify the direct object. The second sentence clarifies and emphasizes the direct object by moving it to the front of the sentence and using 以 with its meaning of "to take," which in Korean is 가지다. Therefore, in Korean, the second sentence would translate as follows: "제어를 가지고 (以齊語) 그의 아들에게 가르쳤다 (敎其子)." The only problem with the second sentence is that the meaning could still be unclear since 以 could also be translated as "to use," which means the sentence could be translated as "Used (以) the Qí (齊) language (語) to teach (敎) his (其) son (子)."

The context of the story would probably clarify the meaning of the above sentence, but since I do not know the story, I can only guess. Finally, the original sentence could also be translated as follows:

Taught (敎) his (其) son (子) to use (以) the Qí (齊) language (語).

The above sentence would effectively have the same meaning as the original sentence in "Du's Handbook."