Parsing in These Happy Golden Years by Laura Ingalls Wilder:
"Scaling yonder peak, I saw an eagle wheeling near its brow"
"'I' is the personal pronoun, first person singular, here used as the subject of the verb 'saw,' past tense of the transitive verb 'to see.' 'Saw' takes as its object the common generic noun, 'eagle,' modified by the singular article, 'an.' '"Scaling yonder peak' is a participial phrase, adjunct of the pronoun, 'I',' hence adjectival. 'Wheeling' is the present participle of the intransitive verb, 'to wheel,' here used as adjunct to the noun, 'eagle,' hence adjectival. 'Near its brow' is a prepositional phrase, adjunct of the present participle of the verb 'to wheel,' hence adverbial." After only a few such sentences, Mr. Williams was satisfied. (and along with hearing a speech summarising US history, decides she knows enough to be a certified schoolteacher!)
Or less formally, just figuring out what a long complex sentence is on about (at the Chalet, usually in German with its predicate at the end of the sentence).
We had to do some in primary school and ds did a bit for Y2 SATS, but I still have no bloody idea what the difference between a verb and a predicate is!
And is construe just translation into Latin?