Sometimes it can be confusing for children to switch back and forth between two different learning methods. For example, in a Montessori children's house, the child will learn the sounds of the cursive letters (via the sandpaper letters) but even before this work is presented, the child spends alot of time playing "sound games": analyzing the sounds of the words by speaking and listening. When she has a sound foundation, she will be introduced to the sandpaper letters. This is a big process that goes on for quite a while, lots of repetition, variations and excitement building before she goes on to the moveable alphabet! So this is one way to support what is going on at school. If the child asks "what letter is this?" answer with the sound the letter makes. The best support you can give is reading with the child, singing, reciting poetry, and also all those outings that you mentioned: natural history museum, zoo, etc. The best prep you can give in the math area is baking! All within the context of reading recipes, measuring, counting 3 tbsp., etc...there are so many indirect preparations for mathematics.
I have seen children in my class who were not interested in working with the materials as much as I would have liked to see, later to find out they are doing alot of workbooks, runoffs, etc(school-like work) at home.
I would not discourage it however, if they are interested, but in agreement with what was said above, only if they ask.
My sweetie and I have a lovely little lady 07/02 and 3 cats