The only Montessori we're really doing right now is we're using Souns. They are letters that a young child can hold, feel, taste. They are called by their most commonly used letter sound. They are introduced in a particular order, becoming new toys in the child's toy box. As the child starts to get it, noticing the individual souns in books, on billboards, in nature, etc, another letter is added to the toy box. Eventually, children begin to sound out the spelling of words, even before they are able to form the letters.
The basic idea of Montessori is that children will explore and learn about the materials in their environment. They do not need to be pushed to learn them. They just need to be given materials that will allow them to learn. There are authentic Montessori materials that you can buy that are the result of generations of experiences of providing materials that will most easily help the child self-teach, and I'll definitely keep my eye on them for ideas on how to expose my children to certain concepts, but I'm not going to be as rigid.
DD asks me all the time what Souns are in her books, and I tell her even though we haven't gotten to them. Yesterday, she kept asking DH what number comes next, and he counted all the way to 62. She wasn't interested in colors until she spent an hour walking around a garden shop with Grandpa, and now she knows all her colors, and she asks me about new colors all the time. "What's that?" is one of the most commonly-heard phrases in our house.
-Physical Science - properties of water, soap, gravity
-Biology - found that she has "milkies" too, learning difference between a toot and poop, learning to clean her own vulva (without soap! - she tried that yesterday), dislikes hair in the tub
-Art - cutting (wants me to), singing along, coloring on different surfaces, asks about colors constantly, playing the piano/guitar/drums, notices sound of some instruments in recordings
-Math - counting to 13 abstractly, starting to count objects, knows that she is 2, matching shapes, struggling with sizes (nesting boxes)
-Interpersonal - is learning to use words to negotiate conflicts, notices feelings, kisses owies
-Literacy - knows 8 Souns (It's time for another), recognizes some numbers, writes "notes" to Grandma using small squiggley shapes that look much like letters (I'm looking at a lined notecard next to me that has more than 20 of these "letters" all between 2 of the lines on the notecard.)
-Home Ec - helps load and unload the washer, loves to play dishes with Mommy, watering plants, holding picked vegetables while Mommy picks more, taking her doll potty/putting to sleep (in our bed), cleans spills, learning pouring (and then more practice cleaning spills), helps pick up for guests
-Religion - beginning to say prayers with us, likes to talk about Jesus (family relations, saying "hi" at church)