The short answer is, you don't. You let your child decide. Which one draws them and makes them happy? That one is the right one. Or, you do both.
The long answer is that these two natural education philosophies seem at complete odds at each other. Waldorf is based on art and imaginative play and has at its core the belief that academics before the age of 7 can be very detrimental. Montessori is based on utilizing all the senses to learn new things and shows children complex concepts in math and language at rather young ages. It also discourages fantasy play in lieu of real life experiences.
Both have research backing up their opposite claims of how children learn and thrive. How can they both be right?
The first answer is that it's important to understand why Maria Montessori concluded that fantasy play had no place in the school environment. In her observations, when a child was presented with the opportunity to either play with a play kitchen or join an adult in a real kitchen, they chose the real kitchen every time. Instead of playing with a doll house, they would rather work in a real garden or help sweep the floor. They wanted to do the things the adults in their lives were doing, and found joy in it.
What parent doesn't know their child prefers to play with a real remote or cell phone over a fake plastic one? Why are toddlers always drawn to the "no touch" things like our computers or car keys? Because those are the things WE are drawn to. They look to us to see what it means to be a human being, and if being a human being means spending hours at the computer, well, they want to spend hours at the computer, too.
So much of Montessori involves Practical Life activities, which revolve around teaching children to do many real things by themselves, using real tools and doing real tasks. Maria Montessori did not discourage fantasy play because that's what she wanted, she excluded it from the learning environment because the children wanted it. They had small sinks and small kitchens and small gardens and helped set real tables arranged real flowers and always they preferred that over other things.
As for learning academics starting at age 3, it was entirely up to the children if and when they would learn math or letters. A teacher presented an activity, and then put it on the shelf, and the children were welcome to spend as little or as much time on that activity as they chose. Of their own accord, they were drawn to numbers and geometric shapes and learning the parts of a flower. She simply provided the opportunities, and they made the choice.
I observed this in my own son early on. He had two sets of toy animals - one Fisher price set of cute animals on Noah's Ark, and one set of realistic-looking hand-painted Schleich animals. He preferred the ones that look real, every time, so that eventually we gave the Fisher Price ones away.
I also crocheted him a lot of play food, but he mostly used them as balls to bat around. I just bought the children a play kitchen because the play kitchen seems to be one of the most universally played with toys. The kids use it most often as a mountain for their animals and figurines. Meanwhile, they have their own aprons, and I am never short of helping hands in our real kitchen. Connor is fantastic at kneading dough.
(The Google founders credit Montessori school with teaching them to take their own initiative)
An overview of activities going on in a Montessori school)
Like a Montessori education, Waldorf is at a child's own pace and gives children a great deal of freedom in their own learning. However, this is done completely emerged in fantasy play. Math is taught using gnomes in a story. The first years revolve primarily around music, finger plays, stories and art. It is in tune with natural changes, such as the seasons, night and day, and other rhythms that make up life. Festivals and holiday celebrations are a large part of both the Waldorf school experience and home experience.
While a Montessori nature table is made up entirely of things the children find outside in nature, the Waldorf nature table integrates colorful cloths, felt dolls and other hand-made items into the collection.
The first seven years of a child's life are considered to be very physical, and so movement and play are emphasized. The schoolwork includes handicrafts such as knitting, woodworking and playing musical instruments The next seven years are more based in the thoughts, and that is seen as the optimal time to focus on the abstract ideas of math and language.
Waldorf educators claim that current brain research is on their side, and that delaying reading until the first grade is beneficial.
(A quick photographic overview of a Waldorf class)
(Overview of Enki, which is similar to Waldorf but without the spiritual (anthroposophy) aspects, integrates some Montessori philosophies)
So how does one choose?
Connor has chosen for us. He prefers Montessori for reading, and Waldorf for math.
On his own without our prompting, he has had an immense desire to learn letters and learn to spell and read. This came from watching us work on the computer. Last year he realized he could look up things he likes on the internet, and started asking us to look up everything from legos to pictures of squids to videos of Doctor Who. When I became pregnant, I didn't want to get up from the couch and type for him anymore, so I started spelling things out for him. That evolved to us writing things down on paper for him to copy. Now he can spell "lego" on his own and is learning to spell such complex words as "schleich" and "Anakin."
And, he has shown serious interest in the sandpaper letters. We have integrated that with learning the phonetic sound of one letter every week, combining it with arts, such as gluing glitter to a letter A or macaroni to a letter B or molding bread dough into the letter C.
Connor is 5 years old, and he wants to read and write. I'm not going to wait until he is seven years old to help him.
Numbers, on the other hand, do not interest him as much. We have tried various Montessori materials but they do not draw his attention. We've tried counting frogs and even online computer games. Math interests him when we are dividing a bag of gummy candy by 4 people, and he counts with me when we bake something and add the ingredients. Mostly, though, math is not something he will be taught. He will learn it when he is ready.
For now, he likes the Waldorf approach of finger plays and books that might talk about numbers or basic addition and subtraction. We can integrate it into his fantasy play - General Grievous has 4 light sabers, Ventress has two, so General Grievous has twice as many. We do subtraction at the library when we tell him he can pick out 5 books, he has picked out 3, so how many more books can he still get? But he has no interest in lining up the number rods, counting sticks or touching the sandpaper numbers.
The conclusion to draw from all of this is that each child has their own complex way of experiencing the world, and sticking to any one philosophy without observing your child in it is a less effective way of doing things. I love the Montessori method, but if some of the activities aren't working for us, as a homeschooling mom it is my prerogative to switch to something else or tweak it up a little so that learning is always something fun and engaging instead of something to just get over with so we can move on.
My three year old is loving all the Montessori materials and jumps at any chance to use them, but when she is done she is ready to grab a costume from her dress up box and run in circles and howl at the moon. She has her practical life, and then she has her fantasy life. She has it all.
The truth is, there's no right and wrong way to homeschool, only right and wrong ways for YOUR child. The same goes for alternative schools. Connor goes to a preschool enrichment school once a week, and it is neither Montessori or Waldorf - it is at his gymnastics school, and the majority of the 3 hour class is spent in physical activity, followed by a little bit if circle time, basic numbers and writing time. Connor LOVES IT.
My favorite Montessori book is Teaching Montessori In The Home, because it includes ways to make some of your own materials. My least favorite is Montessori From The Start, because she seems to go above and beyond Maria herself and comes across as very anti-attachment parenting. Some of her suggestions for children under three made me uncomfortable.
The Montessori-related blogs I read most often are Montessori Matters, My Montessori Journey, The Montessori Goldmine, and Maria Montessori. Montessori Goldmine is especially delicious.
My favorite Waldorf-related book is Seven Times The Sun, which is about establishing daily, weekly, monthly and seasonal rhythms. My copy is well-highlighted and dog-eared. Another good one is The Children's Year: Seasonal Crafts and Clothes. I do not own a copy and check it out from the library frequently.
The three Waldorf related blogs I read most often are The Magic Onions, Rhythm of the Home, and Wee Folk Art. Wee Folk Art isn't necessarily Waldorf based, but the crafts are similar in style and everything is free.