I could use some guiding on how to teach equilateral triangle and rhombus areas in a Montessori way. I think she has gotten the triangle part, but I don't know if I got it enough to know if she is getting to the solution the right way or not.

Being able to perform a multiplication computation using only the standard algorithm is actually a fairly useless skill, especially when most of us carry calculators around in our pockets. It's even more useless if you don't understand what's going on under the surface.

Work in the Montessori elementary is a delicate balancing act between spontaneous curiosity, responsibility to the community, and obligations to society. If there is one principle that underlies everything in Montessori, it is that healthy development happens when a child concentrates intently on a freely chosen activity.

A parent asks: "What are the jobs after your upper El student knows basic operations in fraction, decimal, and integer computation? I’m most interested in ones I might be able to DIY at home. Thanks so much!"

Instead of pretending I know what will help you, I want to answer your questions. So ask away. I'll do my best to answer any questions about Montessori, math, teaching, and Montessori math teaching.

I was recently asked to explain just how the Binomial Cube demonstrates the binomial theorem. So let's start not with the cube, but with the binomial theorem.

The work of young people is to become capable adults who can take their part in society. Children are eager to take on societal expectations. They want to be responsible, and when they are given the message that they can be, most will jump at the opportunity, and take their responsibilities quite seriously.

If taking on our own hard things were merely a way to get kids to work hard at their school assignments, it would still be fundamentally manipulative.

As an adult who spends a good deal of time with children, I’ve come around to the belief that one of my responsibilities is to let the children see me struggle with hard things.

One of the relatively unique features of Montessori schools is multi-age classrooms. There’s a span of at least three years in each class, and they can go up to six years. (I’ve taught a class of 6-11 year olds, myself.) To be honest, I always think it's ironic when schools go to a two-grade "blend" and it's treated as some sort of daring innovation. Montessorians have been "blending" much wider age ranges for a century, and before that, one-room school houses were the norm. In fact, single grade, age-based classrooms are historically a very new invention.

In a Montessori elementary classroom, we expect that children will learn everything that children in local public schools will learn. This isn't such a difficult task, because the typical Montessori lessons incorporate nearly everything that’s in those public school standards. We help the children take responsibility for their learning by making the public school curriculum standards available in the classroom, and helping them understand that society expects them to master these things. I made a child-friendly version that I kept on a shelf in my classroom, as the "official" standards are pretty much impenetrable, and tend to use a lot of words to say remarkably little. I find that the children are eager to take responsibility for themselves, so they tend to check the standards themselves and nag me to give them lessons on what they feel they need help to learn.

A parent posted this question on a Montessori Facebook group recently (used with permission):

"Hello! What does "follow the Child" mean for you during second plane? I confess I am a little confused with my son (7 years old), because he is so independent now that I can't see what he needs. For example, when he was younger I observed his interests and needs and prepared his shelf for them. But now I can't see what he needs/wants to because he is faster! Now he takes what he needs. For example, some days ago I was feeling sick and he said "I want to do a volcano". So he grabbed all the things he needed to do one. It was wonderful but I thought "jeez, It should to be my work to facilitate his activities". I don't know if I am clear."

I want to challenge you to question your assumptions about school. About children. About learning.