We have a lot - at various ages - but here there are all lumped together:
- bead bars
- someone else's eyes
- built-in control of error (anything where the pieces won't finish going in if one answer is wrong)
- figuring the problem two ways
- the human brain (which is mathematically designed)
- intuition developed through experience
- studying mathematics in history and culture
- graphing calculator - middle school; could be introduced as a future tool in upper elementary
Montessori mathematics develops perception and intuition; the children learn their facts through the consistent use of the Montessori mathematics materials. The fact is, they don't *need* a calculator.
Any child or adult with experience in mathematics can figure out how to USE one. So it's not about "teaching them the tools they'll need in the future" - they'll figure it out when they get there.
Graphing calculators are a handy tool - but to gain the maximum benefit, sufficient understanding of the concepts must be applied. Graphing calculators can be useful in middle and high school. Perhaps introduce in upper elementary, but it's not necessary. They have so much else to learn, why hinder them with using a tool that just gets in the way?