There's definitely a strong overlap in that sense. Probably also because these institutions tend to have smaller class sizes which allow better teach/student interaction and more time. Public schooling in the US could do this too, but has been hamstrung for decades.

In math the kids definitely leveraged the binomial/trinomial tools, beads and other tactile methods to have a better understanding of the concepts of mult/div/exponentials/roots long before they would have approached in the standard US arithmetic methods. They were also doing algebra and geometry by the end of Montessori.

Montessori also spends a lot of time working on holistic views with regards to science and history and then give the kids the freedom to do their own research and projects on the topics. The normal school models tend to take more of a cause-effect + memorize the dates method as that's what tracks the testing. It's not generally till university that they then go back to something that usually requires critical thinking.

On critical thinking there's an emphasis there in Montessori on involving the kids in asking more questions and then building a model to analyze and defend their position. Public school is optimizing for learn by rote and it's a culture shock going to Uni where they back to something that's utilizing critical analysis.

My older child is in IB at the moment and they're using much of this as it's taught in more of Uni style.