Berkeley Math Circle or Russian School of Mathematics for 9yo?

Hi friends. Need your collective knowledge on this one. My daughter, age 9 (3rd grade), is very interested in math and would like to learn more challenging math concepts. My concern is that, right now, she really enjoys math and I want to her to remain curious and excited about it. But I also know she's looking for more of a challenge. Knowing this, should I look into Berkeley Math Circle or Russian School of Mathematics? Or is there some other school, tutor or recommendation you'd propose? I'm more interested in her being excited about math and knowing less, then knowing more but it killing her interest in it. Thanks all!

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My kid is signed up for both, and enjoys RSM of math more, because it is easier. BMC is more conveniently located, and much cheaper. Their math problems are abstract. Their classes are large and mostly online at present, though some return to in person is envisioned for next year. Parental help is required, at least for the younger kids, because their homework problems are hard. Russian school of mathematics tests the kids and can place them at various levels, either online or in person. Their problems are much more concrete than BMC problems, though more abstract than what is taught at local schools. Classes are small. No parental involvement is required, because the homework is a straightforward application of the class lesson. BMC teaches students to think like a mathematician and invent techniques; RSM teaches specific math concepts using specific techniques. RSM is a business with many franchises; BMC is a public service run by sometimes-disorganized math professors.

Try beast academy books and in a few years look out for Proof School for middle school. 

Have you also looked into Firecracker math? We had very good experience with their program. Small groups, great teaching with lots of discussion and input from the students, making it into a unique group learning experience. Specifically, my son (in 6th grade at that time) enjoyed the upper division classes taught by Dr. Eli Lebow. These classes were transformative and opened up his eyes to a world of math and math concepts not taught in schools. There was no homework, so no stress and all fun. Later, my son joined BMC which is great in many different ways, but my son still talks about those Firecracker math classes as the best learning experience ever.

I have had two kids do RSM. One joined mid-year in elementary school and initially found it very stressful, but after that stuck with it for 4 years. After 8th grade they decided to do AOPS on their own over the summer, and just completed calculus at Laney as a freshman in high school (they felt too busy for RSM this year). My middle schooler wanted a break from RSM this year as well, but now wants to do it again next year because they realize how much more math instruction they got.
I wouldn’t say either loves math, but they do enjoy being good at it. They both felt like RSM challenged them and made them a lot better at solving problems than they would otherwise have been.

Berkeley math circle is a wonderful program— many of the presentations are by math grad students. It tends to cover topics like number theory and topology that aren’t part of the school curriculum. Ideally she could attend with a friend, as at least in the past boys were over represented. 

Firecracker Math is a group with afterschool classes that I've heard is great.  We didn't use it because our kid didn't turn out to want to do math as

much but maybe you would like it?