What makes you think he is hiding his abilities? Any evidence he has ever been shamed by a teacher or teased by other kids? At this age it is unlikely because kids this age are generally not cognitive of academic differences. It is much more likely that his observant nature at preschool makes it hard for him to focus on "performing" for an assessment. My son had very erratic performance on assessments in K because he had to feel 100% comfortable with the assessor, he didn't really understand what it was about, and he had to feel like actually answering the questions. It is only at age 7 that we are seeing some consistency develop because he now understands the process and what the results can mean for him getting more interesting opportunities at school.
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Two main concerns here:
1) I believe it is important for a school's philosophy and the parents' philosophy should be a fairly close match. A lot of people love the Montessori philosophy and it worked for them and their child, but for others it is the wrong approach (it never would have worked for us). If you are doing a lot of teaching at home and it isn't a match with the Montessori way then this school is not the best choice for your family. You commented that your son is bored, but I wasn't clear if he is bored at school or if he is bored at home when you aren't providing homeschool activities. Is he good at finding self-directed activities or he does he look to you for "entertainment"? This may be having an effect on how he proceeds with work at school.
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2) I understand that different kids reach social stages at different times but that doesn't mean we shouldn't provide just as much instruction in social skills as we do with academic skills. My son is gifted and until this year (2nd grade) most of what I worked with him on at home was dealing with his social-emotional growth and even this year we are starting to do some very targeted work on his "executive skills" (time management, task initiation, emotional response, etc.). It is unclear from the post what other social experiences your son has on a regular basis...does he have playdates? Group activities with you in tow? Chances to practice making brand new friends at a playground? Other? Gifted kids often have trouble with social-emotional skills because the brain is developing in a different order. It is important to provide the structure and instruction to help them thrive or it can end up holding back their academic development.











