Is the primary purpose of public schools indoctrination or education?

Home school student and parent
Home school student and parent
Even though students taught at homes make up just 2 percent of the entire school age population, they are more than 10 percent of the finalists in this year's national spelling bee. They will make up an even higher percentage at National Geographic Society's National Geographic Bee. In 2021, 14-year-old Zaila Avant from Harvey, Louisiana, breezed to the Scripps National Spelling Bee championship on Thursday night, becoming the first African American winner and only the second Black champion in the bee’s 96-year history. She has been home schooled her entire life. In 2007 home schoolers walked away with top honors in four major academic competitions: The National Geographic Bee, the Scripps National Spelling Bee, the Intel International Science & Engineering Fair, and the first GSN National Vocabulary Championship.

Certainly children and learn if education is primary like it was over 100 years ago. Although, nothing in the exam is difficult to learn, how many modern day public high school graduates, let alone 8th grade students, could pass the following 8th grade 1895 exam?
https://www.grc.nasa.gov/WWW/K-12/p_test/1895_Eightgr_test.htm
Is the primary purpose of public schools indoctrination or education?
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