The Go template is executed and rendered at server side, in / by your Go app.
When you select something in the School drop-down list, that happens at client side, in the browser.
The browser cannot execute Go templates. So basically you have 2 options:
1) When the user changes selection of the Schools drop-down, re-render the page. This involves sending a new HTTP request, you may provide the ID of the selected Scool in a URL parameter for example, and the Go template may render only the Students of the selected school in the 2nd drop-down list.
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