Hi @paigeleslie,
This can be achieved with a contact-based workflow. You can trigger a contact-based workflow off a deal property – in this case the stage of your pipeline.
You would then select ‘Send internal email notification’ from the workflow actions. From that point on, you can assemble your student card using personalization tokens. I started doing this in the screenshot below. It’s easiest if your teachers are users in your HubSpot portal, yes.
By the way, HubSpot lets you create more owner properties on top of the default Contact owner. It’s a custom property type. You could create a Teacher owner property, assign a teacher to each contact and automatically send this email to the contact’s Teacher.
Hope this helps!