You're able to set this on a per-group basis so that some groups are added to the recipient's Education section and others are added to the Certificates section.
For the group that you'd like to be added to the Education section go your groups, select your desired group, then under 'advanced settings' go to 'LinkedIn' and select 'University or School' under 'On LinkedIn we are a:
Once that's selected, Save your group.
LinkedIn requires more information for an Education credential. You should add data for the fields 'startYear', 'endYear', and 'fieldOfStudy' to make this process easier for your recipients. You can add these as attributes on your account and then provide data when uploading or creating a credential.