Hi Rita,
For users that does have login in Confluence, once you access the dashboard, in the right side of your screen, you will see a button named Give me the old dashboard. To revert it to the new dashboard, you can refer to this doc, for each user that clicked the button.
However, as you question is related to the Anonymous users not seeing the spaces in the dashboard, one of the options that you can give a try is to edit the dashboard content. For that, you need to access the Global Templates & Blueprints option in your administration console of Confluence. There, you have an option to Edit the Default Welcome Message.
There, it will be like a normal page to add content. To have the spaces displayed for the anonymous, you can select the Spaces List macro through the macro browser of Confluence (*Insert* button in the editor). This macro will display all the spaces of your instance in a list and it will be in the dashboard, once you will be editing that. However, I have created this feature request which fits with your situation: https://jira.atlassian.com/browse/CONF-40221
Hope it helps!
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