Using v. 2.79; the controls I have do not match what you have. For example, I don't have "roughness" as an option. That said, I have done the following which should work but seem not to:
(a) Check the mirror box
(b) Set reflectivity to 1.0
(c) Set Fresnel to 0.0
(d) Gloss at 1.0
The preview shows a near perfect mirror result on the sphere. But when I rotate around the window on my rocket ship there are ZERO reflections to be seen.
The material appears to be appropriately attached to the object, BTW.
In 2.79, I would switch over to the Cycles rendering engine ...
... set the material to use nodes ...
... and then change the surface to use the Principled BSDF shader ...
This should give you all of the material options you need to create the materials like I do in the course. We'll be using the Cycles rendering engine later anyway, so you'll be a step ahead! Just note that the viewport rendering will not be immediate.
Here's what I mean by that:
When you switch over to the Cycles rendering engine, you'll be using Blender's path tracing engine to render when you switch into render view. Unlike Blender's OpenGL viewport and Blender 2.80's new Eevee rendering engine, Cycles is not real-time, so the scene will appear slightly pixelated until it fully processes.
Additionally, the reason you aren't seeing reflections is because there is no default lighting setup in Blender 2.79. The Blender version I use in the course creates a temporary lighting setup in it's new Eevee rendering engine, so materials are easier to work with. Since you're trying to complete this course in Blender 2.79, I'd recommend just copying my material settings for now (other than color). You'll take care of lighting later in the course and then you'll be able to see those reflections.
Are you in Look Dev mode in the 3D viewport?
Also note that the reflections aren't supposed to be super obvious. They're a really small detail in this project.
