Person B was a student of Person A. After watching Person A teach a certain way, utilizing household objects to aid in his teaching, Person B (without being asked) went out and created the crude prototype. He then brought to Person A.
Person A, working closely with Person B, helped refine the prototype before it went in to production, but Person B was the one who actively created and initially managed production of said product. So the reality is that the product was based on Person A's teaching concepts, but the physical product was a result of Person B's ingenuity.
Sounds like you have a good claim to joint inventorship, but person A may contend that it was person A who conceived of the claims, and Person B was just a pair of hands. What matters is what Person B contributed--if Person B contributed something non-obvious and inventive, then Person B might be a co-inventor. But building a prototype without participating in the basic conception may be insufficient to justify treatment as an inventor. You need to retain patent counsel to advise you----the detailed facts and circumstances are what matters here.