Not all the illnesses on the scalp such as eczema, psoriasis, scabbing or rash are contagious. Until a second infection occurs in these areas and cause inflammation. We can define infectiousness as this: if the affected site causes pain, it has inflamed scars and gleet, particularly, a gleet in yellow, then this is the start of an inflammation, and is contagious.
Especially for kids who go to school, the reason for hair eczema can be pediculosis. Pediculosis was thought as related to what the socioeconomic level of a person is and yet, we do not think this is true anymore because children can have pediculosis in places where many people live. If you can see the crab louse/pthirus with your bare eyes, you might not identify the cause of the itchiness and eczema on the scalp. If there is a disease that goes on along with the pediculosis, that disease can be contagious too. In the school kids, the very tiny scaling, and other fungal infections of the scalp are very common. These fungal infections are often seen before the adolescence, before the hair gets greasy. The fungal infections seen in this age group (school kids) are certainly contagious.