Learn Spanish (Latin America): Ellas empiezan a estudiar fotografía el martes. - They start studying photography on Tuesday.

In Spanish, the verb empezar (to start) requires the preposition a when it is followed by another action. The formula is always empezar a + [infinitive]. You cannot just place the two verbs right next to each other without it.

The English translation says "start studying", so why doesn't the Spanish sentence use estudiando?

In English, we can say "start to study" or "start studying". In Spanish, when you link a verb like empezar to a second action, that second action must be in its basic, unchanged dictionary form (the infinitive). Therefore, you must use estudiar, and never the -ando or -iendo form!

Why is it spelled empiezan with an ie instead of "empezan"?

Empezar is a "stem-changing" verb. In the present tense, the second e in the root changes to ie for most subjects (except nosotros and vosotros). That is why it becomes ellas empiezan.

Why does it say el martes instead of using a word for "on"?

In Spanish, you do not use a preposition like en to say "on" a certain day of the week. Instead, you just use the definite article el (the). So, el martes literally translates to "the Tuesday", but it is how Spanish speakers say "on Tuesday".