Mathe ist meinen Ausbildern wichtig.
Mathe ist für meine Ausbilder wichtig.
Do the two sentences have the same meaning?
In your quoted example sentence, both expressions are nearly equal, but:
wichtig sein für jemanden/etwas
means something is important for/to something/someone and
jemandem wichtig sein
means something is considered important by someone
The difference becomes apparent when you use the verbs on something that doesn't normally consider things, like: You can say
Frisches Heu, Wasser und viel Auslauf sind wichtig für ein Pferd.
but rather not
Dem Pferd sind Frisches Heu, Wasser und Auslauf wichtig.
(because you wouldn't imply an opinion on healthy living with a horse)
The sentences carry in fact different meanings, but more on a subtle leevel. Both indicate that math is important for my educators or trainers. But there is a slight difference in which way it is important to them.
Mathe ist meinen Ausbildern wichtig.
In german jemandem wichtig sein expresses that it is important to someone and can even be understood as being dear to someone's heart.
Mathe ist für meine Ausbilder wichtig.
This rather means it is important for them and expresses more an opinion they hold within themelves.
The only context provided is that they are educators and specifically that they are yours. So it is somehow implied that they might also consider math as important for you or that math is very important in education generally, but it is not specifically expressed.
If you replace Mathe with another expression the difference becomes more clear.
Gesunde Ernährung ist meinen Ausbildern wichtig.
My educators care about healthy nutrition.
Gesunde Ernährung ist für meine Ausbilder wichtig.
Healthy nutrition is important for my educators.
Not identical:
Mathe ist meinen Ausbildern wichtig
means that they see this topic as important (for you, or for somebody or anybody else)
Mathe ist für meine Ausbilder wichtig
means that it is important for themselves. Although you might find quite some people using both versions having both meanings, especially in spoken German.
BTW, it's Ausbilder, without the "n"...
Mathe ist meinen Ausbildern wichtig.
In the first sentence the object is an dative object. The kind of syntactic usage of dative case in this special sentence is called dativus commodi. When an object stands in dativus commodi in a German sentence, then it is the beneficiary or aggrieved party of the action.
Neither dative case nor any similar syntactic construction exists in English.
This sentence means:
Math is important to my trainers.
So, as you can see, in Englisch you have to add a preposition (to) that doesn't exist in the German sentence.
But you can do this in German too:
Mathe ist für meine Ausbilder wichtig.
This is the exact equivalent of
Math is important to my trainers.
(just in a different word order)
The part für meine Ausbilder (also the english part to my trainers) is called a prepositional object, because it starts with a preposition. Note, that this prepositional object does not stand in any of the four German cases. But it consists of two inner parts, and one of them is in a grammatical case:
So, both German sentences translate into the same English sentence. (You can also say, that there are two possible German translations for the English sentence.) From this you can read, that both German sentences mean the same.