"Er rennt mit seinem Kind."
Translation:He is running with his child.
"seinen Kind" would only work if Kind was masculine anyway. Since it's neuter, it would have to be "sein Kind" in the accusative.
No, the dative in "mit seinem Kind" is absolutely correct. One way that can sometimes help to get the cases right is to ask the corresponding questions like "Mit wem rennt er?" (In English: "With whom is he running?"). The interrogative pronoun also takes the dative, which has both in English and German an "m" at the end.
I'm sorry, but jjd1123's explanation is terrible. The "Mit wem rennt er?" sort of question ONLY comes in handy for native speakers or people with very advanced German and who have already developed a "feeling/hearing" for grammar without overthinking it. This happens because sometimes native speakers are not sure which case to use, but when they go back to a essential question like that, the case becomes pretty obvious. I have seen many people recommending this tip to learners in vain. Learners tend to end up even more frustrated because they do not always not when to ask "wem" or "wen".
Anyway, the explanation for the dative case in this sentence is VERY simple: There are certain prepositions that require a certain case.
"Mit" is always used with the dative case. This is why "mit seinem Kind" is correct.
My tip is, look up the most common exclusive-case prepositions and learn them by heart. This will make things a lot easier.
Fair enough. Although I suppose in this case the question may still work if you have the corresponding "feeling" for grammar in English since it is the same there. However, if the cases are not the same in German and English I can imagine it not working.
The reason why I recommended this approach is not because this is what native speakers fall back to when they are unsure (although they often do), but because this is how we are taught the cases in primary school. Therefore I thought this may also be a more natural approach that makes learning by heart a lot of prepositions and verbs and the cases objects following them unnecessary, but I can see how you would have to have a certain feel of the language first in order to be able to decide when the question sounds wrong.
I guess then you have to just learn the cases by heart then. Maybe if you are not sure you could use a dictionary like www.leo.org where often the required case (if there is one) will be pointed out. Then in addition to thakelos tip of looking up the exclusive-case prepositions you might consider learning not just the meanings of simple words but of the whole expressions instead, i.e. instead of trying to memorise "with = mit" you could go for "with someone = mit jemandem (dative)" instead. I hope this was a bit more useful.
I am sorry. I sounded pretty rude earlier :( Thanks for your addition.
And yes, I was taught the same thing in elementary school as well, but many of my friends struggled with it and I have seen it being a problem here in duolingo.
I am sorry but I still don't understand the explaination. I know that we need the dative case here, and since Kind is neuter, according to me we should use seinen instead of seinem (masculine). Could someone clarify it for me? I am lost again...
You are right about the cases, but wrong about which endings correspond to which gender. In fact, in the strong inflection the dative ends in "-m" for both masculine and neuter words. See e.g. wikipedias article on German declension: http://en.wikipedia.org/wiki/German_declension#Attributive_adjectives
Also, kangaroopouch is aware that in this sentence the dative is used, he is just pointing out that it would be "sein Kind" instead of "seinen Kind" if it were accusative.