Translation:Can I practice Chinese with you?
"practise" is the British spelling. I am American, but i favor "practise" because it is more fonetic. I am a firm supporter of (ov) English spelling reform; "foneticizing" as i call it; given that millions of English-speakers ar functionally illiterate, no-one (-wun) should be able to, in good conscience, choose the clearly-less-fonetic ov two or more accepted spellings.
一起 means together. Since the context of which this sentence is said is not clear, it works both ways。Previous lessons included 一起 because whatever verb that follows 一起 was done together. For example "我可以跟我的朋友一起来吗?" "Can I come with my friend together?“ （The action "to come" is being done together by both you and your friend)
Now when you apply 一起 to this sentence you have to pay attention to the verb 练习 since that is what 一起 is referring to. Are both you and he practicing? or only you?
我可以跟你一起练习中文吗？means "Can I practice chinese together with you" (Can we practice chinese together?) in better english. It implies both of you are practicing with each other. Whereas 我可以跟你练习中文吗？is just saying "Can I practice chinese with you?" or more accurately, "Can I practice chinese ON you?"
If you're saying this to a fellow chinese student, you'd want to say 一起 whereas if you're asking a native speaker if he'd help you practice chinese by talking to him, you wouldn't.
This is a very helpful explanation - so thank you! But it raises the question for me of whether 一起 is really necessary even when it's clear that the action is jointly undertaken. In English we say, 'I'm going to the store with you' when we mean 'I'm going to the store together with you', because in English you would only add 'together with' for emphasis. If I were to say in Chinese, 我跟你去商店，would that sound strange? That is, would the addition of 一起 be necessary for it to sound good to a native speaker?