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In my experience with children and schoolwork, it's not something you want to push them on if it's not mandatory and they already have difficulty with school in general, you could push them away even more. I know you've been having trouble with Jan recently on his schoolwork in the summer, so I would take it slow.
You could be sneaky about it and use words, that were in his quiz, during the week when speaking with him. You wouldn't be approaching him directly and saying "We need to work on this", which could turn him off. But if you just incorporate the words from his quiz, or similar words, into your vocabulary as a part of everyday conversation he may pick up on it, or ask what they mean.
And then the coming Monday, test him again and see how he does. If he is still having trouble, ask him directly what he is finding difficult.
But as my children got to be older, I would start throwing in words a bit above their grade/age level during my conversations. Myopic, tenure, penchant, aggregate, etc. They would ask me constantly "Mom, what the heck does that mean?" And I was happy to tell them.
Even my son, who was a lot like Jan in not being a huge fan of school, was still inquisitive and wanted to 'know' what those words meant. And then I would sometimes hear him say the words in sentences when his friends were visiting to 'show off' his vocabulary. He may not have remembered what they meant, which is when he would ask me again or look it up, to try and retain it. I mean he had to know if he was going to show off to his friends, right? :)
You definitely know Jan the best and what would work best for him, I can only give my suggestions on what has sometimes worked well for me. Please keep us updated on how works out with him and his vocabulary.