Maybe he needs time to think before giving the answer.

I think it might help if you give a ritual response
to his "I don't know", the same response every time.
That will make it boring, discouraging him from saying
that (as opposed to trying out a whole lot of different
responses, which he might find interesting and would
positively reinforce the "I don't know" response.)

Suggestions for possible responses you can give to his
"I don't know":

-- Silence. Just wait patiently for him to think of
the real answer and give it. If he asks you to continue
reading or something you can say "I'm waiting for you
to answer:" and then repeat the question in abbreviated
form.

-- "Hmm." This models an alternative response he
can give when he needs time to think.

-- "You need time to think." (then silence.) Again, modelling:
he might possibly switch to saying "I need time to think" instead
of "I don't know."

-- "I know you know." This is more of a joke, but might
help.

-- Just repeat the original question, in abbreviated form,
i.e. using pronouns.

Even though I've listed a number of possibilities here,
note that I'm suggesting you choose one and use the
same one every time.

Each of the above suggestions involves expecting him to give
a real answer to the question. Of course,
sometimes he really won't know, so he'll have to say "I really
don't know!" I just hope he won't develop the habit
of saying "I really don't know!" to all your questions!!

Oh -- you could also try asking him fewer questions.
Maybe he's telling you indirectly that he doesn't want
to answer all these questions. You could also introduce
your questions, so that he'll be ready for them:
"I'm going to ask you a question, OK?"
Or introduce the question more specifically: "I'm wondering
why there's a blue mark on your shirt. Maybe you were playing with
a blue marker. Were you playing with a blue marker?" This
would give him time to think about the subject of the specific
question for a few seconds before he's expected to answer.

Also, you could think of what you'd prefer he say instead,
perhaps "Hmm" or "I need time to think" or just holding
up one finger for a period of silence or something.
Then, whenever he asks you a question, you could do
that before answering, to show him how it's done.

I noticed that if someone asks me a question when I'm
about to blow my nose, I always say "I don't know".
In a sense I don't: my conscious mind doesn't know the
answer because I haven't gone to the trouble of
searching my memory for the answer. Even if it's
something I know well. It's a way of making the
questioner leave me alone. I wasn't doing that on
purpose -- it just came out that way. After I blow
my nose I usually remember to give a real answer.

--
Cathy Woodgold
A *much* better world is possible.