As you might know from the page Intelligence, intellect and intelligence
are not the same thing.   Intellect (or smartness) is of the mind, and intelligence is
of the heart (so to speak; "of the spirit" would be more accurate).
Intellect helps us live in the society, climb the social ladder, make our lives on Earth
more comfortable.
Intelligence guides us in healing, helps us avoid spiritual snares and temptations,
helps us live in harmony with each other and nature, helps us reconnect/maintain
connection with Divine Loves (Gods), guides us towards the highest energy
state.
Intellect can take advantage of others and nature, bring about wars and other
unloving things.   Intelligence can do no such things - intelligence is an aspect
of love.

The words "intellect" and "intelligence" tell us their story:
intellect = internal light leads (but) entity can't tell
      Everyone's internal light (spirit) offers guidance, but
      the mind can't tell.
intelligence = internal light leads individual
(towards) godly energy (state) called enlightenment

Neither intelligence nor intellect can be taught, but intellect can be enhanced by
teaching.   Let's see what story the word "teach" reveals.
teach = train entity answers cashed (in the) head
      By teaching, answers are being recorded in the mind,
      enhancing smartness, intellect.

However, deep inside of us, as the spirits we are, we already know
the answers.   Actually, in a way, it's the mind that blocks the access
to the already-known answers.   When the mind gets out of the way,
either temporarily or permanently (enlightenment), some of the
answers are revealed (though not all answers, as by the divine design
different levels of consciousness have different levels of access; only
God of Gods, the highest level of consciousness, knows all the answers).

Intelligence cannot be enhanced by teaching.   Intelligence is of a far higher
order than any earthly teaching.   Teaching is of the mind; intelligence is of
the spirit.   Intelligence reveals answers.   The word "reveal" tells us:
reveal = (by) removing veil answers liberated
      By dissolving the mind, answers are liberated.
(As mentioned above, the mind is not the only veil, though.   Each level of
consciousness is veiled from the deeper levels.   So an enlightened individual
has a deeper understanding of life, of existence, than a "normal"
person, but he/she doesn't know as much as his/her Higher Self, which
doesn't know as much as the Godly Self, which doesn't know as much as
Father God, etc.)

Here is the funny part: for a person to be able to listen to his/her intelligence,
a certain level of smartness is needed; a certain amount of teaching is necessary.
When that person has a certain level of intellectual understanding, it helps as
a stepping stone to getting in touch with his/her intelligence.
For example, let's consider the answers (information) on this website.
It is all intellectual teaching, but when you follow it, such as detoxifying
and going to a chiropractor, it elevates your health and thus helps you
connect with your intelligence.   Once your intelligence takes over,
you don't need as much teaching.   Some teaching still may be necessary,
to substitute for the lack of answers that even your intelligence may not be
able to provide, due to the further veils deeper inside of you.
A helpful analogy may be of a computer.   The operating system and other
programs are akin to intelligence.   The computer's BIOS is akin to the mind.
The different levels of technical support are akin to different levels of
consciousness.
When the computer is powered on, it cannot use the operating
system and the programs right away; it has to boot, to initialize.
The BIOS is a small program embedded on a special chip that awakens
the computer to a level where the operating system can start functioning
and operate the computer.   Even though the operating system, and other
programs, are sophisticated, sometimes they still don't know what to do,
and have to ask the user.   Then there are times that even the user doesn't know
and has to call the technical support.   And then even the technical support
might not have enough answers in some situations and they have to ask
the program developer.

Education should provide us with true answers and ways of reconnecting
with our intelligence, and maintaining that connection.
Please, see the page Education for more info.