Howard Gardner is a great proponent of multiple intelligences - but I think a few more can be added to his traditional seven.
Schools focus for the most part on linguistic intelligence (being able to speak and write clearly, learn languages, and to use language to achieve goals), and logical-mathematical intelligence (carrying out mathematical, analytical and investigative procedures). These are why there's so much emphasis on maths and English at schools. The former is easy to test the latter is deemed a requisite skill of civilisation (to which I agree, I'm just not sure that schools go about enthusing people for literature very well though! A case of too much, too soon as considered by Richard House in his edited collection below.)
That's it. Really just two.
Of course, schools try for more, as many teachers are well aware that children presents more than just two areas of skill to be tested and graded, but at the end of the day, that's what they will be examined on and which will enable to rise higher up the academic ladder. That enables the systems that be (created politically, philosophically, haphazardly, accidentally over decades) to divide and grade pupils on their abilities in these two areas only.
Yet someone poor at maths may be an excellent artist, or vice versa. Now, I often have students who are 'good at exams' but who can't draw/dance/sing, etc, and who are not interested in working on those areas. After all, exams in art and drama and music are not as held in such great esteem as maths and the sciences. But why's that? The mathematically minded pupil is failing in art...shouldn't we help them overcome their inability just as we would an artist struggling with maths? After all, people are more likely to be able to communicate with pictures than they are with numbers.
A useful analogy is the gym addict who is passionate about his (we'll go with the male here as it seems more common) pectoral, abdominal, biceps and deltoids but who doesn't work his hamstrings, glutes and triceps because he can't see them. All muscles need working and our bodies need balance otherwise they end up being overused in some areas that will then increase the risk of injury. We could say the same with the intelligences.
But our academic system predominantly only focuses on two.
Hey ho! What other intelligences according to Gardner's theory do we possess? (The following image is from novamind.com. It's lovely in its visual intelligence.)
Musical intelligence - performing, composing, understanding and appreciating rhythm. Well, that gets killed by much of modern pop culture and school music lessons (for the majority - there are always exceptions, usually propped up by parents and music tutors).
Bodily-kinesthetic intelligence - using parts or the whole body to help solve problems; having great coordination. Now, we certainly are in awe at students and adults with great physical co-ordination, and to some extent it is encouraged at schools, particularly those with good sports resources. Sadly, most of the population come out of our educational institutions will little appreciation of their own physical intelligence - why else do we see growing numbers of unhealthy people in our midst whose resemblance to our hunter-gatherer ancestors is remarkably absent? Who took the fun out of games? Was it the schools or the diet people followed? Was it the advent of 'plug in drugs' such as tv, computer games, and the whole paraphernalia of screens?
Spatial intelligence: understanding and orienteering through space. Some people seem to have a better sense of size, volume and area than others, but I don't think it's wholly genetic. By referring our selves to the world around us, we can certainly gain a better appreciation of size, and who is not awed by a massive mountain, a beautiful valley, or the immensity of the sea or the heavens? If you're not, start measuring things around you!
Interpersonal intelligence: understanding the motivations, intentions and desires/fears of people around. While a prerequisite for sales and teaching, it's also something that can be taught people who believe themselves or who have accepted themselves as lacking in this regard. Mimicry is a good place to begin - copying what others do (politely that is, with permission or watching people on tv), acting out dramatic parts and drawing people's faces can all help here. A tip from the great psychologist and philosopher, Nathaniel Branden, is to take on the poise/posture of the the client you're with - now that's if you want to get an insight into how they are feeling. However, my personal trainer, Guy Baker (Nottingham, Triple B Gym) prefers to sell his great poise to clients - walk like a king and people will want to emulate you, is his philosophy! Either way, you're stretching into other people's thinking. Literature is another great way to help us understand more complex motives.
Intrapersonal intelligence involves being able to get in touch with our selves. This is the fun of introspection - of gaining a sense of the big picture of who we are, where we came from (metaphysically as well as culturally and biologically), and the patterns we have generated in our own lives. This is all about the intelligence needed to master one's life: to know thyself as the Greeks rightly put it.
Others have added:
Environmental intelligence: this is an awareness of one's position relative to the natural world, having a sense of the flows and cycles of nature; being able to navigate the woods say. "I went to the woods to live deeply" ethos. It's interesting that townies are often quite low on this area. We see the ramblers in our neighbourhood, dressed very brightly and tending to make a heck of noise as they stomp through gorgeous English countryside wondering, if they got around to it, why they hadn't seen any deer or badgers. Some country folk are like that too of course. The key is get lie down in a field and just sense the immensity of life all around - to 'ground' oneself (ions, I hear) and moreover to listen and survey the living world, to feel how it grows without effort, to feel the energy of the living systems all around.
Existentialist intelligence: an understanding of greater, metaphysical issues, or at least a keen interest in them. Spiritual experiences, an openness to viewing the planet as a whole, the universe as a whole or querying the nature or existence of God, the universe, and mind. These are often invoked over a glass of wine or a theological seminar, but we're all open to pulling away from ourselves to wonder at our existence. Jean Paul Sartre had us "thrown into the world" without choice. Buddhists claim that we choose to enter this world from the spirit world: we choose physicality.
To these intelligences, I would also add:
Value intelligence: an extension of interpersonal intelligence to commercial values. Some people train their intelligence here to become excellent traders and entrepreneurs - they see value where other people as yet do not; or they know the difference in values across economies or time, so are good at arbitrage or investing. Again, this area can be exercised and trained through such subjects as economics and business studies, but more importantly through experience. Perhaps Gardner incorporates this skill into others, but there is something unique and attractive about someone who reads markets well.
Temporal intelligence: having a conception of the passing of time. Time is ... philosophically awkward ... but some people do have a keener sense of their mortality, impending deadlines, the need to be punctual and timely in comments and replies. There are times when silence is important - and that relates to intra and interpersonal skills, but a sense of timing in the sense of a duration is critical in sports, business, trading, the military, politics, and diplomacy.
Expressive intelligence: this one I owe to my pupil, Zoe Gascoyne. You never know where ideas come from and she, being an artist, thought that her greatest strength lay in being able to express ideas and emotions artistically. It overlaps with other intelligences of course, but in a great sense, all of the above will overlap and should not be construed as sitting pretty by themselves (exclusive of all other categories, logicians would say); but I think she hit upon something. When we look at a dancer, an artist, a composer, a comedian, an actor, a rhetorician ... yes, they are all using verbal-linguistic-musical-spatial skills, but to use them all together to great effect that we appreciate in awe, then the ability to express surely accounts for an intelligence. A bard relates a story so much better than the average reader or reciter. I don't know this book, but I've put it on my wish list!
Any feedback on these ideas are more than welcome - the purpose is to help us all gain a little more understanding of the breadth of intelligences we possess and to cultivate those we are relatively weak in.