I'm sure it should be "platonic idea" because it's a philosophical notion. It's not an idea proposed by Plato or occured to Plato. It's the concept of some "ideal thing/notion" existing in an ideal world and being supreme over any concrete manifestation of the thing in our world.

Like we have "the circle" in our earthly world, and this circle may have this or that radius, may me drawn on paper or made on sand, but somewhere above there exists the very idea of `circle' which is not bount to measure or media but exists as an ideal notion of which any circle in our world is just a projection.

So I'm highly against "ideas of Plato" because it's a wrong interpretation and it shows lacking any understanding.

For "познавательная и практическая" I'm not that sure, but I suppose it may be "cognisable and practical". The difference is between understanding the very core of the platonic core (the notion of `circle') and the practical examples of its projections (real circles which we deal with in real life). In other words, it's the difference between theoretical understanding/knowledge and practical research.

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Note added at 1 hr (2008-02-25 16:37:14 GMT)
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understanding the very core of the platonic IDEA, sorry. As well as for many typos.