| Irrational numbers are inherently difficult, yet, understanding of irrational numbers is extension and reconstruction of the concept of number from the system of rational numbers to the system of real numbers in high school.The paper is an investigation of the juniors' understanding of the concept of irrationality, according to Tirosh, D's conceptual framework and conception of theories of cognition, from the definition, the representations, the algorithm, the property and application of irrationality.The paper is expected to solve some confusion of irrationality and search for the cause of them.Some conclusions after questionnaire survey , literature search and individual interview :(1) with respect to definition of irrationality, juniors remembered well. (2)Juniors' concept image of irrationality is short of in the earlier period, only 14.26% of juniors rememberedπ(3) Juniors' concept image of irrationality is scarce .(4)with respect to Juniors' intuitions and their formal knowledge , there are inconsistencies.(5) with respect to Juniors' intuitions and algorithm knowledge of irrationality,there are inconsistencies.(6) with respect to the property of irrationality, Juniors are subjected to the negative effection of knowledge of rational numbers.(7) with respect to the application of irrationality, Juniors have difficulty in associating real problems.Finally, some solutions are offered:(1) Teaching should be combined with the two competing definitions of irrationality.(2) The content of rational numbers and irrational numbers should be closed arrangement together.(3) Teaching should be combined with the formal knowledge and algorithm knowledge of irrationality.(4) Strenqthen the usage teaching of the irrational number concept.(5) The recognition of changing teaching is aboutπ.(6) Learn irrationality with the aid of history of it. irrationality real numbers conception intuition algorithm...
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