Four papers are presented which view research in mathematics education from different perspectives. The titles are: (1) Review of Recent Research Related to the Concepts of Fractions and of Ratio; (2) Some Trends in Research and the Acquisition and Use of Space and Geometry Concepts; (3) A Portrayal of Traditional Teachers of Mathematics in American Schools; and (4) Hidden Dimensions in the So-Called Reality of a Mathematics Classroom. The first three are related to invited presentations at the second meeting of the International Group for Psychology and Mathematics Education (IGPME) in Osnabruck in September 1978. The fourth was developed as an invited address at the annual meeting of the Special Interest Group for Research in Mathematics Education (SIG/RME), which was run as a pre-session to the National Council of Teachers of Mathematics (NCTM) conference in Boston in April 1979. (MP)