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These materials were written with the aim of reflecting the thinking of the Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics. This report deals with some seventh grade mathematical concepts taught at Cambridge Friends' School. The discovery approach was utilized by the teacher in order to involve students in the classroom discussions. The problematic areas which are dealt with in this report focus on (1) geometry as physics versus geometry as mathematics, (2) proofs and mathematical reasoning, (3) area, and (4) infinite process (approximations). Instructional procedures are described and student reactions to various procedures and activities are listed. [Not available in hard copy due to marginal legibility of original document]. (RP)