2002/01/01 by Alexander Karp
Social Sciences · Mathematics · #Mathematics Education and Teaching Techniques #History and Theory of Mathematics
paper · doi:10.1080/10511970208984035
It is useful to present mathematics problems not as isolated exercises without any connection to one another, but as parts of a coherent whole. Today this fact can be said to be universally recognized. The very expression “making connections” is currently quite common in literature on methodology and is even frequently used as a synonym for the expression “doing mathematics.” The construction of cycles of interconnected problems has a long and rich history in mathematical writing (e.g. the books of problems [2] and [5], to mention two classics). Oddly, however, such assignments are often lacking at the most basic levels of instruction in current teaching practice. Teachers who wish to offer such problems to their students must think about the best way to construct them, and to reflect on the types of connections that can arise between them. Both issues are investigated below.