Technology and mathematics are two things that are interconnected and influence. Technology, such as computer games, can be used to describe abstract mathematical concepts so that they are more easily understood by students. Unfortunately, technology also has some undesirable impacts, such as causing students difficulties in developing their creativity to understand mathematical concepts. On the other hand, spatial ability gets less attention than educators when students are studying mathematics. This paper will discuss how teachers can help students develop their mathematical creativity and spatial ability.

In this paper, we introduce the notion of a directed preserving generator (d.p.g.) from R into R. This d.p.g. can be used to construct new fields which generally have the same properties as R, except that some properties are affected by d.p.g. itself. With this new field, a ν-normed space will be formed. Some of the basic properties of this normed space are also discussed.

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