急：英语语法问题Jack is trying to spread his new idea to the schools

急：英语语法问题
Jack is trying to spread his new idea to the schools willing to use the money for this new idea.
willing 是什么用法?并请给出其它例句以说明,
这是我改编了一下的句子,原句子为:
Now,Joe Gauld is trying to spread his controversial Character First idea to public,inner-city schools willing to use the tax dollars spent on the traditional program for the new approach.
还有这个句子里的 spent 是什么用法?是省略了：“what is”