Functions are all around us, disguised as actions on concrete objects. Composition of functions, too, is all around us, because these actions can be performed in succession, the output of one serving as the input for the next. In terms of Gray and Tall's (2001) "embodied objects" or Lakoff and Nunez's (2000) "mathematical idea…

This paper describes two studies conducted with high school students doing library research and writing research papers, with the objective of examining the effectiveness of this type of assignment. The students were all in grade 11, the first group in Canada, the second in the United States. Students were observed in the classroom before they…