This part of the toolkit considers how the processes of inquiry based learning may be integrated into the teaching of mathematics content. In many schools these two aspects of learning, content and inquiry, are kept separate. Content is taught as a collection of facts and processes to be understood and then replicated, whilst inquiry is developed through investigations that tend not to incorporate the development of important content knowledge or concepts.
The integration of content and process raises many pedagogical challenges. The processes under consideration here are:
- observing and visualising;
- classifying and creating definitions;
- making representations and translating between them;
- finding connections and relationships;
- estimating, measuring and quantifying;
- evaluating, experimenting and controlling variables.
As some have pointed out, these are developments of natural human powers that we employ from birth (Millar, 1994). To some extent, we use them unconsciously all the time. When these powers are harnessed and developed by teachers to help students understand the concepts of mathematics and science, students become much more engaged and involved in their learning.
There are three professional questions in the toolkit for this issue.