Using students' questions to guide the inquiry
Above are the questions and observations of a year 10 (grade 9) class that had experience of carrying out mathematical inquiries. The teacher used a number of the questions to guide the inquiry into the advanced templates. Linking a new template to a specific question is important because students feel they are retaining ownership of the inquiry even when they may not have constructed the template themselves. While the templates emerge in a process of co-construction between teacher and students, they are firmly rooted in students' agency and creativity. Question | Advanced template (general form) |
Can you change the order? Can you use other operations? | ax - b = cx - d ax - b = c - dx a - bx = c - dx |
Can you add on boxes? | ax + b = c(dx = e) a(bx + c) = d(ex + f) (ax + b)/c = dx + e (ax + b)/c = (dx + e)/f |
Can you use other letters? | Simultaneous equations |
Can you use indices? | Quadratic equations ax^{2} + bx + c = d |
The comment about using variables a, b, c and d leads into finding a general solution for each template. Examples of students' attempts to find general solutions are shown below.