Task intent (part two)
Missed part one ?
In this post we’ll look at task intent for a more complicated and nuanced set of questions, which I previewed at the end of part one. Task 1 in the worksheet is below:
There’s a number of observations to make here before we hand this to our eager students. Firstly, we’ll assume most, if not all details are purposeful - so let’s consider the reasoning for having a grid in parts a), b) and c). Part a) permits you (without explicitly saying so) to simply count the squares behind the triangle with relative ease (squares, and half squares). Why would we want do this? One reason could be to allow some scaffold - giving a better chance of feeling successful for some less confident learners perhaps. The ease at which we can count the squares becomes more difficult for b) and c), but still allows for some reasonable estimating without relying much, if at all, on the area formula. Another possibility is that the purpose of the grid is for the teacher to help demonstrate that the area formula, an abstract set of symbols and numbers, does indeed produce the area of a triangle, which we can cross reference with counting the squares. In some ways, it doesn’t really matter what the author’s intent is, so long as the teacher develops their own intent which makes sense, and enhances the questions by giving them additional purpose beyond ‘just give me the answer’. On the other hand, well thought out questions with defined intent are somewhat wasted, and possibly even detrimental if the teacher delivering them has no idea what the author is trying to achieve. Communicating that intent is really difficult, but shouldn’t be thought of as futile. Considering most worksheets come with no guidance, we are often quite in the dark on intent, and have no choice but to rely on our own interpretative skills to get the best out of someone elses’ questions. That shouldn’t deter us necessarily, but should at least serve as a warning for any head of department giving free reign to new teachers, non-specialists, cover teachers and so on. Time is of course precious, but time spent discussing task intent for departmental resources seems valuable.
Back to the questions…
c) is the same dimensions as b), and will produce the same area. We’re assuming on purpose, so again, there’s opportunity here for a teaching point around orientation or commutativity in multiplication or just planting the seeds of ‘triangles with the same area can look different’. The idea is reinforced in e) and f) but without the scaffold of the grids. Maybe I don’t want to draw much attention to those things because i know my students are already comfortable with those ideas, but at least these questions offer me the opportunities - if i know they’re there.
A further observation is that these examples all use a combination of two even numbers, or an odd and an even number for their dimensions, which ensures that all area answers are whole numbers. This keeps things a little more predictable and clean, which is good for building initial confidence, but I’d probably want some more awkward numbers at some point later on.
Which leads us nicely to a point mentioned briefly in part one - it’s important to also notice what this task doesn’t do. In addition we have different orientations, but we don’t have all three dimensions provided, or triangles without right angles. That’s not a problem, but it’s important that those gaps get filled elsewhere.
Once we have a feel for what the task is trying to do, and the pedagogical opportunities it’s presenting us, this in turn gives insights into what the teaching is likely to look like and build up to prior to students attempting the task, and likely areas of new knowledge following on from it (in this example, further development of the orientation of triangles, or new content around, say, pulling the right information from all three sides of a triangle. This again should be a cautionary tale, as inevitably, the tail is beginning to wag the dog. The resource is driving the teaching, rather than the other way around. Hence it’s an incredibly important element of teaching to be able to accurately assess the intent of the practice in your lesson and adjust it to fit what you want to teach rather than what it assumes you’re going to.
